TSTP Solution File: HAL002+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : HAL002+1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n023.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 : 600s
% DateTime : Sat Jul 16 12:45:36 EDT 2022
% Result : Theorem 1.36s 1.61s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 40
% Syntax : Number of formulae : 744 ( 211 unt; 23 typ; 0 def)
% Number of atoms : 8170 (3095 equ; 0 cnn)
% Maximal formula atoms : 7 ( 11 avg)
% Number of connectives : 21595 (2912 ~;3058 |; 120 &;15444 @)
% ( 7 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 5 con; 0-6 aty)
% Number of variables : 3693 ( 0 ^3685 !; 8 ?;3693 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_any1,type,
any1: $i ).
thf(tp_any2,type,
any2: $i ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_commute,type,
commute: $i > $i > $i > $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_exact,type,
exact: $i > $i > $o ).
thf(tp_injection,type,
injection: $i > $o ).
thf(tp_injection_2,type,
injection_2: $i > $o ).
thf(tp_morphism,type,
morphism: $i > $i > $i > $o ).
thf(tp_sK10_SY81,type,
sK10_SY81: $i > $i > $i ).
thf(tp_sK1_El,type,
sK1_El: $i > $i > $i > $i ).
thf(tp_sK2_ElDom,type,
sK2_ElDom: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK3_ElCodDom,type,
sK3_ElCodDom: $i > $i > $i > $i > $i > $i ).
thf(tp_sK4_SY79,type,
sK4_SY79: $i > $i > $i > $i > $i > $i ).
thf(tp_sK5_SY78,type,
sK5_SY78: $i > $i > $i > $i > $i > $i ).
thf(tp_sK6_ElDom,type,
sK6_ElDom: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK7_ElCod,type,
sK7_ElCod: $i > $i > $i > $i ).
thf(tp_sK8_ElDom,type,
sK8_ElDom: $i > $i > $i > $i > $i ).
thf(tp_sK9_El1,type,
sK9_El1: $i > $i > $i ).
thf(tp_subtract,type,
subtract: $i > $i > $i > $i ).
thf(tp_surjection,type,
surjection: $i > $o ).
thf(tp_x,type,
x: $i ).
thf(tp_zero,type,
zero: $i > $i ).
thf(1,axiom,
! [Morphism: $i,Dom: $i,Cod: $i] :
( ( ( morphism @ Morphism @ Dom @ Cod )
& ! [El: $i] :
( ( ( element @ El @ Dom )
& ( ( apply @ Morphism @ El )
= ( zero @ Cod ) ) )
=> ( El
= ( zero @ Dom ) ) ) )
=> ( injection_2 @ Morphism ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_injection_2) ).
thf(2,axiom,
! [Morphism: $i,Dom: $i,Cod: $i] :
( ( ( injection_2 @ Morphism )
& ( morphism @ Morphism @ Dom @ Cod ) )
=> ! [El: $i] :
( ( ( element @ El @ Dom )
& ( ( apply @ Morphism @ El )
= ( zero @ Cod ) ) )
=> ( El
= ( zero @ Dom ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injection_properties_2) ).
thf(3,axiom,
! [Morphism: $i,Dom: $i,Cod: $i] :
( ( morphism @ Morphism @ Dom @ Cod )
=> ! [El1: $i,El2: $i] :
( ( ( element @ El1 @ Dom )
& ( element @ El2 @ Dom ) )
=> ( ( apply @ Morphism @ ( subtract @ Dom @ El1 @ El2 ) )
= ( subtract @ Cod @ ( apply @ Morphism @ El1 ) @ ( apply @ Morphism @ El2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_distribution) ).
thf(4,axiom,
! [Dom: $i,El1: $i,El2: $i] :
( ( ( element @ El1 @ Dom )
& ( element @ El2 @ Dom ) )
=> ( ( subtract @ Dom @ El1 @ ( subtract @ Dom @ El1 @ El2 ) )
= El2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_cancellation) ).
thf(5,axiom,
! [Dom: $i,El: $i] :
( ( element @ El @ Dom )
=> ( ( subtract @ Dom @ El @ El )
= ( zero @ Dom ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_to_0) ).
thf(6,axiom,
! [Dom: $i,El1: $i,El2: $i] :
( ( ( element @ El1 @ Dom )
& ( element @ El2 @ Dom ) )
=> ( element @ ( subtract @ Dom @ El1 @ El2 ) @ Dom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_in_domain) ).
thf(7,axiom,
! [M1: $i,M2: $i,M3: $i,M4: $i,Dom: $i,DomCod1: $i,DomCod2: $i,Cod: $i] :
( ( ( morphism @ M1 @ Dom @ DomCod1 )
& ( morphism @ M2 @ DomCod1 @ Cod )
& ( morphism @ M3 @ Dom @ DomCod2 )
& ( morphism @ M4 @ DomCod2 @ Cod )
& ! [ElDom: $i] :
( ( element @ ElDom @ Dom )
=> ( ( apply @ M2 @ ( apply @ M1 @ ElDom ) )
= ( apply @ M4 @ ( apply @ M3 @ ElDom ) ) ) ) )
=> ( commute @ M1 @ M2 @ M3 @ M4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_commute) ).
thf(8,axiom,
! [M1: $i,M2: $i,M3: $i,M4: $i,Dom: $i,DomCod1: $i,DomCod2: $i,Cod: $i] :
( ( ( commute @ M1 @ M2 @ M3 @ M4 )
& ( morphism @ M1 @ Dom @ DomCod1 )
& ( morphism @ M2 @ DomCod1 @ Cod )
& ( morphism @ M3 @ Dom @ DomCod2 )
& ( morphism @ M4 @ DomCod2 @ Cod ) )
=> ! [ElDom: $i] :
( ( element @ ElDom @ Dom )
=> ( ( apply @ M2 @ ( apply @ M1 @ ElDom ) )
= ( apply @ M4 @ ( apply @ M3 @ ElDom ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commute_properties) ).
thf(9,axiom,
! [Morphism1: $i,Morphism2: $i,Dom: $i,CodDom: $i,Cod: $i] :
( ( ( morphism @ Morphism1 @ Dom @ CodDom )
& ( morphism @ Morphism2 @ CodDom @ Cod )
& ! [ElCodDom: $i] :
( ( ( element @ ElCodDom @ CodDom )
& ( ( apply @ Morphism2 @ ElCodDom )
= ( zero @ Cod ) ) )
<=> ? [ElDom: $i] :
( ( element @ ElDom @ Dom )
& ( ( apply @ Morphism1 @ ElDom )
= ElCodDom ) ) ) )
=> ( exact @ Morphism1 @ Morphism2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_exact) ).
thf(10,axiom,
! [Morphism1: $i,Morphism2: $i,Dom: $i,CodDom: $i,Cod: $i] :
( ( ( exact @ Morphism1 @ Morphism2 )
& ( morphism @ Morphism1 @ Dom @ CodDom )
& ( morphism @ Morphism2 @ CodDom @ Cod ) )
=> ! [ElCodDom: $i] :
( ( ( element @ ElCodDom @ CodDom )
& ( ( apply @ Morphism2 @ ElCodDom )
= ( zero @ Cod ) ) )
<=> ? [ElDom: $i] :
( ( element @ ElDom @ Dom )
& ( ( apply @ Morphism1 @ ElDom )
= ElCodDom ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exact_properties) ).
thf(11,axiom,
! [Morphism: $i,Dom: $i,Cod: $i] :
( ( ( morphism @ Morphism @ Dom @ Cod )
& ! [ElCod: $i] :
( ( element @ ElCod @ Cod )
=> ? [ElDom: $i] :
( ( element @ ElDom @ Dom )
& ( ( apply @ Morphism @ ElDom )
= ElCod ) ) ) )
=> ( surjection @ Morphism ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_surjection) ).
thf(12,axiom,
! [Morphism: $i,Dom: $i,Cod: $i] :
( ( ( surjection @ Morphism )
& ( morphism @ Morphism @ Dom @ Cod ) )
=> ! [ElCod: $i] :
( ( element @ ElCod @ Cod )
=> ? [ElDom: $i] :
( ( element @ ElDom @ Dom )
& ( ( apply @ Morphism @ ElDom )
= ElCod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjection_properties) ).
thf(13,axiom,
! [Morphism: $i,Dom: $i,Cod: $i] :
( ( ( morphism @ Morphism @ Dom @ Cod )
& ! [El1: $i,El2: $i] :
( ( ( element @ El1 @ Dom )
& ( element @ El2 @ Dom )
& ( ( apply @ Morphism @ El1 )
= ( apply @ Morphism @ El2 ) ) )
=> ( El1 = El2 ) ) )
=> ( injection @ Morphism ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_injection) ).
thf(14,axiom,
! [Morphism: $i,Dom: $i,Cod: $i] :
( ( ( injection @ Morphism )
& ( morphism @ Morphism @ Dom @ Cod ) )
=> ! [El1: $i,El2: $i] :
( ( ( element @ El1 @ Dom )
& ( element @ El2 @ Dom )
& ( ( apply @ Morphism @ El1 )
= ( apply @ Morphism @ El2 ) ) )
=> ( El1 = El2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injection_properties) ).
thf(15,axiom,
! [Morphism: $i,Dom: $i,Cod: $i] :
( ( morphism @ Morphism @ Dom @ Cod )
=> ( ! [El: $i] :
( ( element @ El @ Dom )
=> ( element @ ( apply @ Morphism @ El ) @ Cod ) )
& ( ( apply @ Morphism @ ( zero @ Dom ) )
= ( zero @ Cod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',morphism) ).
thf(16,axiom,
morphism @ x @ any1 @ any2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_morphism) ).
thf(17,conjecture,
( ( injection @ x )
<=> ( injection_2 @ x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',my) ).
thf(18,negated_conjecture,
( ( ( injection @ x )
<=> ( injection_2 @ x ) )
= $false ),
inference(negate_conjecture,[status(cth)],[17]) ).
thf(19,plain,
( ( ( injection @ x )
<=> ( injection_2 @ x ) )
= $false ),
inference(unfold_def,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ( ( morphism @ Morphism @ Dom @ Cod )
& ! [El: $i] :
( ( ( element @ El @ Dom )
& ( ( apply @ Morphism @ El )
= ( zero @ Cod ) ) )
=> ( El
= ( zero @ Dom ) ) ) )
=> ( injection_2 @ Morphism ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(21,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ( ( injection_2 @ Morphism )
& ( morphism @ Morphism @ Dom @ Cod ) )
=> ! [El: $i] :
( ( ( element @ El @ Dom )
& ( ( apply @ Morphism @ El )
= ( zero @ Cod ) ) )
=> ( El
= ( zero @ Dom ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(22,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ( morphism @ Morphism @ Dom @ Cod )
=> ! [El1: $i,El2: $i] :
( ( ( element @ El1 @ Dom )
& ( element @ El2 @ Dom ) )
=> ( ( apply @ Morphism @ ( subtract @ Dom @ El1 @ El2 ) )
= ( subtract @ Cod @ ( apply @ Morphism @ El1 ) @ ( apply @ Morphism @ El2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [Dom: $i,El1: $i,El2: $i] :
( ( ( element @ El1 @ Dom )
& ( element @ El2 @ Dom ) )
=> ( ( subtract @ Dom @ El1 @ ( subtract @ Dom @ El1 @ El2 ) )
= El2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(24,plain,
( ( ! [Dom: $i,El: $i] :
( ( element @ El @ Dom )
=> ( ( subtract @ Dom @ El @ El )
= ( zero @ Dom ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(25,plain,
( ( ! [Dom: $i,El1: $i,El2: $i] :
( ( ( element @ El1 @ Dom )
& ( element @ El2 @ Dom ) )
=> ( element @ ( subtract @ Dom @ El1 @ El2 ) @ Dom ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(26,plain,
( ( ! [M1: $i,M2: $i,M3: $i,M4: $i,Dom: $i,DomCod1: $i,DomCod2: $i,Cod: $i] :
( ( ( morphism @ M1 @ Dom @ DomCod1 )
& ( morphism @ M2 @ DomCod1 @ Cod )
& ( morphism @ M3 @ Dom @ DomCod2 )
& ( morphism @ M4 @ DomCod2 @ Cod )
& ! [ElDom: $i] :
( ( element @ ElDom @ Dom )
=> ( ( apply @ M2 @ ( apply @ M1 @ ElDom ) )
= ( apply @ M4 @ ( apply @ M3 @ ElDom ) ) ) ) )
=> ( commute @ M1 @ M2 @ M3 @ M4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(27,plain,
( ( ! [M1: $i,M2: $i,M3: $i,M4: $i,Dom: $i,DomCod1: $i,DomCod2: $i,Cod: $i] :
( ( ( commute @ M1 @ M2 @ M3 @ M4 )
& ( morphism @ M1 @ Dom @ DomCod1 )
& ( morphism @ M2 @ DomCod1 @ Cod )
& ( morphism @ M3 @ Dom @ DomCod2 )
& ( morphism @ M4 @ DomCod2 @ Cod ) )
=> ! [ElDom: $i] :
( ( element @ ElDom @ Dom )
=> ( ( apply @ M2 @ ( apply @ M1 @ ElDom ) )
= ( apply @ M4 @ ( apply @ M3 @ ElDom ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(28,plain,
( ( ! [Morphism1: $i,Morphism2: $i,Dom: $i,CodDom: $i,Cod: $i] :
( ( ( morphism @ Morphism1 @ Dom @ CodDom )
& ( morphism @ Morphism2 @ CodDom @ Cod )
& ! [ElCodDom: $i] :
( ( ( element @ ElCodDom @ CodDom )
& ( ( apply @ Morphism2 @ ElCodDom )
= ( zero @ Cod ) ) )
<=> ? [ElDom: $i] :
( ( element @ ElDom @ Dom )
& ( ( apply @ Morphism1 @ ElDom )
= ElCodDom ) ) ) )
=> ( exact @ Morphism1 @ Morphism2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(29,plain,
( ( ! [Morphism1: $i,Morphism2: $i,Dom: $i,CodDom: $i,Cod: $i] :
( ( ( exact @ Morphism1 @ Morphism2 )
& ( morphism @ Morphism1 @ Dom @ CodDom )
& ( morphism @ Morphism2 @ CodDom @ Cod ) )
=> ! [ElCodDom: $i] :
( ( ( element @ ElCodDom @ CodDom )
& ( ( apply @ Morphism2 @ ElCodDom )
= ( zero @ Cod ) ) )
<=> ? [ElDom: $i] :
( ( element @ ElDom @ Dom )
& ( ( apply @ Morphism1 @ ElDom )
= ElCodDom ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(30,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ( ( morphism @ Morphism @ Dom @ Cod )
& ! [ElCod: $i] :
( ( element @ ElCod @ Cod )
=> ? [ElDom: $i] :
( ( element @ ElDom @ Dom )
& ( ( apply @ Morphism @ ElDom )
= ElCod ) ) ) )
=> ( surjection @ Morphism ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(31,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ( ( surjection @ Morphism )
& ( morphism @ Morphism @ Dom @ Cod ) )
=> ! [ElCod: $i] :
( ( element @ ElCod @ Cod )
=> ? [ElDom: $i] :
( ( element @ ElDom @ Dom )
& ( ( apply @ Morphism @ ElDom )
= ElCod ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(32,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ( ( morphism @ Morphism @ Dom @ Cod )
& ! [El1: $i,El2: $i] :
( ( ( element @ El1 @ Dom )
& ( element @ El2 @ Dom )
& ( ( apply @ Morphism @ El1 )
= ( apply @ Morphism @ El2 ) ) )
=> ( El1 = El2 ) ) )
=> ( injection @ Morphism ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(33,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ( ( injection @ Morphism )
& ( morphism @ Morphism @ Dom @ Cod ) )
=> ! [El1: $i,El2: $i] :
( ( ( element @ El1 @ Dom )
& ( element @ El2 @ Dom )
& ( ( apply @ Morphism @ El1 )
= ( apply @ Morphism @ El2 ) ) )
=> ( El1 = El2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(34,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ( morphism @ Morphism @ Dom @ Cod )
=> ( ! [El: $i] :
( ( element @ El @ Dom )
=> ( element @ ( apply @ Morphism @ El ) @ Cod ) )
& ( ( apply @ Morphism @ ( zero @ Dom ) )
= ( zero @ Cod ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(35,plain,
( ( morphism @ x @ any1 @ any2 )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(36,plain,
( ( ( injection @ x )
=> ( injection_2 @ x ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[19]) ).
thf(37,plain,
( ( ( injection_2 @ x )
=> ( injection @ x ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[19]) ).
thf(38,plain,
( ( ~ ( ( injection @ x )
=> ( injection_2 @ x ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[36]) ).
thf(39,plain,
( ( ~ ( ( injection_2 @ x )
=> ( injection @ x ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[37]) ).
thf(40,plain,
( ( ( injection @ x )
& ~ ( injection_2 @ x ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(41,plain,
( ( ( injection_2 @ x )
& ~ ( injection @ x ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(42,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i,Cod: $i] :
( ( ( ( apply @ Morphism @ ( sK1_El @ Cod @ Dom @ Morphism ) )
= ( zero @ Cod ) )
& ( element @ ( sK1_El @ Cod @ Dom @ Morphism ) @ Dom )
& ( ( sK1_El @ Cod @ Dom @ Morphism )
!= ( zero @ Dom ) ) )
| ~ ( morphism @ Morphism @ Dom @ Cod ) )
| ( injection_2 @ Morphism ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(43,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ~ ( injection_2 @ Morphism )
| ~ ( morphism @ Morphism @ Dom @ Cod )
| ! [El: $i] :
( ( ( apply @ Morphism @ El )
!= ( zero @ Cod ) )
| ~ ( element @ El @ Dom )
| ( El
= ( zero @ Dom ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(44,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ~ ( morphism @ Morphism @ Dom @ Cod )
| ! [El1: $i,El2: $i] :
( ~ ( element @ El1 @ Dom )
| ~ ( element @ El2 @ Dom )
| ( ( apply @ Morphism @ ( subtract @ Dom @ El1 @ El2 ) )
= ( subtract @ Cod @ ( apply @ Morphism @ El1 ) @ ( apply @ Morphism @ El2 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(45,plain,
( ( ! [Dom: $i,El1: $i,El2: $i] :
( ~ ( element @ El1 @ Dom )
| ~ ( element @ El2 @ Dom )
| ( ( subtract @ Dom @ El1 @ ( subtract @ Dom @ El1 @ El2 ) )
= El2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(46,plain,
( ( ! [Dom: $i,El: $i] :
( ~ ( element @ El @ Dom )
| ( ( subtract @ Dom @ El @ El )
= ( zero @ Dom ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(47,plain,
( ( ! [Dom: $i,El1: $i,El2: $i] :
( ~ ( element @ El1 @ Dom )
| ~ ( element @ El2 @ Dom )
| ( element @ ( subtract @ Dom @ El1 @ El2 ) @ Dom ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(48,plain,
( ( ! [M1: $i,M2: $i,M3: $i,M4: $i,Dom: $i,DomCod1: $i] :
( ( ( element @ ( sK2_ElDom @ DomCod1 @ Dom @ M4 @ M3 @ M2 @ M1 ) @ Dom )
& ( ( apply @ M2 @ ( apply @ M1 @ ( sK2_ElDom @ DomCod1 @ Dom @ M4 @ M3 @ M2 @ M1 ) ) )
!= ( apply @ M4 @ ( apply @ M3 @ ( sK2_ElDom @ DomCod1 @ Dom @ M4 @ M3 @ M2 @ M1 ) ) ) ) )
| ! [DomCod2: $i,Cod: $i] :
( ~ ( morphism @ M1 @ Dom @ DomCod1 )
| ~ ( morphism @ M2 @ DomCod1 @ Cod )
| ~ ( morphism @ M3 @ Dom @ DomCod2 )
| ~ ( morphism @ M4 @ DomCod2 @ Cod ) )
| ( commute @ M1 @ M2 @ M3 @ M4 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(49,plain,
( ( ! [M1: $i,M2: $i,M3: $i,M4: $i,Dom: $i,DomCod1: $i] :
( ! [DomCod2: $i,Cod: $i] :
( ~ ( commute @ M1 @ M2 @ M3 @ M4 )
| ~ ( morphism @ M1 @ Dom @ DomCod1 )
| ~ ( morphism @ M2 @ DomCod1 @ Cod )
| ~ ( morphism @ M3 @ Dom @ DomCod2 )
| ~ ( morphism @ M4 @ DomCod2 @ Cod ) )
| ! [ElDom: $i] :
( ~ ( element @ ElDom @ Dom )
| ( ( apply @ M2 @ ( apply @ M1 @ ElDom ) )
= ( apply @ M4 @ ( apply @ M3 @ ElDom ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(50,plain,
( ( ! [Morphism1: $i,Morphism2: $i,Dom: $i] :
( ! [CodDom: $i,Cod: $i] :
( ( ( ( ( apply @ Morphism2 @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
!= ( zero @ Cod ) )
| ~ ( element @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ CodDom )
| ! [SY77: $i] :
( ( ( apply @ Morphism1 @ SY77 )
!= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
| ~ ( element @ SY77 @ Dom ) ) )
& ( ( ( apply @ Morphism2 @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( zero @ Cod ) )
| ( ( ( apply @ Morphism1 @ ( sK5_SY78 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
& ( element @ ( sK5_SY78 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ Dom ) ) )
& ( ( element @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ CodDom )
| ( ( ( apply @ Morphism1 @ ( sK4_SY79 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
& ( element @ ( sK4_SY79 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ Dom ) ) ) )
| ~ ( morphism @ Morphism1 @ Dom @ CodDom )
| ~ ( morphism @ Morphism2 @ CodDom @ Cod ) )
| ( exact @ Morphism1 @ Morphism2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(51,plain,
( ( ! [Morphism1: $i,Morphism2: $i,Dom: $i,CodDom: $i,Cod: $i] :
( ~ ( exact @ Morphism1 @ Morphism2 )
| ~ ( morphism @ Morphism1 @ Dom @ CodDom )
| ~ ( morphism @ Morphism2 @ CodDom @ Cod )
| ( ! [ElCodDom: $i] :
( ( ( apply @ Morphism2 @ ElCodDom )
!= ( zero @ Cod ) )
| ~ ( element @ ElCodDom @ CodDom )
| ( ( ( apply @ Morphism1 @ ( sK6_ElDom @ ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ElCodDom )
& ( element @ ( sK6_ElDom @ ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ Dom ) ) )
& ! [ElCodDom: $i] :
( ! [ElDom: $i] :
( ( ( apply @ Morphism1 @ ElDom )
!= ElCodDom )
| ~ ( element @ ElDom @ Dom ) )
| ( ( apply @ Morphism2 @ ElCodDom )
= ( zero @ Cod ) ) )
& ! [ElCodDom: $i] :
( ! [ElDom: $i] :
( ( ( apply @ Morphism1 @ ElDom )
!= ElCodDom )
| ~ ( element @ ElDom @ Dom ) )
| ( element @ ElCodDom @ CodDom ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(52,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i,Cod: $i] :
( ( ( element @ ( sK7_ElCod @ Cod @ Dom @ Morphism ) @ Cod )
& ! [SY80: $i] :
( ( ( apply @ Morphism @ SY80 )
!= ( sK7_ElCod @ Cod @ Dom @ Morphism ) )
| ~ ( element @ SY80 @ Dom ) ) )
| ~ ( morphism @ Morphism @ Dom @ Cod ) )
| ( surjection @ Morphism ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(53,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ~ ( morphism @ Morphism @ Dom @ Cod )
| ~ ( surjection @ Morphism )
| ! [ElCod: $i] :
( ~ ( element @ ElCod @ Cod )
| ( ( ( apply @ Morphism @ ( sK8_ElDom @ ElCod @ Cod @ Dom @ Morphism ) )
= ElCod )
& ( element @ ( sK8_ElDom @ ElCod @ Cod @ Dom @ Morphism ) @ Dom ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(54,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i] :
( ( ( element @ ( sK9_El1 @ Dom @ Morphism ) @ Dom )
& ( element @ ( sK10_SY81 @ Dom @ Morphism ) @ Dom )
& ( ( apply @ Morphism @ ( sK9_El1 @ Dom @ Morphism ) )
= ( apply @ Morphism @ ( sK10_SY81 @ Dom @ Morphism ) ) )
& ( ( sK9_El1 @ Dom @ Morphism )
!= ( sK10_SY81 @ Dom @ Morphism ) ) )
| ! [Cod: $i] :
~ ( morphism @ Morphism @ Dom @ Cod ) )
| ( injection @ Morphism ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(55,plain,
( ( ! [Morphism: $i,Dom: $i] :
( ~ ( injection @ Morphism )
| ! [Cod: $i] :
~ ( morphism @ Morphism @ Dom @ Cod )
| ! [El1: $i,El2: $i] :
( ~ ( element @ El1 @ Dom )
| ~ ( element @ El2 @ Dom )
| ( ( apply @ Morphism @ El1 )
!= ( apply @ Morphism @ El2 ) )
| ( El1 = El2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(56,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i,Cod: $i] :
( ~ ( morphism @ Morphism @ Dom @ Cod )
| ! [El: $i] :
( ~ ( element @ El @ Dom )
| ( element @ ( apply @ Morphism @ El ) @ Cod ) ) )
& ! [Dom: $i,Cod: $i] :
( ~ ( morphism @ Morphism @ Dom @ Cod )
| ( ( apply @ Morphism @ ( zero @ Dom ) )
= ( zero @ Cod ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(57,plain,
( ( morphism @ x @ any1 @ any2 )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(58,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i,Cod: $i] :
( ~ ( morphism @ Morphism @ Dom @ Cod )
| ! [El: $i] :
( ~ ( element @ El @ Dom )
| ( element @ ( apply @ Morphism @ El ) @ Cod ) ) )
& ! [Dom: $i,Cod: $i] :
( ~ ( morphism @ Morphism @ Dom @ Cod )
| ( ( apply @ Morphism @ ( zero @ Dom ) )
= ( zero @ Cod ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(59,plain,
( ( ! [Morphism: $i,Dom: $i] :
( ~ ( injection @ Morphism )
| ! [Cod: $i] :
~ ( morphism @ Morphism @ Dom @ Cod )
| ! [El1: $i,El2: $i] :
( ~ ( element @ El1 @ Dom )
| ~ ( element @ El2 @ Dom )
| ( ( apply @ Morphism @ El1 )
!= ( apply @ Morphism @ El2 ) )
| ( El1 = El2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(60,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i] :
( ( ( element @ ( sK9_El1 @ Dom @ Morphism ) @ Dom )
& ( element @ ( sK10_SY81 @ Dom @ Morphism ) @ Dom )
& ( ( apply @ Morphism @ ( sK9_El1 @ Dom @ Morphism ) )
= ( apply @ Morphism @ ( sK10_SY81 @ Dom @ Morphism ) ) )
& ( ( sK9_El1 @ Dom @ Morphism )
!= ( sK10_SY81 @ Dom @ Morphism ) ) )
| ! [Cod: $i] :
~ ( morphism @ Morphism @ Dom @ Cod ) )
| ( injection @ Morphism ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(61,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ~ ( morphism @ Morphism @ Dom @ Cod )
| ~ ( surjection @ Morphism )
| ! [ElCod: $i] :
( ~ ( element @ ElCod @ Cod )
| ( ( ( apply @ Morphism @ ( sK8_ElDom @ ElCod @ Cod @ Dom @ Morphism ) )
= ElCod )
& ( element @ ( sK8_ElDom @ ElCod @ Cod @ Dom @ Morphism ) @ Dom ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(62,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i,Cod: $i] :
( ( ( element @ ( sK7_ElCod @ Cod @ Dom @ Morphism ) @ Cod )
& ! [SY80: $i] :
( ( ( apply @ Morphism @ SY80 )
!= ( sK7_ElCod @ Cod @ Dom @ Morphism ) )
| ~ ( element @ SY80 @ Dom ) ) )
| ~ ( morphism @ Morphism @ Dom @ Cod ) )
| ( surjection @ Morphism ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(63,plain,
( ( ! [Morphism1: $i,Morphism2: $i,Dom: $i,CodDom: $i,Cod: $i] :
( ~ ( exact @ Morphism1 @ Morphism2 )
| ~ ( morphism @ Morphism1 @ Dom @ CodDom )
| ~ ( morphism @ Morphism2 @ CodDom @ Cod )
| ( ! [ElCodDom: $i] :
( ( ( apply @ Morphism2 @ ElCodDom )
!= ( zero @ Cod ) )
| ~ ( element @ ElCodDom @ CodDom )
| ( ( ( apply @ Morphism1 @ ( sK6_ElDom @ ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ElCodDom )
& ( element @ ( sK6_ElDom @ ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ Dom ) ) )
& ! [ElCodDom: $i] :
( ! [ElDom: $i] :
( ( ( apply @ Morphism1 @ ElDom )
!= ElCodDom )
| ~ ( element @ ElDom @ Dom ) )
| ( ( apply @ Morphism2 @ ElCodDom )
= ( zero @ Cod ) ) )
& ! [ElCodDom: $i] :
( ! [ElDom: $i] :
( ( ( apply @ Morphism1 @ ElDom )
!= ElCodDom )
| ~ ( element @ ElDom @ Dom ) )
| ( element @ ElCodDom @ CodDom ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(64,plain,
( ( ! [Morphism1: $i,Morphism2: $i,Dom: $i] :
( ! [CodDom: $i,Cod: $i] :
( ( ( ( ( apply @ Morphism2 @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
!= ( zero @ Cod ) )
| ~ ( element @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ CodDom )
| ! [SY77: $i] :
( ( ( apply @ Morphism1 @ SY77 )
!= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
| ~ ( element @ SY77 @ Dom ) ) )
& ( ( ( apply @ Morphism2 @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( zero @ Cod ) )
| ( ( ( apply @ Morphism1 @ ( sK5_SY78 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
& ( element @ ( sK5_SY78 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ Dom ) ) )
& ( ( element @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ CodDom )
| ( ( ( apply @ Morphism1 @ ( sK4_SY79 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
& ( element @ ( sK4_SY79 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ Dom ) ) ) )
| ~ ( morphism @ Morphism1 @ Dom @ CodDom )
| ~ ( morphism @ Morphism2 @ CodDom @ Cod ) )
| ( exact @ Morphism1 @ Morphism2 ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(65,plain,
( ( ! [M1: $i,M2: $i,M3: $i,M4: $i,Dom: $i,DomCod1: $i] :
( ! [DomCod2: $i,Cod: $i] :
( ~ ( commute @ M1 @ M2 @ M3 @ M4 )
| ~ ( morphism @ M1 @ Dom @ DomCod1 )
| ~ ( morphism @ M2 @ DomCod1 @ Cod )
| ~ ( morphism @ M3 @ Dom @ DomCod2 )
| ~ ( morphism @ M4 @ DomCod2 @ Cod ) )
| ! [ElDom: $i] :
( ~ ( element @ ElDom @ Dom )
| ( ( apply @ M2 @ ( apply @ M1 @ ElDom ) )
= ( apply @ M4 @ ( apply @ M3 @ ElDom ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(66,plain,
( ( ! [M1: $i,M2: $i,M3: $i,M4: $i,Dom: $i,DomCod1: $i] :
( ( ( element @ ( sK2_ElDom @ DomCod1 @ Dom @ M4 @ M3 @ M2 @ M1 ) @ Dom )
& ( ( apply @ M2 @ ( apply @ M1 @ ( sK2_ElDom @ DomCod1 @ Dom @ M4 @ M3 @ M2 @ M1 ) ) )
!= ( apply @ M4 @ ( apply @ M3 @ ( sK2_ElDom @ DomCod1 @ Dom @ M4 @ M3 @ M2 @ M1 ) ) ) ) )
| ! [DomCod2: $i,Cod: $i] :
( ~ ( morphism @ M1 @ Dom @ DomCod1 )
| ~ ( morphism @ M2 @ DomCod1 @ Cod )
| ~ ( morphism @ M3 @ Dom @ DomCod2 )
| ~ ( morphism @ M4 @ DomCod2 @ Cod ) )
| ( commute @ M1 @ M2 @ M3 @ M4 ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(67,plain,
( ( ! [Dom: $i,El1: $i,El2: $i] :
( ~ ( element @ El1 @ Dom )
| ~ ( element @ El2 @ Dom )
| ( element @ ( subtract @ Dom @ El1 @ El2 ) @ Dom ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(68,plain,
( ( ! [Dom: $i,El: $i] :
( ~ ( element @ El @ Dom )
| ( ( subtract @ Dom @ El @ El )
= ( zero @ Dom ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(69,plain,
( ( ! [Dom: $i,El1: $i,El2: $i] :
( ~ ( element @ El1 @ Dom )
| ~ ( element @ El2 @ Dom )
| ( ( subtract @ Dom @ El1 @ ( subtract @ Dom @ El1 @ El2 ) )
= El2 ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(70,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ~ ( morphism @ Morphism @ Dom @ Cod )
| ! [El1: $i,El2: $i] :
( ~ ( element @ El1 @ Dom )
| ~ ( element @ El2 @ Dom )
| ( ( apply @ Morphism @ ( subtract @ Dom @ El1 @ El2 ) )
= ( subtract @ Cod @ ( apply @ Morphism @ El1 ) @ ( apply @ Morphism @ El2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(71,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ~ ( injection_2 @ Morphism )
| ~ ( morphism @ Morphism @ Dom @ Cod )
| ! [El: $i] :
( ( ( apply @ Morphism @ El )
!= ( zero @ Cod ) )
| ~ ( element @ El @ Dom )
| ( El
= ( zero @ Dom ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(72,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i,Cod: $i] :
( ( ( ( apply @ Morphism @ ( sK1_El @ Cod @ Dom @ Morphism ) )
= ( zero @ Cod ) )
& ( element @ ( sK1_El @ Cod @ Dom @ Morphism ) @ Dom )
& ( ( sK1_El @ Cod @ Dom @ Morphism )
!= ( zero @ Dom ) ) )
| ~ ( morphism @ Morphism @ Dom @ Cod ) )
| ( injection_2 @ Morphism ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(73,plain,
( ( ( injection @ x )
& ~ ( injection_2 @ x ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 )
| ~ ( ( ( apply @ SX1 @ ( apply @ SX0 @ ( sK2_ElDom @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
!= ( apply @ SX3 @ ( apply @ SX2 @ ( sK2_ElDom @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ! [SX6: $i,SX7: $i] :
( ~ ( morphism @ SX0 @ SX4 @ SX5 )
| ~ ( morphism @ SX1 @ SX5 @ SX7 )
| ~ ( morphism @ SX2 @ SX4 @ SX6 )
| ~ ( morphism @ SX3 @ SX6 @ SX7 ) )
| ( commute @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ! [SX3: $i,SX4: $i] :
( ~ ( ~ ( ( ( apply @ SX1 @ ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( zero @ SX4 ) )
| ~ ( element @ ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ! [SX5: $i] :
( ( ( apply @ SX0 @ SX5 )
!= ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( element @ SX5 @ SX2 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SX1 @ ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
= ( zero @ SX4 ) )
| ~ ( ( ( apply @ SX0 @ ( sK5_SY78 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( element @ ( sK5_SY78 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ~ ( ( ( apply @ SX0 @ ( sK4_SY79 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( element @ ( sK4_SY79 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) ) )
| ~ ( morphism @ SX0 @ SX2 @ SX3 )
| ~ ( morphism @ SX1 @ SX3 @ SX4 ) )
| ( exact @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(76,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ( ( apply @ SX0 @ ( sK1_El @ SX2 @ SX1 @ SX0 ) )
!= ( zero @ SX2 ) )
| ~ ( element @ ( sK1_El @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK1_El @ SX2 @ SX1 @ SX0 )
!= ( zero @ SX1 ) ) ) )
| ~ ( morphism @ SX0 @ SX1 @ SX2 ) )
| ( injection_2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(77,plain,
( ( ~ ( ~ ( injection @ x )
| ~ ~ ( injection_2 @ x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(78,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( morphism @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ SX1 )
| ( element @ ( apply @ SX0 @ SX3 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( morphism @ SX0 @ SX1 @ SX2 )
| ( ( apply @ SX0 @ ( zero @ SX1 ) )
= ( zero @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(79,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( morphism @ SX0 @ SX1 @ SX2 )
| ~ ( surjection @ SX0 )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ SX2 )
| ~ ( ( ( apply @ SX0 @ ( sK8_ElDom @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= SX3 )
| ~ ( element @ ( sK8_ElDom @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(80,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SX1 @ SX0 ) @ SX1 )
| ~ ( element @ ( sK10_SY81 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( apply @ SX0 @ ( sK9_El1 @ SX1 @ SX0 ) )
!= ( apply @ SX0 @ ( sK10_SY81 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK9_El1 @ SX1 @ SX0 )
!= ( sK10_SY81 @ SX1 @ SX0 ) ) ) )
| ! [SX2: $i] :
~ ( morphism @ SX0 @ SX1 @ SX2 ) )
| ( injection @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(81,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( exact @ SX0 @ SX1 )
| ~ ( morphism @ SX0 @ SX2 @ SX3 )
| ~ ( morphism @ SX1 @ SX3 @ SX4 )
| ~ ( ~ ! [SX5: $i] :
( ( ( apply @ SX1 @ SX5 )
!= ( zero @ SX4 ) )
| ~ ( element @ SX5 @ SX3 )
| ~ ( ( ( apply @ SX0 @ ( sK6_ElDom @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= SX5 )
| ~ ( element @ ( sK6_ElDom @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ~ ( ~ ! [SX5: $i] :
( ! [SX6: $i] :
( ( ( apply @ SX0 @ SX6 )
!= SX5 )
| ~ ( element @ SX6 @ SX2 ) )
| ( ( apply @ SX1 @ SX5 )
= ( zero @ SX4 ) ) )
| ~ ! [SX5: $i] :
( ! [SX6: $i] :
( ( ( apply @ SX0 @ SX6 )
!= SX5 )
| ~ ( element @ SX6 @ SX2 ) )
| ( element @ SX5 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(82,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( element @ ( sK7_ElCod @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ! [SX3: $i] :
( ( ( apply @ SX0 @ SX3 )
!= ( sK7_ElCod @ SX2 @ SX1 @ SX0 ) )
| ~ ( element @ SX3 @ SX1 ) ) )
| ~ ( morphism @ SX0 @ SX1 @ SX2 ) )
| ( surjection @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(83,plain,
! [SV1: $i] :
( ( ! [SY82: $i] :
( ~ ( injection @ SV1 )
| ! [SY83: $i] :
~ ( morphism @ SV1 @ SY82 @ SY83 )
| ! [SY84: $i,SY85: $i] :
( ~ ( element @ SY84 @ SY82 )
| ~ ( element @ SY85 @ SY82 )
| ( ( apply @ SV1 @ SY84 )
!= ( apply @ SV1 @ SY85 ) )
| ( SY84 = SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(84,plain,
! [SV2: $i] :
( ( ! [SY86: $i,SY87: $i,SY88: $i,SY89: $i,SY90: $i] :
( ! [SY91: $i,SY92: $i] :
( ~ ( commute @ SV2 @ SY86 @ SY87 @ SY88 )
| ~ ( morphism @ SV2 @ SY89 @ SY90 )
| ~ ( morphism @ SY86 @ SY90 @ SY92 )
| ~ ( morphism @ SY87 @ SY89 @ SY91 )
| ~ ( morphism @ SY88 @ SY91 @ SY92 ) )
| ! [SY93: $i] :
( ~ ( element @ SY93 @ SY89 )
| ( ( apply @ SY86 @ ( apply @ SV2 @ SY93 ) )
= ( apply @ SY88 @ ( apply @ SY87 @ SY93 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(85,plain,
! [SV3: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ~ ( element @ SY94 @ SV3 )
| ~ ( element @ SY95 @ SV3 )
| ( element @ ( subtract @ SV3 @ SY94 @ SY95 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(86,plain,
! [SV4: $i] :
( ( ! [SY96: $i] :
( ~ ( element @ SY96 @ SV4 )
| ( ( subtract @ SV4 @ SY96 @ SY96 )
= ( zero @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(87,plain,
! [SV5: $i] :
( ( ! [SY97: $i,SY98: $i] :
( ~ ( element @ SY97 @ SV5 )
| ~ ( element @ SY98 @ SV5 )
| ( ( subtract @ SV5 @ SY97 @ ( subtract @ SV5 @ SY97 @ SY98 ) )
= SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(88,plain,
! [SV6: $i] :
( ( ! [SY99: $i,SY100: $i] :
( ~ ( morphism @ SV6 @ SY99 @ SY100 )
| ! [SY101: $i,SY102: $i] :
( ~ ( element @ SY101 @ SY99 )
| ~ ( element @ SY102 @ SY99 )
| ( ( apply @ SV6 @ ( subtract @ SY99 @ SY101 @ SY102 ) )
= ( subtract @ SY100 @ ( apply @ SV6 @ SY101 ) @ ( apply @ SV6 @ SY102 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(89,plain,
! [SV7: $i] :
( ( ! [SY103: $i,SY104: $i] :
( ~ ( injection_2 @ SV7 )
| ~ ( morphism @ SV7 @ SY103 @ SY104 )
| ! [SY105: $i] :
( ( ( apply @ SV7 @ SY105 )
!= ( zero @ SY104 ) )
| ~ ( element @ SY105 @ SY103 )
| ( SY105
= ( zero @ SY103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(90,plain,
! [SV8: $i] :
( ( ! [SY106: $i,SY107: $i,SY108: $i,SY109: $i,SY110: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY110 @ SY109 @ SY108 @ SY107 @ SY106 @ SV8 ) @ SY109 )
| ~ ( ( ( apply @ SY106 @ ( apply @ SV8 @ ( sK2_ElDom @ SY110 @ SY109 @ SY108 @ SY107 @ SY106 @ SV8 ) ) )
!= ( apply @ SY108 @ ( apply @ SY107 @ ( sK2_ElDom @ SY110 @ SY109 @ SY108 @ SY107 @ SY106 @ SV8 ) ) ) ) ) )
| ! [SY111: $i,SY112: $i] :
( ~ ( morphism @ SV8 @ SY109 @ SY110 )
| ~ ( morphism @ SY106 @ SY110 @ SY112 )
| ~ ( morphism @ SY107 @ SY109 @ SY111 )
| ~ ( morphism @ SY108 @ SY111 @ SY112 ) )
| ( commute @ SV8 @ SY106 @ SY107 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(91,plain,
! [SV9: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ! [SY115: $i,SY116: $i] :
( ~ ( ~ ( ( ( apply @ SY113 @ ( sK3_ElCodDom @ SY116 @ SY115 @ SY114 @ SY113 @ SV9 ) )
!= ( zero @ SY116 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY116 @ SY115 @ SY114 @ SY113 @ SV9 ) @ SY115 )
| ! [SY117: $i] :
( ( ( apply @ SV9 @ SY117 )
!= ( sK3_ElCodDom @ SY116 @ SY115 @ SY114 @ SY113 @ SV9 ) )
| ~ ( element @ SY117 @ SY114 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SY113 @ ( sK3_ElCodDom @ SY116 @ SY115 @ SY114 @ SY113 @ SV9 ) )
= ( zero @ SY116 ) )
| ~ ( ( ( apply @ SV9 @ ( sK5_SY78 @ SY116 @ SY115 @ SY114 @ SY113 @ SV9 ) )
!= ( sK3_ElCodDom @ SY116 @ SY115 @ SY114 @ SY113 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SY116 @ SY115 @ SY114 @ SY113 @ SV9 ) @ SY114 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY116 @ SY115 @ SY114 @ SY113 @ SV9 ) @ SY115 )
| ~ ( ( ( apply @ SV9 @ ( sK4_SY79 @ SY116 @ SY115 @ SY114 @ SY113 @ SV9 ) )
!= ( sK3_ElCodDom @ SY116 @ SY115 @ SY114 @ SY113 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SY116 @ SY115 @ SY114 @ SY113 @ SV9 ) @ SY114 ) ) ) ) )
| ~ ( morphism @ SV9 @ SY114 @ SY115 )
| ~ ( morphism @ SY113 @ SY115 @ SY116 ) )
| ( exact @ SV9 @ SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(92,plain,
! [SV10: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ~ ( ~ ~ ( ( ( apply @ SV10 @ ( sK1_El @ SY119 @ SY118 @ SV10 ) )
!= ( zero @ SY119 ) )
| ~ ( element @ ( sK1_El @ SY119 @ SY118 @ SV10 ) @ SY118 ) )
| ~ ( ( ( sK1_El @ SY119 @ SY118 @ SV10 )
!= ( zero @ SY118 ) ) ) )
| ~ ( morphism @ SV10 @ SY118 @ SY119 ) )
| ( injection_2 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(93,plain,
( ( ~ ( injection @ x )
| ~ ~ ( injection_2 @ x ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(94,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY120: $i,SY121: $i] :
( ~ ( morphism @ SV11 @ SY120 @ SY121 )
| ! [SY122: $i] :
( ~ ( element @ SY122 @ SY120 )
| ( element @ ( apply @ SV11 @ SY122 ) @ SY121 ) ) )
| ~ ! [SY123: $i,SY124: $i] :
( ~ ( morphism @ SV11 @ SY123 @ SY124 )
| ( ( apply @ SV11 @ ( zero @ SY123 ) )
= ( zero @ SY124 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(95,plain,
! [SV12: $i] :
( ( ! [SY125: $i,SY126: $i] :
( ~ ( morphism @ SV12 @ SY125 @ SY126 )
| ~ ( surjection @ SV12 )
| ! [SY127: $i] :
( ~ ( element @ SY127 @ SY126 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SY127 @ SY126 @ SY125 @ SV12 ) )
!= SY127 )
| ~ ( element @ ( sK8_ElDom @ SY127 @ SY126 @ SY125 @ SV12 ) @ SY125 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(96,plain,
! [SV13: $i] :
( ( ! [SY128: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SY128 @ SV13 ) @ SY128 )
| ~ ( element @ ( sK10_SY81 @ SY128 @ SV13 ) @ SY128 ) )
| ( ( apply @ SV13 @ ( sK9_El1 @ SY128 @ SV13 ) )
!= ( apply @ SV13 @ ( sK10_SY81 @ SY128 @ SV13 ) ) ) )
| ~ ( ( ( sK9_El1 @ SY128 @ SV13 )
!= ( sK10_SY81 @ SY128 @ SV13 ) ) ) )
| ! [SY129: $i] :
~ ( morphism @ SV13 @ SY128 @ SY129 ) )
| ( injection @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(97,plain,
! [SV14: $i] :
( ( ! [SY130: $i,SY131: $i,SY132: $i,SY133: $i] :
( ~ ( exact @ SV14 @ SY130 )
| ~ ( morphism @ SV14 @ SY131 @ SY132 )
| ~ ( morphism @ SY130 @ SY132 @ SY133 )
| ~ ( ~ ! [SY134: $i] :
( ( ( apply @ SY130 @ SY134 )
!= ( zero @ SY133 ) )
| ~ ( element @ SY134 @ SY132 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY134 @ SY133 @ SY132 @ SY131 @ SY130 @ SV14 ) )
!= SY134 )
| ~ ( element @ ( sK6_ElDom @ SY134 @ SY133 @ SY132 @ SY131 @ SY130 @ SV14 ) @ SY131 ) ) )
| ~ ~ ( ~ ! [SY135: $i] :
( ! [SY136: $i] :
( ( ( apply @ SV14 @ SY136 )
!= SY135 )
| ~ ( element @ SY136 @ SY131 ) )
| ( ( apply @ SY130 @ SY135 )
= ( zero @ SY133 ) ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
( ( ( apply @ SV14 @ SY138 )
!= SY137 )
| ~ ( element @ SY138 @ SY131 ) )
| ( element @ SY137 @ SY132 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(98,plain,
! [SV15: $i] :
( ( ! [SY139: $i,SY140: $i] :
( ~ ( ~ ( element @ ( sK7_ElCod @ SY140 @ SY139 @ SV15 ) @ SY140 )
| ~ ! [SY141: $i] :
( ( ( apply @ SV15 @ SY141 )
!= ( sK7_ElCod @ SY140 @ SY139 @ SV15 ) )
| ~ ( element @ SY141 @ SY139 ) ) )
| ~ ( morphism @ SV15 @ SY139 @ SY140 ) )
| ( surjection @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(99,plain,
! [SV16: $i,SV1: $i] :
( ( ~ ( injection @ SV1 )
| ! [SY142: $i] :
~ ( morphism @ SV1 @ SV16 @ SY142 )
| ! [SY143: $i,SY144: $i] :
( ~ ( element @ SY143 @ SV16 )
| ~ ( element @ SY144 @ SV16 )
| ( ( apply @ SV1 @ SY143 )
!= ( apply @ SV1 @ SY144 ) )
| ( SY143 = SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(100,plain,
! [SV17: $i,SV2: $i] :
( ( ! [SY145: $i,SY146: $i,SY147: $i,SY148: $i] :
( ! [SY149: $i,SY150: $i] :
( ~ ( commute @ SV2 @ SV17 @ SY145 @ SY146 )
| ~ ( morphism @ SV2 @ SY147 @ SY148 )
| ~ ( morphism @ SV17 @ SY148 @ SY150 )
| ~ ( morphism @ SY145 @ SY147 @ SY149 )
| ~ ( morphism @ SY146 @ SY149 @ SY150 ) )
| ! [SY151: $i] :
( ~ ( element @ SY151 @ SY147 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY151 ) )
= ( apply @ SY146 @ ( apply @ SY145 @ SY151 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(101,plain,
! [SV3: $i,SV18: $i] :
( ( ! [SY152: $i] :
( ~ ( element @ SV18 @ SV3 )
| ~ ( element @ SY152 @ SV3 )
| ( element @ ( subtract @ SV3 @ SV18 @ SY152 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(102,plain,
! [SV4: $i,SV19: $i] :
( ( ~ ( element @ SV19 @ SV4 )
| ( ( subtract @ SV4 @ SV19 @ SV19 )
= ( zero @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(103,plain,
! [SV5: $i,SV20: $i] :
( ( ! [SY153: $i] :
( ~ ( element @ SV20 @ SV5 )
| ~ ( element @ SY153 @ SV5 )
| ( ( subtract @ SV5 @ SV20 @ ( subtract @ SV5 @ SV20 @ SY153 ) )
= SY153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(104,plain,
! [SV21: $i,SV6: $i] :
( ( ! [SY154: $i] :
( ~ ( morphism @ SV6 @ SV21 @ SY154 )
| ! [SY155: $i,SY156: $i] :
( ~ ( element @ SY155 @ SV21 )
| ~ ( element @ SY156 @ SV21 )
| ( ( apply @ SV6 @ ( subtract @ SV21 @ SY155 @ SY156 ) )
= ( subtract @ SY154 @ ( apply @ SV6 @ SY155 ) @ ( apply @ SV6 @ SY156 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(105,plain,
! [SV22: $i,SV7: $i] :
( ( ! [SY157: $i] :
( ~ ( injection_2 @ SV7 )
| ~ ( morphism @ SV7 @ SV22 @ SY157 )
| ! [SY158: $i] :
( ( ( apply @ SV7 @ SY158 )
!= ( zero @ SY157 ) )
| ~ ( element @ SY158 @ SV22 )
| ( SY158
= ( zero @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(106,plain,
! [SV8: $i,SV23: $i] :
( ( ! [SY159: $i,SY160: $i,SY161: $i,SY162: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY162 @ SY161 @ SY160 @ SY159 @ SV23 @ SV8 ) @ SY161 )
| ~ ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SY162 @ SY161 @ SY160 @ SY159 @ SV23 @ SV8 ) ) )
!= ( apply @ SY160 @ ( apply @ SY159 @ ( sK2_ElDom @ SY162 @ SY161 @ SY160 @ SY159 @ SV23 @ SV8 ) ) ) ) ) )
| ! [SY163: $i,SY164: $i] :
( ~ ( morphism @ SV8 @ SY161 @ SY162 )
| ~ ( morphism @ SV23 @ SY162 @ SY164 )
| ~ ( morphism @ SY159 @ SY161 @ SY163 )
| ~ ( morphism @ SY160 @ SY163 @ SY164 ) )
| ( commute @ SV8 @ SV23 @ SY159 @ SY160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(107,plain,
! [SV9: $i,SV24: $i] :
( ( ! [SY165: $i] :
( ! [SY166: $i,SY167: $i] :
( ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY167 @ SY166 @ SY165 @ SV24 @ SV9 ) )
!= ( zero @ SY167 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY167 @ SY166 @ SY165 @ SV24 @ SV9 ) @ SY166 )
| ! [SY168: $i] :
( ( ( apply @ SV9 @ SY168 )
!= ( sK3_ElCodDom @ SY167 @ SY166 @ SY165 @ SV24 @ SV9 ) )
| ~ ( element @ SY168 @ SY165 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY167 @ SY166 @ SY165 @ SV24 @ SV9 ) )
= ( zero @ SY167 ) )
| ~ ( ( ( apply @ SV9 @ ( sK5_SY78 @ SY167 @ SY166 @ SY165 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SY167 @ SY166 @ SY165 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SY167 @ SY166 @ SY165 @ SV24 @ SV9 ) @ SY165 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY167 @ SY166 @ SY165 @ SV24 @ SV9 ) @ SY166 )
| ~ ( ( ( apply @ SV9 @ ( sK4_SY79 @ SY167 @ SY166 @ SY165 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SY167 @ SY166 @ SY165 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SY167 @ SY166 @ SY165 @ SV24 @ SV9 ) @ SY165 ) ) ) ) )
| ~ ( morphism @ SV9 @ SY165 @ SY166 )
| ~ ( morphism @ SV24 @ SY166 @ SY167 ) )
| ( exact @ SV9 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(108,plain,
! [SV10: $i] :
( ( ( ! [SY118: $i,SY119: $i] :
( ~ ( ~ ~ ( ( ( apply @ SV10 @ ( sK1_El @ SY119 @ SY118 @ SV10 ) )
!= ( zero @ SY119 ) )
| ~ ( element @ ( sK1_El @ SY119 @ SY118 @ SV10 ) @ SY118 ) )
| ~ ( ( ( sK1_El @ SY119 @ SY118 @ SV10 )
!= ( zero @ SY118 ) ) ) )
| ~ ( morphism @ SV10 @ SY118 @ SY119 ) ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(109,plain,
( ( ~ ( injection @ x ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(110,plain,
( ( ~ ~ ( injection_2 @ x ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(111,plain,
! [SV11: $i] :
( ( ~ ! [SY120: $i,SY121: $i] :
( ~ ( morphism @ SV11 @ SY120 @ SY121 )
| ! [SY122: $i] :
( ~ ( element @ SY122 @ SY120 )
| ( element @ ( apply @ SV11 @ SY122 ) @ SY121 ) ) )
| ~ ! [SY123: $i,SY124: $i] :
( ~ ( morphism @ SV11 @ SY123 @ SY124 )
| ( ( apply @ SV11 @ ( zero @ SY123 ) )
= ( zero @ SY124 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(112,plain,
! [SV25: $i,SV12: $i] :
( ( ! [SY169: $i] :
( ~ ( morphism @ SV12 @ SV25 @ SY169 )
| ~ ( surjection @ SV12 )
| ! [SY170: $i] :
( ~ ( element @ SY170 @ SY169 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SY170 @ SY169 @ SV25 @ SV12 ) )
!= SY170 )
| ~ ( element @ ( sK8_ElDom @ SY170 @ SY169 @ SV25 @ SV12 ) @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(113,plain,
! [SV13: $i] :
( ( ( ! [SY128: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SY128 @ SV13 ) @ SY128 )
| ~ ( element @ ( sK10_SY81 @ SY128 @ SV13 ) @ SY128 ) )
| ( ( apply @ SV13 @ ( sK9_El1 @ SY128 @ SV13 ) )
!= ( apply @ SV13 @ ( sK10_SY81 @ SY128 @ SV13 ) ) ) )
| ~ ( ( ( sK9_El1 @ SY128 @ SV13 )
!= ( sK10_SY81 @ SY128 @ SV13 ) ) ) )
| ! [SY129: $i] :
~ ( morphism @ SV13 @ SY128 @ SY129 ) ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(114,plain,
! [SV26: $i,SV14: $i] :
( ( ! [SY171: $i,SY172: $i,SY173: $i] :
( ~ ( exact @ SV14 @ SV26 )
| ~ ( morphism @ SV14 @ SY171 @ SY172 )
| ~ ( morphism @ SV26 @ SY172 @ SY173 )
| ~ ( ~ ! [SY174: $i] :
( ( ( apply @ SV26 @ SY174 )
!= ( zero @ SY173 ) )
| ~ ( element @ SY174 @ SY172 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY174 @ SY173 @ SY172 @ SY171 @ SV26 @ SV14 ) )
!= SY174 )
| ~ ( element @ ( sK6_ElDom @ SY174 @ SY173 @ SY172 @ SY171 @ SV26 @ SV14 ) @ SY171 ) ) )
| ~ ~ ( ~ ! [SY175: $i] :
( ! [SY136: $i] :
( ( ( apply @ SV14 @ SY136 )
!= SY175 )
| ~ ( element @ SY136 @ SY171 ) )
| ( ( apply @ SV26 @ SY175 )
= ( zero @ SY173 ) ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
( ( ( apply @ SV14 @ SY138 )
!= SY137 )
| ~ ( element @ SY138 @ SY171 ) )
| ( element @ SY137 @ SY172 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(115,plain,
! [SV15: $i] :
( ( ( ! [SY139: $i,SY140: $i] :
( ~ ( ~ ( element @ ( sK7_ElCod @ SY140 @ SY139 @ SV15 ) @ SY140 )
| ~ ! [SY141: $i] :
( ( ( apply @ SV15 @ SY141 )
!= ( sK7_ElCod @ SY140 @ SY139 @ SV15 ) )
| ~ ( element @ SY141 @ SY139 ) ) )
| ~ ( morphism @ SV15 @ SY139 @ SY140 ) ) )
= $true )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(116,plain,
! [SV16: $i,SV1: $i] :
( ( ( ~ ( injection @ SV1 )
| ! [SY142: $i] :
~ ( morphism @ SV1 @ SV16 @ SY142 ) )
= $true )
| ( ( ! [SY143: $i,SY144: $i] :
( ~ ( element @ SY143 @ SV16 )
| ~ ( element @ SY144 @ SV16 )
| ( ( apply @ SV1 @ SY143 )
!= ( apply @ SV1 @ SY144 ) )
| ( SY143 = SY144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(117,plain,
! [SV27: $i,SV17: $i,SV2: $i] :
( ( ! [SY179: $i,SY180: $i,SY181: $i] :
( ! [SY182: $i,SY183: $i] :
( ~ ( commute @ SV2 @ SV17 @ SV27 @ SY179 )
| ~ ( morphism @ SV2 @ SY180 @ SY181 )
| ~ ( morphism @ SV17 @ SY181 @ SY183 )
| ~ ( morphism @ SV27 @ SY180 @ SY182 )
| ~ ( morphism @ SY179 @ SY182 @ SY183 ) )
| ! [SY184: $i] :
( ~ ( element @ SY184 @ SY180 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY184 ) )
= ( apply @ SY179 @ ( apply @ SV27 @ SY184 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(118,plain,
! [SV28: $i,SV3: $i,SV18: $i] :
( ( ~ ( element @ SV18 @ SV3 )
| ~ ( element @ SV28 @ SV3 )
| ( element @ ( subtract @ SV3 @ SV18 @ SV28 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(119,plain,
! [SV4: $i,SV19: $i] :
( ( ( ~ ( element @ SV19 @ SV4 ) )
= $true )
| ( ( ( subtract @ SV4 @ SV19 @ SV19 )
= ( zero @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(120,plain,
! [SV29: $i,SV5: $i,SV20: $i] :
( ( ~ ( element @ SV20 @ SV5 )
| ~ ( element @ SV29 @ SV5 )
| ( ( subtract @ SV5 @ SV20 @ ( subtract @ SV5 @ SV20 @ SV29 ) )
= SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(121,plain,
! [SV30: $i,SV21: $i,SV6: $i] :
( ( ~ ( morphism @ SV6 @ SV21 @ SV30 )
| ! [SY185: $i,SY186: $i] :
( ~ ( element @ SY185 @ SV21 )
| ~ ( element @ SY186 @ SV21 )
| ( ( apply @ SV6 @ ( subtract @ SV21 @ SY185 @ SY186 ) )
= ( subtract @ SV30 @ ( apply @ SV6 @ SY185 ) @ ( apply @ SV6 @ SY186 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(122,plain,
! [SV31: $i,SV22: $i,SV7: $i] :
( ( ~ ( injection_2 @ SV7 )
| ~ ( morphism @ SV7 @ SV22 @ SV31 )
| ! [SY187: $i] :
( ( ( apply @ SV7 @ SY187 )
!= ( zero @ SV31 ) )
| ~ ( element @ SY187 @ SV22 )
| ( SY187
= ( zero @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(123,plain,
! [SV8: $i,SV23: $i,SV32: $i] :
( ( ! [SY188: $i,SY189: $i,SY190: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY190 @ SY189 @ SY188 @ SV32 @ SV23 @ SV8 ) @ SY189 )
| ~ ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SY190 @ SY189 @ SY188 @ SV32 @ SV23 @ SV8 ) ) )
!= ( apply @ SY188 @ ( apply @ SV32 @ ( sK2_ElDom @ SY190 @ SY189 @ SY188 @ SV32 @ SV23 @ SV8 ) ) ) ) ) )
| ! [SY191: $i,SY192: $i] :
( ~ ( morphism @ SV8 @ SY189 @ SY190 )
| ~ ( morphism @ SV23 @ SY190 @ SY192 )
| ~ ( morphism @ SV32 @ SY189 @ SY191 )
| ~ ( morphism @ SY188 @ SY191 @ SY192 ) )
| ( commute @ SV8 @ SV23 @ SV32 @ SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(124,plain,
! [SV9: $i,SV33: $i,SV24: $i] :
( ( ! [SY193: $i,SY194: $i] :
( ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) )
!= ( zero @ SY194 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) @ SY193 )
| ! [SY195: $i] :
( ( ( apply @ SV9 @ SY195 )
!= ( sK3_ElCodDom @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ SY195 @ SV33 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SY194 ) )
| ~ ( ( ( apply @ SV9 @ ( sK5_SY78 @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) @ SY193 )
| ~ ( ( ( apply @ SV9 @ ( sK4_SY79 @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) ) ) )
| ~ ( morphism @ SV9 @ SV33 @ SY193 )
| ~ ( morphism @ SV24 @ SY193 @ SY194 ) )
| ( exact @ SV9 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(125,plain,
! [SV34: $i,SV10: $i] :
( ( ( ! [SY196: $i] :
( ~ ( ~ ~ ( ( ( apply @ SV10 @ ( sK1_El @ SY196 @ SV34 @ SV10 ) )
!= ( zero @ SY196 ) )
| ~ ( element @ ( sK1_El @ SY196 @ SV34 @ SV10 ) @ SV34 ) )
| ~ ( ( ( sK1_El @ SY196 @ SV34 @ SV10 )
!= ( zero @ SV34 ) ) ) )
| ~ ( morphism @ SV10 @ SV34 @ SY196 ) ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(126,plain,
( ( injection @ x )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(127,plain,
( ( ~ ( injection_2 @ x ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(128,plain,
! [SV11: $i] :
( ( ~ ! [SY120: $i,SY121: $i] :
( ~ ( morphism @ SV11 @ SY120 @ SY121 )
| ! [SY122: $i] :
( ~ ( element @ SY122 @ SY120 )
| ( element @ ( apply @ SV11 @ SY122 ) @ SY121 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(129,plain,
! [SV11: $i] :
( ( ~ ! [SY123: $i,SY124: $i] :
( ~ ( morphism @ SV11 @ SY123 @ SY124 )
| ( ( apply @ SV11 @ ( zero @ SY123 ) )
= ( zero @ SY124 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(130,plain,
! [SV35: $i,SV25: $i,SV12: $i] :
( ( ~ ( morphism @ SV12 @ SV25 @ SV35 )
| ~ ( surjection @ SV12 )
| ! [SY197: $i] :
( ~ ( element @ SY197 @ SV35 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SY197 @ SV35 @ SV25 @ SV12 ) )
!= SY197 )
| ~ ( element @ ( sK8_ElDom @ SY197 @ SV35 @ SV25 @ SV12 ) @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(131,plain,
! [SV13: $i,SV36: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV36 @ SV13 ) @ SV36 )
| ~ ( element @ ( sK10_SY81 @ SV36 @ SV13 ) @ SV36 ) )
| ( ( apply @ SV13 @ ( sK9_El1 @ SV36 @ SV13 ) )
!= ( apply @ SV13 @ ( sK10_SY81 @ SV36 @ SV13 ) ) ) )
| ~ ( ( ( sK9_El1 @ SV36 @ SV13 )
!= ( sK10_SY81 @ SV36 @ SV13 ) ) ) )
| ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(132,plain,
! [SV37: $i,SV26: $i,SV14: $i] :
( ( ! [SY199: $i,SY200: $i] :
( ~ ( exact @ SV14 @ SV26 )
| ~ ( morphism @ SV14 @ SV37 @ SY199 )
| ~ ( morphism @ SV26 @ SY199 @ SY200 )
| ~ ( ~ ! [SY201: $i] :
( ( ( apply @ SV26 @ SY201 )
!= ( zero @ SY200 ) )
| ~ ( element @ SY201 @ SY199 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY201 @ SY200 @ SY199 @ SV37 @ SV26 @ SV14 ) )
!= SY201 )
| ~ ( element @ ( sK6_ElDom @ SY201 @ SY200 @ SY199 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
| ~ ~ ( ~ ! [SY202: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY202 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY202 )
= ( zero @ SY200 ) ) )
| ~ ! [SY204: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY204 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY204 @ SY199 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(133,plain,
! [SV15: $i,SV38: $i] :
( ( ( ! [SY206: $i] :
( ~ ( ~ ( element @ ( sK7_ElCod @ SY206 @ SV38 @ SV15 ) @ SY206 )
| ~ ! [SY207: $i] :
( ( ( apply @ SV15 @ SY207 )
!= ( sK7_ElCod @ SY206 @ SV38 @ SV15 ) )
| ~ ( element @ SY207 @ SV38 ) ) )
| ~ ( morphism @ SV15 @ SV38 @ SY206 ) ) )
= $true )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(134,plain,
! [SV16: $i,SV1: $i] :
( ( ( ~ ( injection @ SV1 ) )
= $true )
| ( ( ! [SY142: $i] :
~ ( morphism @ SV1 @ SV16 @ SY142 ) )
= $true )
| ( ( ! [SY143: $i,SY144: $i] :
( ~ ( element @ SY143 @ SV16 )
| ~ ( element @ SY144 @ SV16 )
| ( ( apply @ SV1 @ SY143 )
!= ( apply @ SV1 @ SY144 ) )
| ( SY143 = SY144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(135,plain,
! [SV39: $i,SV27: $i,SV17: $i,SV2: $i] :
( ( ! [SY208: $i,SY209: $i] :
( ! [SY210: $i,SY211: $i] :
( ~ ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
| ~ ( morphism @ SV2 @ SY208 @ SY209 )
| ~ ( morphism @ SV17 @ SY209 @ SY211 )
| ~ ( morphism @ SV27 @ SY208 @ SY210 )
| ~ ( morphism @ SV39 @ SY210 @ SY211 ) )
| ! [SY212: $i] :
( ~ ( element @ SY212 @ SY208 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY212 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY212 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(136,plain,
! [SV28: $i,SV3: $i,SV18: $i] :
( ( ( ~ ( element @ SV18 @ SV3 )
| ~ ( element @ SV28 @ SV3 ) )
= $true )
| ( ( element @ ( subtract @ SV3 @ SV18 @ SV28 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(137,plain,
! [SV4: $i,SV19: $i] :
( ( ( element @ SV19 @ SV4 )
= $false )
| ( ( ( subtract @ SV4 @ SV19 @ SV19 )
= ( zero @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(138,plain,
! [SV29: $i,SV5: $i,SV20: $i] :
( ( ( ~ ( element @ SV20 @ SV5 )
| ~ ( element @ SV29 @ SV5 ) )
= $true )
| ( ( ( subtract @ SV5 @ SV20 @ ( subtract @ SV5 @ SV20 @ SV29 ) )
= SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(139,plain,
! [SV30: $i,SV21: $i,SV6: $i] :
( ( ( ~ ( morphism @ SV6 @ SV21 @ SV30 ) )
= $true )
| ( ( ! [SY185: $i,SY186: $i] :
( ~ ( element @ SY185 @ SV21 )
| ~ ( element @ SY186 @ SV21 )
| ( ( apply @ SV6 @ ( subtract @ SV21 @ SY185 @ SY186 ) )
= ( subtract @ SV30 @ ( apply @ SV6 @ SY185 ) @ ( apply @ SV6 @ SY186 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(140,plain,
! [SV31: $i,SV22: $i,SV7: $i] :
( ( ( ~ ( injection_2 @ SV7 )
| ~ ( morphism @ SV7 @ SV22 @ SV31 ) )
= $true )
| ( ( ! [SY187: $i] :
( ( ( apply @ SV7 @ SY187 )
!= ( zero @ SV31 ) )
| ~ ( element @ SY187 @ SV22 )
| ( SY187
= ( zero @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(141,plain,
! [SV8: $i,SV23: $i,SV32: $i,SV40: $i] :
( ( ! [SY213: $i,SY214: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY214 @ SY213 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SY213 )
| ~ ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SY214 @ SY213 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
!= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SY214 @ SY213 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) ) ) )
| ! [SY215: $i,SY216: $i] :
( ~ ( morphism @ SV8 @ SY213 @ SY214 )
| ~ ( morphism @ SV23 @ SY214 @ SY216 )
| ~ ( morphism @ SV32 @ SY213 @ SY215 )
| ~ ( morphism @ SV40 @ SY215 @ SY216 ) )
| ( commute @ SV8 @ SV23 @ SV32 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(142,plain,
! [SV9: $i,SV33: $i,SV24: $i] :
( ( ( ! [SY193: $i,SY194: $i] :
( ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) )
!= ( zero @ SY194 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) @ SY193 )
| ! [SY195: $i] :
( ( ( apply @ SV9 @ SY195 )
!= ( sK3_ElCodDom @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ SY195 @ SV33 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SY194 ) )
| ~ ( ( ( apply @ SV9 @ ( sK5_SY78 @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) @ SY193 )
| ~ ( ( ( apply @ SV9 @ ( sK4_SY79 @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SY194 @ SY193 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) ) ) )
| ~ ( morphism @ SV9 @ SV33 @ SY193 )
| ~ ( morphism @ SV24 @ SY193 @ SY194 ) ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(143,plain,
! [SV34: $i,SV41: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ( ( apply @ SV10 @ ( sK1_El @ SV41 @ SV34 @ SV10 ) )
!= ( zero @ SV41 ) )
| ~ ( element @ ( sK1_El @ SV41 @ SV34 @ SV10 ) @ SV34 ) )
| ~ ( ( ( sK1_El @ SV41 @ SV34 @ SV10 )
!= ( zero @ SV34 ) ) ) )
| ~ ( morphism @ SV10 @ SV34 @ SV41 ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(144,plain,
( ( injection_2 @ x )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(145,plain,
! [SV11: $i] :
( ( ! [SY120: $i,SY121: $i] :
( ~ ( morphism @ SV11 @ SY120 @ SY121 )
| ! [SY122: $i] :
( ~ ( element @ SY122 @ SY120 )
| ( element @ ( apply @ SV11 @ SY122 ) @ SY121 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(146,plain,
! [SV11: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ~ ( morphism @ SV11 @ SY123 @ SY124 )
| ( ( apply @ SV11 @ ( zero @ SY123 ) )
= ( zero @ SY124 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(147,plain,
! [SV35: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( morphism @ SV12 @ SV25 @ SV35 )
| ~ ( surjection @ SV12 ) )
= $true )
| ( ( ! [SY197: $i] :
( ~ ( element @ SY197 @ SV35 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SY197 @ SV35 @ SV25 @ SV12 ) )
!= SY197 )
| ~ ( element @ ( sK8_ElDom @ SY197 @ SV35 @ SV25 @ SV12 ) @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(148,plain,
! [SV13: $i,SV36: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV36 @ SV13 ) @ SV36 )
| ~ ( element @ ( sK10_SY81 @ SV36 @ SV13 ) @ SV36 ) )
| ( ( apply @ SV13 @ ( sK9_El1 @ SV36 @ SV13 ) )
!= ( apply @ SV13 @ ( sK10_SY81 @ SV36 @ SV13 ) ) ) )
| ~ ( ( ( sK9_El1 @ SV36 @ SV13 )
!= ( sK10_SY81 @ SV36 @ SV13 ) ) ) ) )
= $true )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(149,plain,
! [SV42: $i,SV37: $i,SV26: $i,SV14: $i] :
( ( ! [SY217: $i] :
( ~ ( exact @ SV14 @ SV26 )
| ~ ( morphism @ SV14 @ SV37 @ SV42 )
| ~ ( morphism @ SV26 @ SV42 @ SY217 )
| ~ ( ~ ! [SY218: $i] :
( ( ( apply @ SV26 @ SY218 )
!= ( zero @ SY217 ) )
| ~ ( element @ SY218 @ SV42 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY218 @ SY217 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SY218 )
| ~ ( element @ ( sK6_ElDom @ SY218 @ SY217 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
| ~ ~ ( ~ ! [SY202: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY202 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY202 )
= ( zero @ SY217 ) ) )
| ~ ! [SY221: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY221 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY221 @ SV42 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(150,plain,
! [SV15: $i,SV38: $i,SV43: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) @ SV43 )
| ~ ! [SY223: $i] :
( ( ( apply @ SV15 @ SY223 )
!= ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) )
| ~ ( element @ SY223 @ SV38 ) ) )
| ~ ( morphism @ SV15 @ SV38 @ SV43 ) )
= $true )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(151,plain,
! [SV16: $i,SV1: $i] :
( ( ( injection @ SV1 )
= $false )
| ( ( ! [SY142: $i] :
~ ( morphism @ SV1 @ SV16 @ SY142 ) )
= $true )
| ( ( ! [SY143: $i,SY144: $i] :
( ~ ( element @ SY143 @ SV16 )
| ~ ( element @ SY144 @ SV16 )
| ( ( apply @ SV1 @ SY143 )
!= ( apply @ SV1 @ SY144 ) )
| ( SY143 = SY144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(152,plain,
! [SV44: $i,SV39: $i,SV27: $i,SV17: $i,SV2: $i] :
( ( ! [SY224: $i] :
( ! [SY225: $i,SY226: $i] :
( ~ ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
| ~ ( morphism @ SV2 @ SV44 @ SY224 )
| ~ ( morphism @ SV17 @ SY224 @ SY226 )
| ~ ( morphism @ SV27 @ SV44 @ SY225 )
| ~ ( morphism @ SV39 @ SY225 @ SY226 ) )
| ! [SY227: $i] :
( ~ ( element @ SY227 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY227 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY227 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(153,plain,
! [SV28: $i,SV3: $i,SV18: $i] :
( ( ( ~ ( element @ SV18 @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV28 @ SV3 ) )
= $true )
| ( ( element @ ( subtract @ SV3 @ SV18 @ SV28 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(154,plain,
! [SV29: $i,SV5: $i,SV20: $i] :
( ( ( ~ ( element @ SV20 @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV29 @ SV5 ) )
= $true )
| ( ( ( subtract @ SV5 @ SV20 @ ( subtract @ SV5 @ SV20 @ SV29 ) )
= SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(155,plain,
! [SV30: $i,SV21: $i,SV6: $i] :
( ( ( morphism @ SV6 @ SV21 @ SV30 )
= $false )
| ( ( ! [SY185: $i,SY186: $i] :
( ~ ( element @ SY185 @ SV21 )
| ~ ( element @ SY186 @ SV21 )
| ( ( apply @ SV6 @ ( subtract @ SV21 @ SY185 @ SY186 ) )
= ( subtract @ SV30 @ ( apply @ SV6 @ SY185 ) @ ( apply @ SV6 @ SY186 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(156,plain,
! [SV31: $i,SV22: $i,SV7: $i] :
( ( ( ~ ( injection_2 @ SV7 ) )
= $true )
| ( ( ~ ( morphism @ SV7 @ SV22 @ SV31 ) )
= $true )
| ( ( ! [SY187: $i] :
( ( ( apply @ SV7 @ SY187 )
!= ( zero @ SV31 ) )
| ~ ( element @ SY187 @ SV22 )
| ( SY187
= ( zero @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(157,plain,
! [SV8: $i,SV23: $i,SV32: $i,SV40: $i,SV45: $i] :
( ( ! [SY228: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY228 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
| ~ ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SY228 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
!= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SY228 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) ) ) )
| ! [SY229: $i,SY230: $i] :
( ~ ( morphism @ SV8 @ SV45 @ SY228 )
| ~ ( morphism @ SV23 @ SY228 @ SY230 )
| ~ ( morphism @ SV32 @ SV45 @ SY229 )
| ~ ( morphism @ SV40 @ SY229 @ SY230 ) )
| ( commute @ SV8 @ SV23 @ SV32 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(158,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV24: $i] :
( ( ( ! [SY231: $i] :
( ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY231 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( zero @ SY231 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY231 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ! [SY232: $i] :
( ( ( apply @ SV9 @ SY232 )
!= ( sK3_ElCodDom @ SY231 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ SY232 @ SV33 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY231 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SY231 ) )
| ~ ( ( ( apply @ SV9 @ ( sK5_SY78 @ SY231 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SY231 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SY231 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY231 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ~ ( ( ( apply @ SV9 @ ( sK4_SY79 @ SY231 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SY231 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SY231 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) ) ) )
| ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SY231 ) ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(159,plain,
! [SV34: $i,SV41: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ( ( apply @ SV10 @ ( sK1_El @ SV41 @ SV34 @ SV10 ) )
!= ( zero @ SV41 ) )
| ~ ( element @ ( sK1_El @ SV41 @ SV34 @ SV10 ) @ SV34 ) )
| ~ ( ( ( sK1_El @ SV41 @ SV34 @ SV10 )
!= ( zero @ SV34 ) ) ) ) )
= $true )
| ( ( ~ ( morphism @ SV10 @ SV34 @ SV41 ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(160,plain,
! [SV47: $i,SV11: $i] :
( ( ! [SY233: $i] :
( ~ ( morphism @ SV11 @ SV47 @ SY233 )
| ! [SY234: $i] :
( ~ ( element @ SY234 @ SV47 )
| ( element @ ( apply @ SV11 @ SY234 ) @ SY233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(161,plain,
! [SV48: $i,SV11: $i] :
( ( ! [SY235: $i] :
( ~ ( morphism @ SV11 @ SV48 @ SY235 )
| ( ( apply @ SV11 @ ( zero @ SV48 ) )
= ( zero @ SY235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(162,plain,
! [SV35: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( morphism @ SV12 @ SV25 @ SV35 ) )
= $true )
| ( ( ~ ( surjection @ SV12 ) )
= $true )
| ( ( ! [SY197: $i] :
( ~ ( element @ SY197 @ SV35 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SY197 @ SV35 @ SV25 @ SV12 ) )
!= SY197 )
| ~ ( element @ ( sK8_ElDom @ SY197 @ SV35 @ SV25 @ SV12 ) @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(163,plain,
! [SV13: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV36 @ SV13 ) @ SV36 )
| ~ ( element @ ( sK10_SY81 @ SV36 @ SV13 ) @ SV36 ) )
| ( ( apply @ SV13 @ ( sK9_El1 @ SV36 @ SV13 ) )
!= ( apply @ SV13 @ ( sK10_SY81 @ SV36 @ SV13 ) ) ) )
| ~ ( ( ( sK9_El1 @ SV36 @ SV13 )
!= ( sK10_SY81 @ SV36 @ SV13 ) ) ) )
= $false )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(164,plain,
! [SV49: $i,SV42: $i,SV37: $i,SV26: $i,SV14: $i] :
( ( ~ ( exact @ SV14 @ SV26 )
| ~ ( morphism @ SV14 @ SV37 @ SV42 )
| ~ ( morphism @ SV26 @ SV42 @ SV49 )
| ~ ( ~ ! [SY236: $i] :
( ( ( apply @ SV26 @ SY236 )
!= ( zero @ SV49 ) )
| ~ ( element @ SY236 @ SV42 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SY236 )
| ~ ( element @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
| ~ ~ ( ~ ! [SY237: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY237 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY237 )
= ( zero @ SV49 ) ) )
| ~ ! [SY221: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY221 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY221 @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(165,plain,
! [SV15: $i,SV38: $i,SV43: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) @ SV43 )
| ~ ! [SY223: $i] :
( ( ( apply @ SV15 @ SY223 )
!= ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) )
| ~ ( element @ SY223 @ SV38 ) ) ) )
= $true )
| ( ( ~ ( morphism @ SV15 @ SV38 @ SV43 ) )
= $true )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(166,plain,
! [SV50: $i,SV16: $i,SV1: $i] :
( ( ( ~ ( morphism @ SV1 @ SV16 @ SV50 ) )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( ! [SY143: $i,SY144: $i] :
( ~ ( element @ SY143 @ SV16 )
| ~ ( element @ SY144 @ SV16 )
| ( ( apply @ SV1 @ SY143 )
!= ( apply @ SV1 @ SY144 ) )
| ( SY143 = SY144 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(167,plain,
! [SV51: $i,SV44: $i,SV39: $i,SV27: $i,SV17: $i,SV2: $i] :
( ( ! [SY241: $i,SY242: $i] :
( ~ ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
| ~ ( morphism @ SV2 @ SV44 @ SV51 )
| ~ ( morphism @ SV17 @ SV51 @ SY242 )
| ~ ( morphism @ SV27 @ SV44 @ SY241 )
| ~ ( morphism @ SV39 @ SY241 @ SY242 ) )
| ! [SY227: $i] :
( ~ ( element @ SY227 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY227 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY227 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(168,plain,
! [SV28: $i,SV3: $i,SV18: $i] :
( ( ( element @ SV18 @ SV3 )
= $false )
| ( ( ~ ( element @ SV28 @ SV3 ) )
= $true )
| ( ( element @ ( subtract @ SV3 @ SV18 @ SV28 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(169,plain,
! [SV29: $i,SV5: $i,SV20: $i] :
( ( ( element @ SV20 @ SV5 )
= $false )
| ( ( ~ ( element @ SV29 @ SV5 ) )
= $true )
| ( ( ( subtract @ SV5 @ SV20 @ ( subtract @ SV5 @ SV20 @ SV29 ) )
= SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(170,plain,
! [SV30: $i,SV6: $i,SV21: $i,SV52: $i] :
( ( ( ! [SY244: $i] :
( ~ ( element @ SV52 @ SV21 )
| ~ ( element @ SY244 @ SV21 )
| ( ( apply @ SV6 @ ( subtract @ SV21 @ SV52 @ SY244 ) )
= ( subtract @ SV30 @ ( apply @ SV6 @ SV52 ) @ ( apply @ SV6 @ SY244 ) ) ) ) )
= $true )
| ( ( morphism @ SV6 @ SV21 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(171,plain,
! [SV31: $i,SV22: $i,SV7: $i] :
( ( ( injection_2 @ SV7 )
= $false )
| ( ( ~ ( morphism @ SV7 @ SV22 @ SV31 ) )
= $true )
| ( ( ! [SY187: $i] :
( ( ( apply @ SV7 @ SY187 )
!= ( zero @ SV31 ) )
| ~ ( element @ SY187 @ SV22 )
| ( SY187
= ( zero @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(172,plain,
! [SV8: $i,SV23: $i,SV32: $i,SV40: $i,SV45: $i,SV53: $i] :
( ( ~ ( ~ ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
| ~ ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
!= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) ) ) )
| ! [SY245: $i,SY246: $i] :
( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SY246 )
| ~ ( morphism @ SV32 @ SV45 @ SY245 )
| ~ ( morphism @ SV40 @ SY245 @ SY246 ) )
| ( commute @ SV8 @ SV23 @ SV32 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(173,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( zero @ SV54 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ! [SY247: $i] :
( ( ( apply @ SV9 @ SY247 )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ SY247 @ SV33 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
| ~ ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ~ ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) ) ) )
| ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(174,plain,
! [SV34: $i,SV41: $i,SV10: $i] :
( ( ( ~ ~ ( ( ( apply @ SV10 @ ( sK1_El @ SV41 @ SV34 @ SV10 ) )
!= ( zero @ SV41 ) )
| ~ ( element @ ( sK1_El @ SV41 @ SV34 @ SV10 ) @ SV34 ) )
| ~ ( ( ( sK1_El @ SV41 @ SV34 @ SV10 )
!= ( zero @ SV34 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV10 @ SV34 @ SV41 ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(175,plain,
! [SV55: $i,SV47: $i,SV11: $i] :
( ( ~ ( morphism @ SV11 @ SV47 @ SV55 )
| ! [SY248: $i] :
( ~ ( element @ SY248 @ SV47 )
| ( element @ ( apply @ SV11 @ SY248 ) @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(176,plain,
! [SV56: $i,SV48: $i,SV11: $i] :
( ( ~ ( morphism @ SV11 @ SV48 @ SV56 )
| ( ( apply @ SV11 @ ( zero @ SV48 ) )
= ( zero @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(177,plain,
! [SV35: $i,SV25: $i,SV12: $i] :
( ( ( morphism @ SV12 @ SV25 @ SV35 )
= $false )
| ( ( ~ ( surjection @ SV12 ) )
= $true )
| ( ( ! [SY197: $i] :
( ~ ( element @ SY197 @ SV35 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SY197 @ SV35 @ SV25 @ SV12 ) )
!= SY197 )
| ~ ( element @ ( sK8_ElDom @ SY197 @ SV35 @ SV25 @ SV12 ) @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(178,plain,
! [SV13: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV36 @ SV13 ) @ SV36 )
| ~ ( element @ ( sK10_SY81 @ SV36 @ SV13 ) @ SV36 ) )
| ( ( apply @ SV13 @ ( sK9_El1 @ SV36 @ SV13 ) )
!= ( apply @ SV13 @ ( sK10_SY81 @ SV36 @ SV13 ) ) ) ) )
= $false )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(179,plain,
! [SV13: $i,SV36: $i] :
( ( ( ~ ( ( ( sK9_El1 @ SV36 @ SV13 )
!= ( sK10_SY81 @ SV36 @ SV13 ) ) ) )
= $false )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(180,plain,
! [SV49: $i,SV42: $i,SV37: $i,SV26: $i,SV14: $i] :
( ( ( ~ ( exact @ SV14 @ SV26 )
| ~ ( morphism @ SV14 @ SV37 @ SV42 )
| ~ ( morphism @ SV26 @ SV42 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY236: $i] :
( ( ( apply @ SV26 @ SY236 )
!= ( zero @ SV49 ) )
| ~ ( element @ SY236 @ SV42 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SY236 )
| ~ ( element @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
| ~ ~ ( ~ ! [SY237: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY237 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY237 )
= ( zero @ SV49 ) ) )
| ~ ! [SY221: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY221 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY221 @ SV42 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(181,plain,
! [SV15: $i,SV38: $i,SV43: $i] :
( ( ( ~ ( element @ ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) @ SV43 )
| ~ ! [SY223: $i] :
( ( ( apply @ SV15 @ SY223 )
!= ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) )
| ~ ( element @ SY223 @ SV38 ) ) )
= $false )
| ( ( ~ ( morphism @ SV15 @ SV38 @ SV43 ) )
= $true )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(182,plain,
! [SV50: $i,SV16: $i,SV1: $i] :
( ( ( morphism @ SV1 @ SV16 @ SV50 )
= $false )
| ( ( injection @ SV1 )
= $false )
| ( ( ! [SY143: $i,SY144: $i] :
( ~ ( element @ SY143 @ SV16 )
| ~ ( element @ SY144 @ SV16 )
| ( ( apply @ SV1 @ SY143 )
!= ( apply @ SV1 @ SY144 ) )
| ( SY143 = SY144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(183,plain,
! [SV51: $i,SV44: $i,SV39: $i,SV27: $i,SV17: $i,SV2: $i] :
( ( ( ! [SY241: $i,SY242: $i] :
( ~ ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
| ~ ( morphism @ SV2 @ SV44 @ SV51 )
| ~ ( morphism @ SV17 @ SV51 @ SY242 )
| ~ ( morphism @ SV27 @ SV44 @ SY241 )
| ~ ( morphism @ SV39 @ SY241 @ SY242 ) ) )
= $true )
| ( ( ! [SY227: $i] :
( ~ ( element @ SY227 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY227 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY227 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(184,plain,
! [SV18: $i,SV3: $i,SV28: $i] :
( ( ( element @ SV28 @ SV3 )
= $false )
| ( ( element @ SV18 @ SV3 )
= $false )
| ( ( element @ ( subtract @ SV3 @ SV18 @ SV28 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(185,plain,
! [SV20: $i,SV5: $i,SV29: $i] :
( ( ( element @ SV29 @ SV5 )
= $false )
| ( ( element @ SV20 @ SV5 )
= $false )
| ( ( ( subtract @ SV5 @ SV20 @ ( subtract @ SV5 @ SV20 @ SV29 ) )
= SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(186,plain,
! [SV30: $i,SV6: $i,SV57: $i,SV21: $i,SV52: $i] :
( ( ( ~ ( element @ SV52 @ SV21 )
| ~ ( element @ SV57 @ SV21 )
| ( ( apply @ SV6 @ ( subtract @ SV21 @ SV52 @ SV57 ) )
= ( subtract @ SV30 @ ( apply @ SV6 @ SV52 ) @ ( apply @ SV6 @ SV57 ) ) ) )
= $true )
| ( ( morphism @ SV6 @ SV21 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(187,plain,
! [SV31: $i,SV22: $i,SV7: $i] :
( ( ( morphism @ SV7 @ SV22 @ SV31 )
= $false )
| ( ( injection_2 @ SV7 )
= $false )
| ( ( ! [SY187: $i] :
( ( ( apply @ SV7 @ SY187 )
!= ( zero @ SV31 ) )
| ~ ( element @ SY187 @ SV22 )
| ( SY187
= ( zero @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(188,plain,
! [SV8: $i,SV23: $i,SV32: $i,SV40: $i,SV45: $i,SV53: $i] :
( ( ( ~ ( ~ ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
| ~ ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
!= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) ) ) )
| ! [SY245: $i,SY246: $i] :
( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SY246 )
| ~ ( morphism @ SV32 @ SV45 @ SY245 )
| ~ ( morphism @ SV40 @ SY245 @ SY246 ) ) )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(189,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( zero @ SV54 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ! [SY247: $i] :
( ( ( apply @ SV9 @ SY247 )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ SY247 @ SV33 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
| ~ ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ~ ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) ) ) ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(190,plain,
! [SV34: $i,SV41: $i,SV10: $i] :
( ( ( ~ ~ ( ( ( apply @ SV10 @ ( sK1_El @ SV41 @ SV34 @ SV10 ) )
!= ( zero @ SV41 ) )
| ~ ( element @ ( sK1_El @ SV41 @ SV34 @ SV10 ) @ SV34 ) ) )
= $false )
| ( ( ~ ( morphism @ SV10 @ SV34 @ SV41 ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(191,plain,
! [SV10: $i,SV34: $i,SV41: $i] :
( ( ( ~ ( ( ( sK1_El @ SV41 @ SV34 @ SV10 )
!= ( zero @ SV34 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV10 @ SV34 @ SV41 ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(192,plain,
! [SV55: $i,SV47: $i,SV11: $i] :
( ( ( ~ ( morphism @ SV11 @ SV47 @ SV55 ) )
= $true )
| ( ( ! [SY248: $i] :
( ~ ( element @ SY248 @ SV47 )
| ( element @ ( apply @ SV11 @ SY248 ) @ SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(193,plain,
! [SV56: $i,SV48: $i,SV11: $i] :
( ( ( ~ ( morphism @ SV11 @ SV48 @ SV56 ) )
= $true )
| ( ( ( apply @ SV11 @ ( zero @ SV48 ) )
= ( zero @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(194,plain,
! [SV35: $i,SV25: $i,SV12: $i] :
( ( ( surjection @ SV12 )
= $false )
| ( ( morphism @ SV12 @ SV25 @ SV35 )
= $false )
| ( ( ! [SY197: $i] :
( ~ ( element @ SY197 @ SV35 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SY197 @ SV35 @ SV25 @ SV12 ) )
!= SY197 )
| ~ ( element @ ( sK8_ElDom @ SY197 @ SV35 @ SV25 @ SV12 ) @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(195,plain,
! [SV13: $i,SV36: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV36 @ SV13 ) @ SV36 )
| ~ ( element @ ( sK10_SY81 @ SV36 @ SV13 ) @ SV36 ) )
| ( ( apply @ SV13 @ ( sK9_El1 @ SV36 @ SV13 ) )
!= ( apply @ SV13 @ ( sK10_SY81 @ SV36 @ SV13 ) ) ) ) )
= $true )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(196,plain,
! [SV13: $i,SV36: $i] :
( ( ( ( ( sK9_El1 @ SV36 @ SV13 )
!= ( sK10_SY81 @ SV36 @ SV13 ) ) )
= $true )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(197,plain,
! [SV49: $i,SV42: $i,SV37: $i,SV26: $i,SV14: $i] :
( ( ( ~ ( exact @ SV14 @ SV26 )
| ~ ( morphism @ SV14 @ SV37 @ SV42 ) )
= $true )
| ( ( ~ ( morphism @ SV26 @ SV42 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY236: $i] :
( ( ( apply @ SV26 @ SY236 )
!= ( zero @ SV49 ) )
| ~ ( element @ SY236 @ SV42 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SY236 )
| ~ ( element @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
| ~ ~ ( ~ ! [SY237: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY237 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY237 )
= ( zero @ SV49 ) ) )
| ~ ! [SY221: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY221 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY221 @ SV42 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(198,plain,
! [SV15: $i,SV38: $i,SV43: $i] :
( ( ( ~ ( element @ ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) @ SV43 ) )
= $false )
| ( ( ~ ( morphism @ SV15 @ SV38 @ SV43 ) )
= $true )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(199,plain,
! [SV38: $i,SV43: $i,SV15: $i] :
( ( ( ~ ! [SY223: $i] :
( ( ( apply @ SV15 @ SY223 )
!= ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) )
| ~ ( element @ SY223 @ SV38 ) ) )
= $false )
| ( ( ~ ( morphism @ SV15 @ SV38 @ SV43 ) )
= $true )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(200,plain,
! [SV50: $i,SV1: $i,SV16: $i,SV58: $i] :
( ( ( ! [SY249: $i] :
( ~ ( element @ SV58 @ SV16 )
| ~ ( element @ SY249 @ SV16 )
| ( ( apply @ SV1 @ SV58 )
!= ( apply @ SV1 @ SY249 ) )
| ( SV58 = SY249 ) ) )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV16 @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(201,plain,
! [SV59: $i,SV51: $i,SV44: $i,SV39: $i,SV27: $i,SV17: $i,SV2: $i] :
( ( ( ! [SY250: $i] :
( ~ ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
| ~ ( morphism @ SV2 @ SV44 @ SV51 )
| ~ ( morphism @ SV17 @ SV51 @ SY250 )
| ~ ( morphism @ SV27 @ SV44 @ SV59 )
| ~ ( morphism @ SV39 @ SV59 @ SY250 ) ) )
= $true )
| ( ( ! [SY227: $i] :
( ~ ( element @ SY227 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY227 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY227 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(202,plain,
! [SV30: $i,SV6: $i,SV57: $i,SV21: $i,SV52: $i] :
( ( ( ~ ( element @ SV52 @ SV21 )
| ~ ( element @ SV57 @ SV21 ) )
= $true )
| ( ( ( apply @ SV6 @ ( subtract @ SV21 @ SV52 @ SV57 ) )
= ( subtract @ SV30 @ ( apply @ SV6 @ SV52 ) @ ( apply @ SV6 @ SV57 ) ) )
= $true )
| ( ( morphism @ SV6 @ SV21 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(203,plain,
! [SV22: $i,SV31: $i,SV60: $i,SV7: $i] :
( ( ( ( ( apply @ SV7 @ SV60 )
!= ( zero @ SV31 ) )
| ~ ( element @ SV60 @ SV22 )
| ( SV60
= ( zero @ SV22 ) ) )
= $true )
| ( ( injection_2 @ SV7 )
= $false )
| ( ( morphism @ SV7 @ SV22 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(204,plain,
! [SV8: $i,SV23: $i,SV32: $i,SV40: $i,SV45: $i,SV53: $i] :
( ( ( ~ ( ~ ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
| ~ ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
!= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY245: $i,SY246: $i] :
( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SY246 )
| ~ ( morphism @ SV32 @ SV45 @ SY245 )
| ~ ( morphism @ SV40 @ SY245 @ SY246 ) ) )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(205,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( zero @ SV54 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ! [SY247: $i] :
( ( ( apply @ SV9 @ SY247 )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ SY247 @ SV33 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
| ~ ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ~ ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(206,plain,
! [SV34: $i,SV41: $i,SV10: $i] :
( ( ( ~ ( ( ( apply @ SV10 @ ( sK1_El @ SV41 @ SV34 @ SV10 ) )
!= ( zero @ SV41 ) )
| ~ ( element @ ( sK1_El @ SV41 @ SV34 @ SV10 ) @ SV34 ) ) )
= $true )
| ( ( ~ ( morphism @ SV10 @ SV34 @ SV41 ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(207,plain,
! [SV10: $i,SV34: $i,SV41: $i] :
( ( ( ( ( sK1_El @ SV41 @ SV34 @ SV10 )
!= ( zero @ SV34 ) ) )
= $true )
| ( ( ~ ( morphism @ SV10 @ SV34 @ SV41 ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(208,plain,
! [SV55: $i,SV47: $i,SV11: $i] :
( ( ( morphism @ SV11 @ SV47 @ SV55 )
= $false )
| ( ( ! [SY248: $i] :
( ~ ( element @ SY248 @ SV47 )
| ( element @ ( apply @ SV11 @ SY248 ) @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(209,plain,
! [SV56: $i,SV48: $i,SV11: $i] :
( ( ( morphism @ SV11 @ SV48 @ SV56 )
= $false )
| ( ( ( apply @ SV11 @ ( zero @ SV48 ) )
= ( zero @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(210,plain,
! [SV25: $i,SV12: $i,SV35: $i,SV61: $i] :
( ( ( ~ ( element @ SV61 @ SV35 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SV61 @ SV35 @ SV25 @ SV12 ) )
!= SV61 )
| ~ ( element @ ( sK8_ElDom @ SV61 @ SV35 @ SV25 @ SV12 ) @ SV25 ) ) )
= $true )
| ( ( morphism @ SV12 @ SV25 @ SV35 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(211,plain,
! [SV13: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV36 @ SV13 ) @ SV36 )
| ~ ( element @ ( sK10_SY81 @ SV36 @ SV13 ) @ SV36 ) )
| ( ( apply @ SV13 @ ( sK9_El1 @ SV36 @ SV13 ) )
!= ( apply @ SV13 @ ( sK10_SY81 @ SV36 @ SV13 ) ) ) )
= $false )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(212,plain,
! [SV13: $i,SV36: $i] :
( ( ( ( sK9_El1 @ SV36 @ SV13 )
= ( sK10_SY81 @ SV36 @ SV13 ) )
= $false )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(213,plain,
! [SV49: $i,SV42: $i,SV37: $i,SV26: $i,SV14: $i] :
( ( ( ~ ( exact @ SV14 @ SV26 ) )
= $true )
| ( ( ~ ( morphism @ SV14 @ SV37 @ SV42 ) )
= $true )
| ( ( ~ ( morphism @ SV26 @ SV42 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY236: $i] :
( ( ( apply @ SV26 @ SY236 )
!= ( zero @ SV49 ) )
| ~ ( element @ SY236 @ SV42 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SY236 )
| ~ ( element @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
| ~ ~ ( ~ ! [SY237: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY237 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY237 )
= ( zero @ SV49 ) ) )
| ~ ! [SY221: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY221 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY221 @ SV42 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(214,plain,
! [SV15: $i,SV38: $i,SV43: $i] :
( ( ( element @ ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) @ SV43 )
= $true )
| ( ( ~ ( morphism @ SV15 @ SV38 @ SV43 ) )
= $true )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(215,plain,
! [SV38: $i,SV43: $i,SV15: $i] :
( ( ( ! [SY223: $i] :
( ( ( apply @ SV15 @ SY223 )
!= ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) )
| ~ ( element @ SY223 @ SV38 ) ) )
= $true )
| ( ( ~ ( morphism @ SV15 @ SV38 @ SV43 ) )
= $true )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(216,plain,
! [SV50: $i,SV1: $i,SV62: $i,SV16: $i,SV58: $i] :
( ( ( ~ ( element @ SV58 @ SV16 )
| ~ ( element @ SV62 @ SV16 )
| ( ( apply @ SV1 @ SV58 )
!= ( apply @ SV1 @ SV62 ) )
| ( SV58 = SV62 ) )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV16 @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(217,plain,
! [SV59: $i,SV63: $i,SV51: $i,SV44: $i,SV39: $i,SV27: $i,SV17: $i,SV2: $i] :
( ( ( ~ ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
| ~ ( morphism @ SV2 @ SV44 @ SV51 )
| ~ ( morphism @ SV17 @ SV51 @ SV63 )
| ~ ( morphism @ SV27 @ SV44 @ SV59 )
| ~ ( morphism @ SV39 @ SV59 @ SV63 ) )
= $true )
| ( ( ! [SY227: $i] :
( ~ ( element @ SY227 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY227 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY227 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(218,plain,
! [SV30: $i,SV6: $i,SV57: $i,SV21: $i,SV52: $i] :
( ( ( ~ ( element @ SV52 @ SV21 ) )
= $true )
| ( ( ~ ( element @ SV57 @ SV21 ) )
= $true )
| ( ( ( apply @ SV6 @ ( subtract @ SV21 @ SV52 @ SV57 ) )
= ( subtract @ SV30 @ ( apply @ SV6 @ SV52 ) @ ( apply @ SV6 @ SV57 ) ) )
= $true )
| ( ( morphism @ SV6 @ SV21 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(219,plain,
! [SV22: $i,SV31: $i,SV60: $i,SV7: $i] :
( ( ( ( ( apply @ SV7 @ SV60 )
!= ( zero @ SV31 ) )
| ~ ( element @ SV60 @ SV22 ) )
= $true )
| ( ( SV60
= ( zero @ SV22 ) )
= $true )
| ( ( injection_2 @ SV7 )
= $false )
| ( ( morphism @ SV7 @ SV22 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(220,plain,
! [SV8: $i,SV23: $i,SV32: $i,SV40: $i,SV45: $i,SV53: $i] :
( ( ( ~ ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
| ~ ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
!= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) ) ) )
= $false )
| ( ( ! [SY245: $i,SY246: $i] :
( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SY246 )
| ~ ( morphism @ SV32 @ SV45 @ SY245 )
| ~ ( morphism @ SV40 @ SY245 @ SY246 ) ) )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(221,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( zero @ SV54 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ! [SY247: $i] :
( ( ( apply @ SV9 @ SY247 )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ SY247 @ SV33 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(222,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV54: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
| ~ ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ~ ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(223,plain,
! [SV34: $i,SV41: $i,SV10: $i] :
( ( ( ( ( apply @ SV10 @ ( sK1_El @ SV41 @ SV34 @ SV10 ) )
!= ( zero @ SV41 ) )
| ~ ( element @ ( sK1_El @ SV41 @ SV34 @ SV10 ) @ SV34 ) )
= $false )
| ( ( ~ ( morphism @ SV10 @ SV34 @ SV41 ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(224,plain,
! [SV10: $i,SV34: $i,SV41: $i] :
( ( ( ( sK1_El @ SV41 @ SV34 @ SV10 )
= ( zero @ SV34 ) )
= $false )
| ( ( ~ ( morphism @ SV10 @ SV34 @ SV41 ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(225,plain,
! [SV55: $i,SV11: $i,SV47: $i,SV64: $i] :
( ( ( ~ ( element @ SV64 @ SV47 )
| ( element @ ( apply @ SV11 @ SV64 ) @ SV55 ) )
= $true )
| ( ( morphism @ SV11 @ SV47 @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(226,plain,
! [SV25: $i,SV12: $i,SV35: $i,SV61: $i] :
( ( ( ~ ( element @ SV61 @ SV35 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SV61 @ SV35 @ SV25 @ SV12 ) )
!= SV61 )
| ~ ( element @ ( sK8_ElDom @ SV61 @ SV35 @ SV25 @ SV12 ) @ SV25 ) ) )
= $true )
| ( ( morphism @ SV12 @ SV25 @ SV35 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(227,plain,
! [SV13: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV36 @ SV13 ) @ SV36 )
| ~ ( element @ ( sK10_SY81 @ SV36 @ SV13 ) @ SV36 ) ) )
= $false )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(228,plain,
! [SV36: $i,SV13: $i] :
( ( ( ( ( apply @ SV13 @ ( sK9_El1 @ SV36 @ SV13 ) )
!= ( apply @ SV13 @ ( sK10_SY81 @ SV36 @ SV13 ) ) ) )
= $false )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(229,plain,
! [SV65: $i,SV36: $i,SV13: $i] :
( ( ( ~ ( morphism @ SV13 @ SV36 @ SV65 ) )
= $true )
| ( ( ( sK9_El1 @ SV36 @ SV13 )
= ( sK10_SY81 @ SV36 @ SV13 ) )
= $false )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(230,plain,
! [SV49: $i,SV42: $i,SV37: $i,SV26: $i,SV14: $i] :
( ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( ~ ( morphism @ SV14 @ SV37 @ SV42 ) )
= $true )
| ( ( ~ ( morphism @ SV26 @ SV42 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY236: $i] :
( ( ( apply @ SV26 @ SY236 )
!= ( zero @ SV49 ) )
| ~ ( element @ SY236 @ SV42 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SY236 )
| ~ ( element @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
| ~ ~ ( ~ ! [SY237: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY237 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY237 )
= ( zero @ SV49 ) ) )
| ~ ! [SY221: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY221 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY221 @ SV42 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(231,plain,
! [SV43: $i,SV38: $i,SV15: $i] :
( ( ( morphism @ SV15 @ SV38 @ SV43 )
= $false )
| ( ( element @ ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) @ SV43 )
= $true )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(232,plain,
! [SV38: $i,SV43: $i,SV66: $i,SV15: $i] :
( ( ( ( ( apply @ SV15 @ SV66 )
!= ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) )
| ~ ( element @ SV66 @ SV38 ) )
= $true )
| ( ( ~ ( morphism @ SV15 @ SV38 @ SV43 ) )
= $true )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(233,plain,
! [SV50: $i,SV1: $i,SV62: $i,SV16: $i,SV58: $i] :
( ( ( ~ ( element @ SV58 @ SV16 )
| ~ ( element @ SV62 @ SV16 )
| ( ( apply @ SV1 @ SV58 )
!= ( apply @ SV1 @ SV62 ) ) )
= $true )
| ( ( SV58 = SV62 )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV16 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(234,plain,
! [SV59: $i,SV63: $i,SV51: $i,SV44: $i,SV39: $i,SV27: $i,SV17: $i,SV2: $i] :
( ( ( ~ ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
| ~ ( morphism @ SV2 @ SV44 @ SV51 )
| ~ ( morphism @ SV17 @ SV51 @ SV63 )
| ~ ( morphism @ SV27 @ SV44 @ SV59 ) )
= $true )
| ( ( ~ ( morphism @ SV39 @ SV59 @ SV63 ) )
= $true )
| ( ( ! [SY227: $i] :
( ~ ( element @ SY227 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY227 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY227 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(235,plain,
! [SV30: $i,SV6: $i,SV57: $i,SV21: $i,SV52: $i] :
( ( ( element @ SV52 @ SV21 )
= $false )
| ( ( ~ ( element @ SV57 @ SV21 ) )
= $true )
| ( ( ( apply @ SV6 @ ( subtract @ SV21 @ SV52 @ SV57 ) )
= ( subtract @ SV30 @ ( apply @ SV6 @ SV52 ) @ ( apply @ SV6 @ SV57 ) ) )
= $true )
| ( ( morphism @ SV6 @ SV21 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(236,plain,
! [SV22: $i,SV31: $i,SV60: $i,SV7: $i] :
( ( ( ( ( apply @ SV7 @ SV60 )
!= ( zero @ SV31 ) ) )
= $true )
| ( ( ~ ( element @ SV60 @ SV22 ) )
= $true )
| ( ( SV60
= ( zero @ SV22 ) )
= $true )
| ( ( injection_2 @ SV7 )
= $false )
| ( ( morphism @ SV7 @ SV22 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(237,plain,
! [SV8: $i,SV23: $i,SV32: $i,SV40: $i,SV45: $i,SV53: $i] :
( ( ( ~ ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 ) )
= $false )
| ( ( ! [SY245: $i,SY246: $i] :
( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SY246 )
| ~ ( morphism @ SV32 @ SV45 @ SY245 )
| ~ ( morphism @ SV40 @ SY245 @ SY246 ) ) )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(238,plain,
! [SV32: $i,SV40: $i,SV45: $i,SV53: $i,SV8: $i,SV23: $i] :
( ( ( ~ ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
!= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) ) ) )
= $false )
| ( ( ! [SY245: $i,SY246: $i] :
( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SY246 )
| ~ ( morphism @ SV32 @ SV45 @ SY245 )
| ~ ( morphism @ SV40 @ SY245 @ SY246 ) ) )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(239,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV54: $i,SV24: $i] :
( ( ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( zero @ SV54 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ! [SY247: $i] :
( ( ( apply @ SV9 @ SY247 )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ SY247 @ SV33 ) ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(240,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
| ~ ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ~ ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) ) ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(241,plain,
! [SV34: $i,SV41: $i,SV10: $i] :
( ( ( ( ( apply @ SV10 @ ( sK1_El @ SV41 @ SV34 @ SV10 ) )
!= ( zero @ SV41 ) ) )
= $false )
| ( ( ~ ( morphism @ SV10 @ SV34 @ SV41 ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(242,plain,
! [SV10: $i,SV34: $i,SV41: $i] :
( ( ( ~ ( element @ ( sK1_El @ SV41 @ SV34 @ SV10 ) @ SV34 ) )
= $false )
| ( ( ~ ( morphism @ SV10 @ SV34 @ SV41 ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(243,plain,
! [SV41: $i,SV34: $i,SV10: $i] :
( ( ( morphism @ SV10 @ SV34 @ SV41 )
= $false )
| ( ( ( sK1_El @ SV41 @ SV34 @ SV10 )
= ( zero @ SV34 ) )
= $false )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(244,plain,
! [SV55: $i,SV11: $i,SV47: $i,SV64: $i] :
( ( ( ~ ( element @ SV64 @ SV47 ) )
= $true )
| ( ( element @ ( apply @ SV11 @ SV64 ) @ SV55 )
= $true )
| ( ( morphism @ SV11 @ SV47 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(245,plain,
! [SV25: $i,SV12: $i,SV35: $i,SV61: $i] :
( ( ( element @ SV61 @ SV35 )
= $false )
| ( ( ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SV61 @ SV35 @ SV25 @ SV12 ) )
!= SV61 )
| ~ ( element @ ( sK8_ElDom @ SV61 @ SV35 @ SV25 @ SV12 ) @ SV25 ) ) )
= $true )
| ( ( morphism @ SV12 @ SV25 @ SV35 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(246,plain,
! [SV13: $i,SV36: $i] :
( ( ( ~ ( ~ ( element @ ( sK9_El1 @ SV36 @ SV13 ) @ SV36 )
| ~ ( element @ ( sK10_SY81 @ SV36 @ SV13 ) @ SV36 ) ) )
= $true )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(247,plain,
! [SV36: $i,SV13: $i] :
( ( ( ( apply @ SV13 @ ( sK9_El1 @ SV36 @ SV13 ) )
= ( apply @ SV13 @ ( sK10_SY81 @ SV36 @ SV13 ) ) )
= $true )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(248,plain,
! [SV65: $i,SV36: $i,SV13: $i] :
( ( ( morphism @ SV13 @ SV36 @ SV65 )
= $false )
| ( ( ( sK9_El1 @ SV36 @ SV13 )
= ( sK10_SY81 @ SV36 @ SV13 ) )
= $false )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(249,plain,
! [SV49: $i,SV26: $i,SV42: $i,SV37: $i,SV14: $i] :
( ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( ~ ( morphism @ SV26 @ SV42 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY236: $i] :
( ( ( apply @ SV26 @ SY236 )
!= ( zero @ SV49 ) )
| ~ ( element @ SY236 @ SV42 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SY236 )
| ~ ( element @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
| ~ ~ ( ~ ! [SY237: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY237 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY237 )
= ( zero @ SV49 ) ) )
| ~ ! [SY221: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY221 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY221 @ SV42 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(250,plain,
! [SV38: $i,SV43: $i,SV66: $i,SV15: $i] :
( ( ( ( ( apply @ SV15 @ SV66 )
!= ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) ) )
= $true )
| ( ( ~ ( element @ SV66 @ SV38 ) )
= $true )
| ( ( ~ ( morphism @ SV15 @ SV38 @ SV43 ) )
= $true )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(251,plain,
! [SV50: $i,SV1: $i,SV62: $i,SV16: $i,SV58: $i] :
( ( ( ~ ( element @ SV58 @ SV16 )
| ~ ( element @ SV62 @ SV16 ) )
= $true )
| ( ( ( ( apply @ SV1 @ SV58 )
!= ( apply @ SV1 @ SV62 ) ) )
= $true )
| ( ( SV58 = SV62 )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV16 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(252,plain,
! [SV59: $i,SV63: $i,SV51: $i,SV44: $i,SV39: $i,SV27: $i,SV17: $i,SV2: $i] :
( ( ( ~ ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
| ~ ( morphism @ SV2 @ SV44 @ SV51 )
| ~ ( morphism @ SV17 @ SV51 @ SV63 ) )
= $true )
| ( ( ~ ( morphism @ SV27 @ SV44 @ SV59 ) )
= $true )
| ( ( ~ ( morphism @ SV39 @ SV59 @ SV63 ) )
= $true )
| ( ( ! [SY227: $i] :
( ~ ( element @ SY227 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY227 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY227 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(253,plain,
! [SV30: $i,SV6: $i,SV52: $i,SV21: $i,SV57: $i] :
( ( ( element @ SV57 @ SV21 )
= $false )
| ( ( element @ SV52 @ SV21 )
= $false )
| ( ( ( apply @ SV6 @ ( subtract @ SV21 @ SV52 @ SV57 ) )
= ( subtract @ SV30 @ ( apply @ SV6 @ SV52 ) @ ( apply @ SV6 @ SV57 ) ) )
= $true )
| ( ( morphism @ SV6 @ SV21 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(254,plain,
! [SV22: $i,SV31: $i,SV60: $i,SV7: $i] :
( ( ( ( apply @ SV7 @ SV60 )
= ( zero @ SV31 ) )
= $false )
| ( ( ~ ( element @ SV60 @ SV22 ) )
= $true )
| ( ( SV60
= ( zero @ SV22 ) )
= $true )
| ( ( injection_2 @ SV7 )
= $false )
| ( ( morphism @ SV7 @ SV22 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(255,plain,
! [SV8: $i,SV23: $i,SV32: $i,SV40: $i,SV45: $i,SV53: $i] :
( ( ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
= $true )
| ( ( ! [SY245: $i,SY246: $i] :
( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SY246 )
| ~ ( morphism @ SV32 @ SV45 @ SY245 )
| ~ ( morphism @ SV40 @ SY245 @ SY246 ) ) )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(256,plain,
! [SV32: $i,SV40: $i,SV45: $i,SV53: $i,SV8: $i,SV23: $i] :
( ( ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
!= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) ) )
= $true )
| ( ( ! [SY245: $i,SY246: $i] :
( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SY246 )
| ~ ( morphism @ SV32 @ SV45 @ SY245 )
| ~ ( morphism @ SV40 @ SY245 @ SY246 ) ) )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(257,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV54: $i,SV24: $i] :
( ( ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( zero @ SV54 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 ) )
= $true )
| ( ( ! [SY247: $i] :
( ( ( apply @ SV9 @ SY247 )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ SY247 @ SV33 ) ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(258,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
| ~ ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ~ ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(259,plain,
! [SV34: $i,SV41: $i,SV10: $i] :
( ( ( ( apply @ SV10 @ ( sK1_El @ SV41 @ SV34 @ SV10 ) )
= ( zero @ SV41 ) )
= $true )
| ( ( ~ ( morphism @ SV10 @ SV34 @ SV41 ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(260,plain,
! [SV10: $i,SV34: $i,SV41: $i] :
( ( ( element @ ( sK1_El @ SV41 @ SV34 @ SV10 ) @ SV34 )
= $true )
| ( ( ~ ( morphism @ SV10 @ SV34 @ SV41 ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(261,plain,
! [SV55: $i,SV11: $i,SV47: $i,SV64: $i] :
( ( ( element @ SV64 @ SV47 )
= $false )
| ( ( element @ ( apply @ SV11 @ SV64 ) @ SV55 )
= $true )
| ( ( morphism @ SV11 @ SV47 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(262,plain,
! [SV25: $i,SV35: $i,SV61: $i,SV12: $i] :
( ( ( ( ( apply @ SV12 @ ( sK8_ElDom @ SV61 @ SV35 @ SV25 @ SV12 ) )
!= SV61 )
| ~ ( element @ ( sK8_ElDom @ SV61 @ SV35 @ SV25 @ SV12 ) @ SV25 ) )
= $false )
| ( ( element @ SV61 @ SV35 )
= $false )
| ( ( morphism @ SV12 @ SV25 @ SV35 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(263,plain,
! [SV13: $i,SV36: $i] :
( ( ( ~ ( element @ ( sK9_El1 @ SV36 @ SV13 ) @ SV36 )
| ~ ( element @ ( sK10_SY81 @ SV36 @ SV13 ) @ SV36 ) )
= $false )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(264,plain,
! [SV67: $i,SV36: $i,SV13: $i] :
( ( ( ~ ( morphism @ SV13 @ SV36 @ SV67 ) )
= $true )
| ( ( ( apply @ SV13 @ ( sK9_El1 @ SV36 @ SV13 ) )
= ( apply @ SV13 @ ( sK10_SY81 @ SV36 @ SV13 ) ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(265,plain,
! [SV37: $i,SV14: $i,SV49: $i,SV42: $i,SV26: $i] :
( ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( ~ ( ~ ! [SY236: $i] :
( ( ( apply @ SV26 @ SY236 )
!= ( zero @ SV49 ) )
| ~ ( element @ SY236 @ SV42 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SY236 )
| ~ ( element @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
| ~ ~ ( ~ ! [SY237: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY237 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY237 )
= ( zero @ SV49 ) ) )
| ~ ! [SY221: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY221 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY221 @ SV42 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(266,plain,
! [SV38: $i,SV43: $i,SV66: $i,SV15: $i] :
( ( ( ( apply @ SV15 @ SV66 )
= ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) )
= $false )
| ( ( ~ ( element @ SV66 @ SV38 ) )
= $true )
| ( ( ~ ( morphism @ SV15 @ SV38 @ SV43 ) )
= $true )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(267,plain,
! [SV50: $i,SV1: $i,SV62: $i,SV16: $i,SV58: $i] :
( ( ( ~ ( element @ SV58 @ SV16 ) )
= $true )
| ( ( ~ ( element @ SV62 @ SV16 ) )
= $true )
| ( ( ( ( apply @ SV1 @ SV58 )
!= ( apply @ SV1 @ SV62 ) ) )
= $true )
| ( ( SV58 = SV62 )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV16 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(268,plain,
! [SV59: $i,SV63: $i,SV51: $i,SV44: $i,SV39: $i,SV27: $i,SV17: $i,SV2: $i] :
( ( ( ~ ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
| ~ ( morphism @ SV2 @ SV44 @ SV51 ) )
= $true )
| ( ( ~ ( morphism @ SV17 @ SV51 @ SV63 ) )
= $true )
| ( ( ~ ( morphism @ SV27 @ SV44 @ SV59 ) )
= $true )
| ( ( ~ ( morphism @ SV39 @ SV59 @ SV63 ) )
= $true )
| ( ( ! [SY227: $i] :
( ~ ( element @ SY227 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY227 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY227 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(269,plain,
! [SV31: $i,SV7: $i,SV22: $i,SV60: $i] :
( ( ( element @ SV60 @ SV22 )
= $false )
| ( ( ( apply @ SV7 @ SV60 )
= ( zero @ SV31 ) )
= $false )
| ( ( SV60
= ( zero @ SV22 ) )
= $true )
| ( ( injection_2 @ SV7 )
= $false )
| ( ( morphism @ SV7 @ SV22 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(270,plain,
! [SV40: $i,SV68: $i,SV32: $i,SV23: $i,SV53: $i,SV45: $i,SV8: $i] :
( ( ( ! [SY251: $i] :
( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SY251 )
| ~ ( morphism @ SV32 @ SV45 @ SV68 )
| ~ ( morphism @ SV40 @ SV68 @ SY251 ) ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(271,plain,
! [SV32: $i,SV40: $i,SV45: $i,SV53: $i,SV8: $i,SV23: $i] :
( ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) )
= $false )
| ( ( ! [SY245: $i,SY246: $i] :
( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SY246 )
| ~ ( morphism @ SV32 @ SV45 @ SY245 )
| ~ ( morphism @ SV40 @ SY245 @ SY246 ) ) )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(272,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV54: $i,SV24: $i] :
( ( ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( zero @ SV54 ) ) )
= $true )
| ( ( ~ ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 ) )
= $true )
| ( ( ! [SY247: $i] :
( ( ( apply @ SV9 @ SY247 )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ SY247 @ SV33 ) ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(273,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
| ~ ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(274,plain,
! [SV9: $i,SV24: $i,SV33: $i,SV46: $i,SV54: $i] :
( ( ( ~ ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ~ ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(275,plain,
! [SV41: $i,SV34: $i,SV10: $i] :
( ( ( morphism @ SV10 @ SV34 @ SV41 )
= $false )
| ( ( ( apply @ SV10 @ ( sK1_El @ SV41 @ SV34 @ SV10 ) )
= ( zero @ SV41 ) )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(276,plain,
! [SV41: $i,SV34: $i,SV10: $i] :
( ( ( morphism @ SV10 @ SV34 @ SV41 )
= $false )
| ( ( element @ ( sK1_El @ SV41 @ SV34 @ SV10 ) @ SV34 )
= $true )
| ( ( injection_2 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(277,plain,
! [SV25: $i,SV35: $i,SV61: $i,SV12: $i] :
( ( ( ( ( apply @ SV12 @ ( sK8_ElDom @ SV61 @ SV35 @ SV25 @ SV12 ) )
!= SV61 ) )
= $false )
| ( ( element @ SV61 @ SV35 )
= $false )
| ( ( morphism @ SV12 @ SV25 @ SV35 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(278,plain,
! [SV12: $i,SV25: $i,SV35: $i,SV61: $i] :
( ( ( ~ ( element @ ( sK8_ElDom @ SV61 @ SV35 @ SV25 @ SV12 ) @ SV25 ) )
= $false )
| ( ( element @ SV61 @ SV35 )
= $false )
| ( ( morphism @ SV12 @ SV25 @ SV35 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(279,plain,
! [SV13: $i,SV36: $i] :
( ( ( ~ ( element @ ( sK9_El1 @ SV36 @ SV13 ) @ SV36 ) )
= $false )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(280,plain,
! [SV13: $i,SV36: $i] :
( ( ( ~ ( element @ ( sK10_SY81 @ SV36 @ SV13 ) @ SV36 ) )
= $false )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(281,plain,
! [SV67: $i,SV36: $i,SV13: $i] :
( ( ( morphism @ SV13 @ SV36 @ SV67 )
= $false )
| ( ( ( apply @ SV13 @ ( sK9_El1 @ SV36 @ SV13 ) )
= ( apply @ SV13 @ ( sK10_SY81 @ SV36 @ SV13 ) ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(282,plain,
! [SV37: $i,SV14: $i,SV42: $i,SV49: $i,SV26: $i] :
( ( ( ~ ! [SY236: $i] :
( ( ( apply @ SV26 @ SY236 )
!= ( zero @ SV49 ) )
| ~ ( element @ SY236 @ SV42 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SY236 )
| ~ ( element @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
| ~ ~ ( ~ ! [SY237: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY237 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY237 )
= ( zero @ SV49 ) ) )
| ~ ! [SY221: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY221 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY221 @ SV42 ) ) ) )
= $false )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(283,plain,
! [SV43: $i,SV15: $i,SV38: $i,SV66: $i] :
( ( ( element @ SV66 @ SV38 )
= $false )
| ( ( ( apply @ SV15 @ SV66 )
= ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) )
= $false )
| ( ( ~ ( morphism @ SV15 @ SV38 @ SV43 ) )
= $true )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(284,plain,
! [SV50: $i,SV1: $i,SV62: $i,SV16: $i,SV58: $i] :
( ( ( element @ SV58 @ SV16 )
= $false )
| ( ( ~ ( element @ SV62 @ SV16 ) )
= $true )
| ( ( ( ( apply @ SV1 @ SV58 )
!= ( apply @ SV1 @ SV62 ) ) )
= $true )
| ( ( SV58 = SV62 )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV16 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(285,plain,
! [SV59: $i,SV63: $i,SV51: $i,SV44: $i,SV39: $i,SV27: $i,SV17: $i,SV2: $i] :
( ( ( ~ ( commute @ SV2 @ SV17 @ SV27 @ SV39 ) )
= $true )
| ( ( ~ ( morphism @ SV2 @ SV44 @ SV51 ) )
= $true )
| ( ( ~ ( morphism @ SV17 @ SV51 @ SV63 ) )
= $true )
| ( ( ~ ( morphism @ SV27 @ SV44 @ SV59 ) )
= $true )
| ( ( ~ ( morphism @ SV39 @ SV59 @ SV63 ) )
= $true )
| ( ( ! [SY227: $i] :
( ~ ( element @ SY227 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY227 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY227 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(286,plain,
! [SV40: $i,SV68: $i,SV32: $i,SV69: $i,SV23: $i,SV53: $i,SV45: $i,SV8: $i] :
( ( ( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SV69 )
| ~ ( morphism @ SV32 @ SV45 @ SV68 )
| ~ ( morphism @ SV40 @ SV68 @ SV69 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(287,plain,
! [SV40: $i,SV70: $i,SV32: $i,SV23: $i,SV53: $i,SV45: $i,SV8: $i] :
( ( ( ! [SY252: $i] :
( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SY252 )
| ~ ( morphism @ SV32 @ SV45 @ SV70 )
| ~ ( morphism @ SV40 @ SV70 @ SY252 ) ) )
= $true )
| ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) )
= $false )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(288,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV54: $i,SV24: $i] :
( ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $false )
| ( ( ~ ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 ) )
= $true )
| ( ( ! [SY247: $i] :
( ( ( apply @ SV9 @ SY247 )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ SY247 @ SV33 ) ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(289,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV54: $i,SV24: $i] :
( ( ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
| ~ ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(290,plain,
! [SV9: $i,SV24: $i,SV33: $i,SV46: $i,SV54: $i] :
( ( ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
| ~ ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(291,plain,
! [SV25: $i,SV35: $i,SV61: $i,SV12: $i] :
( ( ( ( apply @ SV12 @ ( sK8_ElDom @ SV61 @ SV35 @ SV25 @ SV12 ) )
= SV61 )
= $true )
| ( ( element @ SV61 @ SV35 )
= $false )
| ( ( morphism @ SV12 @ SV25 @ SV35 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(292,plain,
! [SV12: $i,SV25: $i,SV35: $i,SV61: $i] :
( ( ( element @ ( sK8_ElDom @ SV61 @ SV35 @ SV25 @ SV12 ) @ SV25 )
= $true )
| ( ( element @ SV61 @ SV35 )
= $false )
| ( ( morphism @ SV12 @ SV25 @ SV35 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(293,plain,
! [SV13: $i,SV36: $i] :
( ( ( element @ ( sK9_El1 @ SV36 @ SV13 ) @ SV36 )
= $true )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(294,plain,
! [SV13: $i,SV36: $i] :
( ( ( element @ ( sK10_SY81 @ SV36 @ SV13 ) @ SV36 )
= $true )
| ( ( ! [SY198: $i] :
~ ( morphism @ SV13 @ SV36 @ SY198 ) )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(295,plain,
! [SV37: $i,SV14: $i,SV42: $i,SV49: $i,SV26: $i] :
( ( ( ~ ! [SY236: $i] :
( ( ( apply @ SV26 @ SY236 )
!= ( zero @ SV49 ) )
| ~ ( element @ SY236 @ SV42 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SY236 )
| ~ ( element @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) ) )
= $false )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(296,plain,
! [SV42: $i,SV49: $i,SV26: $i,SV37: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ! [SY237: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY237 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY237 )
= ( zero @ SV49 ) ) )
| ~ ! [SY221: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY221 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY221 @ SV42 ) ) ) )
= $false )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(297,plain,
! [SV66: $i,SV43: $i,SV38: $i,SV15: $i] :
( ( ( morphism @ SV15 @ SV38 @ SV43 )
= $false )
| ( ( ( apply @ SV15 @ SV66 )
= ( sK7_ElCod @ SV43 @ SV38 @ SV15 ) )
= $false )
| ( ( element @ SV66 @ SV38 )
= $false )
| ( ( surjection @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(298,plain,
! [SV50: $i,SV1: $i,SV58: $i,SV16: $i,SV62: $i] :
( ( ( element @ SV62 @ SV16 )
= $false )
| ( ( element @ SV58 @ SV16 )
= $false )
| ( ( ( ( apply @ SV1 @ SV58 )
!= ( apply @ SV1 @ SV62 ) ) )
= $true )
| ( ( SV58 = SV62 )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV16 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(299,plain,
! [SV59: $i,SV63: $i,SV51: $i,SV44: $i,SV39: $i,SV27: $i,SV17: $i,SV2: $i] :
( ( ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
= $false )
| ( ( ~ ( morphism @ SV2 @ SV44 @ SV51 ) )
= $true )
| ( ( ~ ( morphism @ SV17 @ SV51 @ SV63 ) )
= $true )
| ( ( ~ ( morphism @ SV27 @ SV44 @ SV59 ) )
= $true )
| ( ( ~ ( morphism @ SV39 @ SV59 @ SV63 ) )
= $true )
| ( ( ! [SY227: $i] :
( ~ ( element @ SY227 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY227 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY227 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(300,plain,
! [SV40: $i,SV68: $i,SV32: $i,SV69: $i,SV23: $i,SV53: $i,SV45: $i,SV8: $i] :
( ( ( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SV69 )
| ~ ( morphism @ SV32 @ SV45 @ SV68 ) )
= $true )
| ( ( ~ ( morphism @ SV40 @ SV68 @ SV69 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(301,plain,
! [SV40: $i,SV70: $i,SV32: $i,SV71: $i,SV23: $i,SV53: $i,SV45: $i,SV8: $i] :
( ( ( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SV71 )
| ~ ( morphism @ SV32 @ SV45 @ SV70 )
| ~ ( morphism @ SV40 @ SV70 @ SV71 ) )
= $true )
| ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) )
= $false )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(302,plain,
! [SV9: $i,SV24: $i,SV33: $i,SV46: $i,SV54: $i] :
( ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $false )
| ( ( ! [SY247: $i] :
( ( ( apply @ SV9 @ SY247 )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ SY247 @ SV33 ) ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(303,plain,
! [SV9: $i,SV33: $i,SV46: $i,SV54: $i,SV24: $i] :
( ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(304,plain,
! [SV9: $i,SV24: $i,SV33: $i,SV46: $i,SV54: $i] :
( ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $true )
| ( ( ~ ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(305,plain,
! [SV72: $i,SV36: $i,SV13: $i] :
( ( ( ~ ( morphism @ SV13 @ SV36 @ SV72 ) )
= $true )
| ( ( element @ ( sK9_El1 @ SV36 @ SV13 ) @ SV36 )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(306,plain,
! [SV73: $i,SV36: $i,SV13: $i] :
( ( ( ~ ( morphism @ SV13 @ SV36 @ SV73 ) )
= $true )
| ( ( element @ ( sK10_SY81 @ SV36 @ SV13 ) @ SV36 )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(307,plain,
! [SV37: $i,SV14: $i,SV42: $i,SV49: $i,SV26: $i] :
( ( ( ! [SY236: $i] :
( ( ( apply @ SV26 @ SY236 )
!= ( zero @ SV49 ) )
| ~ ( element @ SY236 @ SV42 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SY236 )
| ~ ( element @ ( sK6_ElDom @ SY236 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(308,plain,
! [SV42: $i,SV49: $i,SV26: $i,SV37: $i,SV14: $i] :
( ( ( ~ ( ~ ! [SY237: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY237 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY237 )
= ( zero @ SV49 ) ) )
| ~ ! [SY221: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY221 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY221 @ SV42 ) ) ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(309,plain,
! [SV50: $i,SV16: $i,SV62: $i,SV58: $i,SV1: $i] :
( ( ( ( apply @ SV1 @ SV58 )
= ( apply @ SV1 @ SV62 ) )
= $false )
| ( ( element @ SV58 @ SV16 )
= $false )
| ( ( element @ SV62 @ SV16 )
= $false )
| ( ( SV58 = SV62 )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV16 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(310,plain,
! [SV59: $i,SV63: $i,SV39: $i,SV27: $i,SV17: $i,SV51: $i,SV44: $i,SV2: $i] :
( ( ( morphism @ SV2 @ SV44 @ SV51 )
= $false )
| ( ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
= $false )
| ( ( ~ ( morphism @ SV17 @ SV51 @ SV63 ) )
= $true )
| ( ( ~ ( morphism @ SV27 @ SV44 @ SV59 ) )
= $true )
| ( ( ~ ( morphism @ SV39 @ SV59 @ SV63 ) )
= $true )
| ( ( ! [SY227: $i] :
( ~ ( element @ SY227 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY227 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY227 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(311,plain,
! [SV40: $i,SV68: $i,SV32: $i,SV69: $i,SV23: $i,SV53: $i,SV45: $i,SV8: $i] :
( ( ( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SV69 ) )
= $true )
| ( ( ~ ( morphism @ SV32 @ SV45 @ SV68 ) )
= $true )
| ( ( ~ ( morphism @ SV40 @ SV68 @ SV69 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(312,plain,
! [SV40: $i,SV70: $i,SV32: $i,SV71: $i,SV23: $i,SV53: $i,SV45: $i,SV8: $i] :
( ( ( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SV71 )
| ~ ( morphism @ SV32 @ SV45 @ SV70 ) )
= $true )
| ( ( ~ ( morphism @ SV40 @ SV70 @ SV71 ) )
= $true )
| ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) )
= $false )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(313,plain,
! [SV24: $i,SV33: $i,SV46: $i,SV54: $i,SV74: $i,SV9: $i] :
( ( ( ( ( apply @ SV9 @ SV74 )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ SV74 @ SV33 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $false )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(314,plain,
! [SV24: $i,SV33: $i,SV46: $i,SV54: $i,SV9: $i] :
( ( ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(315,plain,
! [SV24: $i,SV33: $i,SV46: $i,SV54: $i,SV9: $i] :
( ( ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
| ~ ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(316,plain,
! [SV72: $i,SV36: $i,SV13: $i] :
( ( ( morphism @ SV13 @ SV36 @ SV72 )
= $false )
| ( ( element @ ( sK9_El1 @ SV36 @ SV13 ) @ SV36 )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(317,plain,
! [SV73: $i,SV36: $i,SV13: $i] :
( ( ( morphism @ SV13 @ SV36 @ SV73 )
= $false )
| ( ( element @ ( sK10_SY81 @ SV36 @ SV13 ) @ SV36 )
= $true )
| ( ( injection @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(318,plain,
! [SV37: $i,SV14: $i,SV42: $i,SV49: $i,SV75: $i,SV26: $i] :
( ( ( ( ( apply @ SV26 @ SV75 )
!= ( zero @ SV49 ) )
| ~ ( element @ SV75 @ SV42 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SV75 )
| ~ ( element @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(319,plain,
! [SV42: $i,SV49: $i,SV26: $i,SV37: $i,SV14: $i] :
( ( ( ~ ! [SY237: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY237 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY237 )
= ( zero @ SV49 ) ) )
| ~ ! [SY221: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY221 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY221 @ SV42 ) ) )
= $false )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(320,plain,
! [SV59: $i,SV44: $i,SV39: $i,SV27: $i,SV2: $i,SV63: $i,SV51: $i,SV17: $i] :
( ( ( morphism @ SV17 @ SV51 @ SV63 )
= $false )
| ( ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
= $false )
| ( ( morphism @ SV2 @ SV44 @ SV51 )
= $false )
| ( ( ~ ( morphism @ SV27 @ SV44 @ SV59 ) )
= $true )
| ( ( ~ ( morphism @ SV39 @ SV59 @ SV63 ) )
= $true )
| ( ( ! [SY227: $i] :
( ~ ( element @ SY227 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY227 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY227 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(321,plain,
! [SV40: $i,SV68: $i,SV32: $i,SV69: $i,SV23: $i,SV53: $i,SV45: $i,SV8: $i] :
( ( ( ~ ( morphism @ SV8 @ SV45 @ SV53 ) )
= $true )
| ( ( ~ ( morphism @ SV23 @ SV53 @ SV69 ) )
= $true )
| ( ( ~ ( morphism @ SV32 @ SV45 @ SV68 ) )
= $true )
| ( ( ~ ( morphism @ SV40 @ SV68 @ SV69 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(322,plain,
! [SV40: $i,SV70: $i,SV32: $i,SV71: $i,SV23: $i,SV53: $i,SV45: $i,SV8: $i] :
( ( ( ~ ( morphism @ SV8 @ SV45 @ SV53 )
| ~ ( morphism @ SV23 @ SV53 @ SV71 ) )
= $true )
| ( ( ~ ( morphism @ SV32 @ SV45 @ SV70 ) )
= $true )
| ( ( ~ ( morphism @ SV40 @ SV70 @ SV71 ) )
= $true )
| ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) )
= $false )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(323,plain,
! [SV24: $i,SV33: $i,SV46: $i,SV54: $i,SV74: $i,SV9: $i] :
( ( ( ( ( apply @ SV9 @ SV74 )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) ) )
= $true )
| ( ( ~ ( element @ SV74 @ SV33 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $false )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(324,plain,
! [SV24: $i,SV33: $i,SV46: $i,SV54: $i,SV9: $i] :
( ( ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) ) )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(325,plain,
! [SV9: $i,SV24: $i,SV33: $i,SV46: $i,SV54: $i] :
( ( ( ~ ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(326,plain,
! [SV24: $i,SV33: $i,SV46: $i,SV54: $i,SV9: $i] :
( ( ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
!= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(327,plain,
! [SV9: $i,SV24: $i,SV33: $i,SV46: $i,SV54: $i] :
( ( ( ~ ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(328,plain,
! [SV37: $i,SV14: $i,SV42: $i,SV49: $i,SV75: $i,SV26: $i] :
( ( ( ( ( apply @ SV26 @ SV75 )
!= ( zero @ SV49 ) )
| ~ ( element @ SV75 @ SV42 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SV75 )
| ~ ( element @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(329,plain,
! [SV42: $i,SV49: $i,SV26: $i,SV37: $i,SV14: $i] :
( ( ( ~ ! [SY237: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY237 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY237 )
= ( zero @ SV49 ) ) ) )
= $false )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(330,plain,
! [SV49: $i,SV26: $i,SV42: $i,SV37: $i,SV14: $i] :
( ( ( ~ ! [SY221: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY221 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY221 @ SV42 ) ) )
= $false )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(331,plain,
! [SV63: $i,SV39: $i,SV17: $i,SV51: $i,SV2: $i,SV59: $i,SV44: $i,SV27: $i] :
( ( ( morphism @ SV27 @ SV44 @ SV59 )
= $false )
| ( ( morphism @ SV2 @ SV44 @ SV51 )
= $false )
| ( ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
= $false )
| ( ( morphism @ SV17 @ SV51 @ SV63 )
= $false )
| ( ( ~ ( morphism @ SV39 @ SV59 @ SV63 ) )
= $true )
| ( ( ! [SY227: $i] :
( ~ ( element @ SY227 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY227 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY227 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(332,plain,
! [SV40: $i,SV68: $i,SV32: $i,SV69: $i,SV23: $i,SV53: $i,SV45: $i,SV8: $i] :
( ( ( morphism @ SV8 @ SV45 @ SV53 )
= $false )
| ( ( ~ ( morphism @ SV23 @ SV53 @ SV69 ) )
= $true )
| ( ( ~ ( morphism @ SV32 @ SV45 @ SV68 ) )
= $true )
| ( ( ~ ( morphism @ SV40 @ SV68 @ SV69 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(333,plain,
! [SV40: $i,SV70: $i,SV32: $i,SV71: $i,SV23: $i,SV53: $i,SV45: $i,SV8: $i] :
( ( ( ~ ( morphism @ SV8 @ SV45 @ SV53 ) )
= $true )
| ( ( ~ ( morphism @ SV23 @ SV53 @ SV71 ) )
= $true )
| ( ( ~ ( morphism @ SV32 @ SV45 @ SV70 ) )
= $true )
| ( ( ~ ( morphism @ SV40 @ SV70 @ SV71 ) )
= $true )
| ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) )
= $false )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(334,plain,
! [SV24: $i,SV33: $i,SV46: $i,SV54: $i,SV74: $i,SV9: $i] :
( ( ( ( apply @ SV9 @ SV74 )
= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= $false )
| ( ( ~ ( element @ SV74 @ SV33 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $false )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(335,plain,
! [SV24: $i,SV33: $i,SV46: $i,SV54: $i,SV9: $i] :
( ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(336,plain,
! [SV9: $i,SV24: $i,SV33: $i,SV46: $i,SV54: $i] :
( ( ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(337,plain,
! [SV24: $i,SV33: $i,SV46: $i,SV54: $i,SV9: $i] :
( ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(338,plain,
! [SV9: $i,SV24: $i,SV33: $i,SV46: $i,SV54: $i] :
( ( ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(339,plain,
! [SV37: $i,SV14: $i,SV42: $i,SV49: $i,SV75: $i,SV26: $i] :
( ( ( ( ( apply @ SV26 @ SV75 )
!= ( zero @ SV49 ) ) )
= $true )
| ( ( ~ ( element @ SV75 @ SV42 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SV75 )
| ~ ( element @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(340,plain,
! [SV42: $i,SV49: $i,SV26: $i,SV37: $i,SV14: $i] :
( ( ( ! [SY237: $i] :
( ! [SY203: $i] :
( ( ( apply @ SV14 @ SY203 )
!= SY237 )
| ~ ( element @ SY203 @ SV37 ) )
| ( ( apply @ SV26 @ SY237 )
= ( zero @ SV49 ) ) ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(341,plain,
! [SV49: $i,SV26: $i,SV42: $i,SV37: $i,SV14: $i] :
( ( ( ! [SY221: $i] :
( ! [SY205: $i] :
( ( ( apply @ SV14 @ SY205 )
!= SY221 )
| ~ ( element @ SY205 @ SV37 ) )
| ( element @ SY221 @ SV42 ) ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(342,plain,
! [SV44: $i,SV27: $i,SV2: $i,SV51: $i,SV17: $i,SV63: $i,SV59: $i,SV39: $i] :
( ( ( morphism @ SV39 @ SV59 @ SV63 )
= $false )
| ( ( morphism @ SV17 @ SV51 @ SV63 )
= $false )
| ( ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
= $false )
| ( ( morphism @ SV2 @ SV44 @ SV51 )
= $false )
| ( ( morphism @ SV27 @ SV44 @ SV59 )
= $false )
| ( ( ! [SY227: $i] :
( ~ ( element @ SY227 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SY227 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SY227 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(343,plain,
! [SV40: $i,SV68: $i,SV32: $i,SV45: $i,SV8: $i,SV69: $i,SV53: $i,SV23: $i] :
( ( ( morphism @ SV23 @ SV53 @ SV69 )
= $false )
| ( ( morphism @ SV8 @ SV45 @ SV53 )
= $false )
| ( ( ~ ( morphism @ SV32 @ SV45 @ SV68 ) )
= $true )
| ( ( ~ ( morphism @ SV40 @ SV68 @ SV69 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(344,plain,
! [SV40: $i,SV70: $i,SV32: $i,SV71: $i,SV23: $i,SV53: $i,SV45: $i,SV8: $i] :
( ( ( morphism @ SV8 @ SV45 @ SV53 )
= $false )
| ( ( ~ ( morphism @ SV23 @ SV53 @ SV71 ) )
= $true )
| ( ( ~ ( morphism @ SV32 @ SV45 @ SV70 ) )
= $true )
| ( ( ~ ( morphism @ SV40 @ SV70 @ SV71 ) )
= $true )
| ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) )
= $false )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(345,plain,
! [SV24: $i,SV46: $i,SV54: $i,SV9: $i,SV33: $i,SV74: $i] :
( ( ( element @ SV74 @ SV33 )
= $false )
| ( ( ( apply @ SV9 @ SV74 )
= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $false )
| ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 )
| ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(346,plain,
! [SV54: $i,SV24: $i,SV46: $i,SV33: $i,SV9: $i] :
( ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 ) )
= $true )
| ( ( ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $true )
| ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(347,plain,
! [SV54: $i,SV24: $i,SV46: $i,SV33: $i,SV9: $i] :
( ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 ) )
= $true )
| ( ( ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $true )
| ( ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(348,plain,
! [SV54: $i,SV24: $i,SV46: $i,SV33: $i,SV9: $i] :
( ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 ) )
= $true )
| ( ( ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $true )
| ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(349,plain,
! [SV54: $i,SV24: $i,SV46: $i,SV33: $i,SV9: $i] :
( ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 ) )
= $true )
| ( ( ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $true )
| ( ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(350,plain,
! [SV37: $i,SV14: $i,SV42: $i,SV49: $i,SV75: $i,SV26: $i] :
( ( ( ( apply @ SV26 @ SV75 )
= ( zero @ SV49 ) )
= $false )
| ( ( ~ ( element @ SV75 @ SV42 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SV75 )
| ~ ( element @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(351,plain,
! [SV42: $i,SV49: $i,SV26: $i,SV37: $i,SV76: $i,SV14: $i] :
( ( ( ! [SY253: $i] :
( ( ( apply @ SV14 @ SY253 )
!= SV76 )
| ~ ( element @ SY253 @ SV37 ) )
| ( ( apply @ SV26 @ SV76 )
= ( zero @ SV49 ) ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(352,plain,
! [SV49: $i,SV26: $i,SV42: $i,SV37: $i,SV77: $i,SV14: $i] :
( ( ( ! [SY254: $i] :
( ( ( apply @ SV14 @ SY254 )
!= SV77 )
| ~ ( element @ SY254 @ SV37 ) )
| ( element @ SV77 @ SV42 ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(353,plain,
! [SV63: $i,SV51: $i,SV59: $i,SV27: $i,SV39: $i,SV2: $i,SV17: $i,SV44: $i,SV78: $i] :
( ( ( ~ ( element @ SV78 @ SV44 )
| ( ( apply @ SV17 @ ( apply @ SV2 @ SV78 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SV78 ) ) ) )
= $true )
| ( ( morphism @ SV27 @ SV44 @ SV59 )
= $false )
| ( ( morphism @ SV2 @ SV44 @ SV51 )
= $false )
| ( ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
= $false )
| ( ( morphism @ SV17 @ SV51 @ SV63 )
= $false )
| ( ( morphism @ SV39 @ SV59 @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(354,plain,
! [SV40: $i,SV69: $i,SV23: $i,SV53: $i,SV8: $i,SV68: $i,SV45: $i,SV32: $i] :
( ( ( morphism @ SV32 @ SV45 @ SV68 )
= $false )
| ( ( morphism @ SV8 @ SV45 @ SV53 )
= $false )
| ( ( morphism @ SV23 @ SV53 @ SV69 )
= $false )
| ( ( ~ ( morphism @ SV40 @ SV68 @ SV69 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(355,plain,
! [SV40: $i,SV70: $i,SV32: $i,SV45: $i,SV8: $i,SV71: $i,SV53: $i,SV23: $i] :
( ( ( morphism @ SV23 @ SV53 @ SV71 )
= $false )
| ( ( morphism @ SV8 @ SV45 @ SV53 )
= $false )
| ( ( ~ ( morphism @ SV32 @ SV45 @ SV70 ) )
= $true )
| ( ( ~ ( morphism @ SV40 @ SV70 @ SV71 ) )
= $true )
| ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) )
= $false )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(356,plain,
! [SV74: $i,SV54: $i,SV24: $i,SV46: $i,SV33: $i,SV9: $i] :
( ( ( ~ ( morphism @ SV9 @ SV33 @ SV46 ) )
= $true )
| ( ( ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $false )
| ( ( ( apply @ SV9 @ SV74 )
= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= $false )
| ( ( element @ SV74 @ SV33 )
= $false )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(357,plain,
! [SV54: $i,SV24: $i,SV46: $i,SV33: $i,SV9: $i] :
( ( ( morphism @ SV9 @ SV33 @ SV46 )
= $false )
| ( ( ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $true )
| ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(358,plain,
! [SV54: $i,SV24: $i,SV46: $i,SV33: $i,SV9: $i] :
( ( ( morphism @ SV9 @ SV33 @ SV46 )
= $false )
| ( ( ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $true )
| ( ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(359,plain,
! [SV54: $i,SV24: $i,SV46: $i,SV33: $i,SV9: $i] :
( ( ( morphism @ SV9 @ SV33 @ SV46 )
= $false )
| ( ( ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $true )
| ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(360,plain,
! [SV54: $i,SV24: $i,SV46: $i,SV33: $i,SV9: $i] :
( ( ( morphism @ SV9 @ SV33 @ SV46 )
= $false )
| ( ( ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $true )
| ( ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(361,plain,
! [SV37: $i,SV14: $i,SV49: $i,SV26: $i,SV42: $i,SV75: $i] :
( ( ( element @ SV75 @ SV42 )
= $false )
| ( ( ( apply @ SV26 @ SV75 )
= ( zero @ SV49 ) )
= $false )
| ( ( ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SV75 )
| ~ ( element @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(362,plain,
! [SV42: $i,SV49: $i,SV26: $i,SV37: $i,SV76: $i,SV14: $i] :
( ( ( ! [SY253: $i] :
( ( ( apply @ SV14 @ SY253 )
!= SV76 )
| ~ ( element @ SY253 @ SV37 ) ) )
= $true )
| ( ( ( apply @ SV26 @ SV76 )
= ( zero @ SV49 ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(363,plain,
! [SV49: $i,SV26: $i,SV42: $i,SV37: $i,SV77: $i,SV14: $i] :
( ( ( ! [SY254: $i] :
( ( ( apply @ SV14 @ SY254 )
!= SV77 )
| ~ ( element @ SY254 @ SV37 ) ) )
= $true )
| ( ( element @ SV77 @ SV42 )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(364,plain,
! [SV63: $i,SV51: $i,SV59: $i,SV27: $i,SV39: $i,SV2: $i,SV17: $i,SV44: $i,SV78: $i] :
( ( ( ~ ( element @ SV78 @ SV44 ) )
= $true )
| ( ( ( apply @ SV17 @ ( apply @ SV2 @ SV78 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SV78 ) ) )
= $true )
| ( ( morphism @ SV27 @ SV44 @ SV59 )
= $false )
| ( ( morphism @ SV2 @ SV44 @ SV51 )
= $false )
| ( ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
= $false )
| ( ( morphism @ SV17 @ SV51 @ SV63 )
= $false )
| ( ( morphism @ SV39 @ SV59 @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(365,plain,
! [SV32: $i,SV45: $i,SV8: $i,SV53: $i,SV23: $i,SV69: $i,SV68: $i,SV40: $i] :
( ( ( morphism @ SV40 @ SV68 @ SV69 )
= $false )
| ( ( morphism @ SV23 @ SV53 @ SV69 )
= $false )
| ( ( morphism @ SV8 @ SV45 @ SV53 )
= $false )
| ( ( morphism @ SV32 @ SV45 @ SV68 )
= $false )
| ( ( element @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) @ SV45 )
= $true )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(366,plain,
! [SV40: $i,SV71: $i,SV23: $i,SV53: $i,SV8: $i,SV70: $i,SV45: $i,SV32: $i] :
( ( ( morphism @ SV32 @ SV45 @ SV70 )
= $false )
| ( ( morphism @ SV8 @ SV45 @ SV53 )
= $false )
| ( ( morphism @ SV23 @ SV53 @ SV71 )
= $false )
| ( ( ~ ( morphism @ SV40 @ SV70 @ SV71 ) )
= $true )
| ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) )
= $false )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(367,plain,
! [SV74: $i,SV54: $i,SV24: $i,SV46: $i,SV33: $i,SV9: $i] :
( ( ( morphism @ SV9 @ SV33 @ SV46 )
= $false )
| ( ( ~ ( morphism @ SV24 @ SV46 @ SV54 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $false )
| ( ( ( apply @ SV9 @ SV74 )
= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= $false )
| ( ( element @ SV74 @ SV33 )
= $false )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(368,plain,
! [SV33: $i,SV9: $i,SV54: $i,SV46: $i,SV24: $i] :
( ( ( morphism @ SV24 @ SV46 @ SV54 )
= $false )
| ( ( morphism @ SV9 @ SV33 @ SV46 )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $true )
| ( ( ( apply @ SV9 @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(369,plain,
! [SV33: $i,SV9: $i,SV54: $i,SV46: $i,SV24: $i] :
( ( ( morphism @ SV24 @ SV46 @ SV54 )
= $false )
| ( ( morphism @ SV9 @ SV33 @ SV46 )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $true )
| ( ( element @ ( sK5_SY78 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(370,plain,
! [SV33: $i,SV9: $i,SV54: $i,SV46: $i,SV24: $i] :
( ( ( morphism @ SV24 @ SV46 @ SV54 )
= $false )
| ( ( morphism @ SV9 @ SV33 @ SV46 )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $true )
| ( ( ( apply @ SV9 @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(371,plain,
! [SV33: $i,SV9: $i,SV54: $i,SV46: $i,SV24: $i] :
( ( ( morphism @ SV24 @ SV46 @ SV54 )
= $false )
| ( ( morphism @ SV9 @ SV33 @ SV46 )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $true )
| ( ( element @ ( sK4_SY79 @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV33 )
= $true )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(372,plain,
! [SV26: $i,SV37: $i,SV42: $i,SV49: $i,SV75: $i,SV14: $i] :
( ( ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SV75 )
| ~ ( element @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) )
= $false )
| ( ( ( apply @ SV26 @ SV75 )
= ( zero @ SV49 ) )
= $false )
| ( ( element @ SV75 @ SV42 )
= $false )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(373,plain,
! [SV42: $i,SV49: $i,SV26: $i,SV37: $i,SV76: $i,SV79: $i,SV14: $i] :
( ( ( ( ( apply @ SV14 @ SV79 )
!= SV76 )
| ~ ( element @ SV79 @ SV37 ) )
= $true )
| ( ( ( apply @ SV26 @ SV76 )
= ( zero @ SV49 ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(374,plain,
! [SV49: $i,SV26: $i,SV42: $i,SV37: $i,SV77: $i,SV80: $i,SV14: $i] :
( ( ( ( ( apply @ SV14 @ SV80 )
!= SV77 )
| ~ ( element @ SV80 @ SV37 ) )
= $true )
| ( ( element @ SV77 @ SV42 )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(375,plain,
! [SV63: $i,SV51: $i,SV59: $i,SV27: $i,SV39: $i,SV2: $i,SV17: $i,SV44: $i,SV78: $i] :
( ( ( element @ SV78 @ SV44 )
= $false )
| ( ( ( apply @ SV17 @ ( apply @ SV2 @ SV78 ) )
= ( apply @ SV39 @ ( apply @ SV27 @ SV78 ) ) )
= $true )
| ( ( morphism @ SV27 @ SV44 @ SV59 )
= $false )
| ( ( morphism @ SV2 @ SV44 @ SV51 )
= $false )
| ( ( commute @ SV2 @ SV17 @ SV27 @ SV39 )
= $false )
| ( ( morphism @ SV17 @ SV51 @ SV63 )
= $false )
| ( ( morphism @ SV39 @ SV59 @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(376,plain,
! [SV32: $i,SV45: $i,SV8: $i,SV53: $i,SV23: $i,SV71: $i,SV70: $i,SV40: $i] :
( ( ( morphism @ SV40 @ SV70 @ SV71 )
= $false )
| ( ( morphism @ SV23 @ SV53 @ SV71 )
= $false )
| ( ( morphism @ SV8 @ SV45 @ SV53 )
= $false )
| ( ( morphism @ SV32 @ SV45 @ SV70 )
= $false )
| ( ( ( apply @ SV23 @ ( apply @ SV8 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) )
= ( apply @ SV40 @ ( apply @ SV32 @ ( sK2_ElDom @ SV53 @ SV45 @ SV40 @ SV32 @ SV23 @ SV8 ) ) ) )
= $false )
| ( ( commute @ SV8 @ SV23 @ SV32 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(377,plain,
! [SV74: $i,SV33: $i,SV9: $i,SV54: $i,SV46: $i,SV24: $i] :
( ( ( morphism @ SV24 @ SV46 @ SV54 )
= $false )
| ( ( morphism @ SV9 @ SV33 @ SV46 )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) @ SV46 )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= ( zero @ SV54 ) )
= $false )
| ( ( ( apply @ SV9 @ SV74 )
= ( sK3_ElCodDom @ SV54 @ SV46 @ SV33 @ SV24 @ SV9 ) )
= $false )
| ( ( element @ SV74 @ SV33 )
= $false )
| ( ( exact @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(378,plain,
! [SV26: $i,SV37: $i,SV42: $i,SV49: $i,SV75: $i,SV14: $i] :
( ( ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
!= SV75 ) )
= $false )
| ( ( ( apply @ SV26 @ SV75 )
= ( zero @ SV49 ) )
= $false )
| ( ( element @ SV75 @ SV42 )
= $false )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(379,plain,
! [SV14: $i,SV26: $i,SV37: $i,SV42: $i,SV49: $i,SV75: $i] :
( ( ( ~ ( element @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 ) )
= $false )
| ( ( ( apply @ SV26 @ SV75 )
= ( zero @ SV49 ) )
= $false )
| ( ( element @ SV75 @ SV42 )
= $false )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(380,plain,
! [SV42: $i,SV49: $i,SV26: $i,SV37: $i,SV76: $i,SV79: $i,SV14: $i] :
( ( ( ( ( apply @ SV14 @ SV79 )
!= SV76 ) )
= $true )
| ( ( ~ ( element @ SV79 @ SV37 ) )
= $true )
| ( ( ( apply @ SV26 @ SV76 )
= ( zero @ SV49 ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(381,plain,
! [SV49: $i,SV26: $i,SV42: $i,SV37: $i,SV77: $i,SV80: $i,SV14: $i] :
( ( ( ( ( apply @ SV14 @ SV80 )
!= SV77 ) )
= $true )
| ( ( ~ ( element @ SV80 @ SV37 ) )
= $true )
| ( ( element @ SV77 @ SV42 )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(382,plain,
! [SV26: $i,SV37: $i,SV42: $i,SV49: $i,SV75: $i,SV14: $i] :
( ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) )
= SV75 )
= $true )
| ( ( ( apply @ SV26 @ SV75 )
= ( zero @ SV49 ) )
= $false )
| ( ( element @ SV75 @ SV42 )
= $false )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(383,plain,
! [SV14: $i,SV26: $i,SV37: $i,SV42: $i,SV49: $i,SV75: $i] :
( ( ( element @ ( sK6_ElDom @ SV75 @ SV49 @ SV42 @ SV37 @ SV26 @ SV14 ) @ SV37 )
= $true )
| ( ( ( apply @ SV26 @ SV75 )
= ( zero @ SV49 ) )
= $false )
| ( ( element @ SV75 @ SV42 )
= $false )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(384,plain,
! [SV42: $i,SV49: $i,SV26: $i,SV37: $i,SV76: $i,SV79: $i,SV14: $i] :
( ( ( ( apply @ SV14 @ SV79 )
= SV76 )
= $false )
| ( ( ~ ( element @ SV79 @ SV37 ) )
= $true )
| ( ( ( apply @ SV26 @ SV76 )
= ( zero @ SV49 ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(385,plain,
! [SV49: $i,SV26: $i,SV42: $i,SV37: $i,SV77: $i,SV80: $i,SV14: $i] :
( ( ( ( apply @ SV14 @ SV80 )
= SV77 )
= $false )
| ( ( ~ ( element @ SV80 @ SV37 ) )
= $true )
| ( ( element @ SV77 @ SV42 )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(386,plain,
! [SV42: $i,SV49: $i,SV26: $i,SV76: $i,SV14: $i,SV37: $i,SV79: $i] :
( ( ( element @ SV79 @ SV37 )
= $false )
| ( ( ( apply @ SV14 @ SV79 )
= SV76 )
= $false )
| ( ( ( apply @ SV26 @ SV76 )
= ( zero @ SV49 ) )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(387,plain,
! [SV49: $i,SV26: $i,SV42: $i,SV77: $i,SV14: $i,SV37: $i,SV80: $i] :
( ( ( element @ SV80 @ SV37 )
= $false )
| ( ( ( apply @ SV14 @ SV80 )
= SV77 )
= $false )
| ( ( element @ SV77 @ SV42 )
= $true )
| ( ( morphism @ SV14 @ SV37 @ SV42 )
= $false )
| ( ( exact @ SV14 @ SV26 )
= $false )
| ( ( morphism @ SV26 @ SV42 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(388,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[57,387,386,383,382,377,376,375,371,370,369,368,365,317,316,309,297,292,291,281,276,275,269,261,253,248,243,231,209,185,184,144,137,126]) ).
thf(389,plain,
( ( morphism @ x @ any1 @ any2 )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(390,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i,Cod: $i] :
( ~ ( morphism @ Morphism @ Dom @ Cod )
| ! [El: $i] :
( ~ ( element @ El @ Dom )
| ( element @ ( apply @ Morphism @ El ) @ Cod ) ) )
& ! [Dom: $i,Cod: $i] :
( ~ ( morphism @ Morphism @ Dom @ Cod )
| ( ( apply @ Morphism @ ( zero @ Dom ) )
= ( zero @ Cod ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(391,plain,
( ( ! [Morphism: $i,Dom: $i] :
( ~ ( injection @ Morphism )
| ! [Cod: $i] :
~ ( morphism @ Morphism @ Dom @ Cod )
| ! [El1: $i,El2: $i] :
( ~ ( element @ El1 @ Dom )
| ~ ( element @ El2 @ Dom )
| ( ( apply @ Morphism @ El1 )
!= ( apply @ Morphism @ El2 ) )
| ( El1 = El2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(392,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i] :
( ( ( element @ ( sK9_El1 @ Dom @ Morphism ) @ Dom )
& ( element @ ( sK10_SY81 @ Dom @ Morphism ) @ Dom )
& ( ( apply @ Morphism @ ( sK9_El1 @ Dom @ Morphism ) )
= ( apply @ Morphism @ ( sK10_SY81 @ Dom @ Morphism ) ) )
& ( ( sK9_El1 @ Dom @ Morphism )
!= ( sK10_SY81 @ Dom @ Morphism ) ) )
| ! [Cod: $i] :
~ ( morphism @ Morphism @ Dom @ Cod ) )
| ( injection @ Morphism ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(393,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ~ ( morphism @ Morphism @ Dom @ Cod )
| ~ ( surjection @ Morphism )
| ! [ElCod: $i] :
( ~ ( element @ ElCod @ Cod )
| ( ( ( apply @ Morphism @ ( sK8_ElDom @ ElCod @ Cod @ Dom @ Morphism ) )
= ElCod )
& ( element @ ( sK8_ElDom @ ElCod @ Cod @ Dom @ Morphism ) @ Dom ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(394,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i,Cod: $i] :
( ( ( element @ ( sK7_ElCod @ Cod @ Dom @ Morphism ) @ Cod )
& ! [SY80: $i] :
( ( ( apply @ Morphism @ SY80 )
!= ( sK7_ElCod @ Cod @ Dom @ Morphism ) )
| ~ ( element @ SY80 @ Dom ) ) )
| ~ ( morphism @ Morphism @ Dom @ Cod ) )
| ( surjection @ Morphism ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(395,plain,
( ( ! [Morphism1: $i,Morphism2: $i,Dom: $i,CodDom: $i,Cod: $i] :
( ~ ( exact @ Morphism1 @ Morphism2 )
| ~ ( morphism @ Morphism1 @ Dom @ CodDom )
| ~ ( morphism @ Morphism2 @ CodDom @ Cod )
| ( ! [ElCodDom: $i] :
( ( ( apply @ Morphism2 @ ElCodDom )
!= ( zero @ Cod ) )
| ~ ( element @ ElCodDom @ CodDom )
| ( ( ( apply @ Morphism1 @ ( sK6_ElDom @ ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ElCodDom )
& ( element @ ( sK6_ElDom @ ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ Dom ) ) )
& ! [ElCodDom: $i] :
( ! [ElDom: $i] :
( ( ( apply @ Morphism1 @ ElDom )
!= ElCodDom )
| ~ ( element @ ElDom @ Dom ) )
| ( ( apply @ Morphism2 @ ElCodDom )
= ( zero @ Cod ) ) )
& ! [ElCodDom: $i] :
( ! [ElDom: $i] :
( ( ( apply @ Morphism1 @ ElDom )
!= ElCodDom )
| ~ ( element @ ElDom @ Dom ) )
| ( element @ ElCodDom @ CodDom ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(396,plain,
( ( ! [Morphism1: $i,Morphism2: $i,Dom: $i] :
( ! [CodDom: $i,Cod: $i] :
( ( ( ( ( apply @ Morphism2 @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
!= ( zero @ Cod ) )
| ~ ( element @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ CodDom )
| ! [SY77: $i] :
( ( ( apply @ Morphism1 @ SY77 )
!= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
| ~ ( element @ SY77 @ Dom ) ) )
& ( ( ( apply @ Morphism2 @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( zero @ Cod ) )
| ( ( ( apply @ Morphism1 @ ( sK5_SY78 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
& ( element @ ( sK5_SY78 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ Dom ) ) )
& ( ( element @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ CodDom )
| ( ( ( apply @ Morphism1 @ ( sK4_SY79 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
& ( element @ ( sK4_SY79 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ Dom ) ) ) )
| ~ ( morphism @ Morphism1 @ Dom @ CodDom )
| ~ ( morphism @ Morphism2 @ CodDom @ Cod ) )
| ( exact @ Morphism1 @ Morphism2 ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(397,plain,
( ( ! [M1: $i,M2: $i,M3: $i,M4: $i,Dom: $i,DomCod1: $i] :
( ! [DomCod2: $i,Cod: $i] :
( ~ ( commute @ M1 @ M2 @ M3 @ M4 )
| ~ ( morphism @ M1 @ Dom @ DomCod1 )
| ~ ( morphism @ M2 @ DomCod1 @ Cod )
| ~ ( morphism @ M3 @ Dom @ DomCod2 )
| ~ ( morphism @ M4 @ DomCod2 @ Cod ) )
| ! [ElDom: $i] :
( ~ ( element @ ElDom @ Dom )
| ( ( apply @ M2 @ ( apply @ M1 @ ElDom ) )
= ( apply @ M4 @ ( apply @ M3 @ ElDom ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(398,plain,
( ( ! [M1: $i,M2: $i,M3: $i,M4: $i,Dom: $i,DomCod1: $i] :
( ( ( element @ ( sK2_ElDom @ DomCod1 @ Dom @ M4 @ M3 @ M2 @ M1 ) @ Dom )
& ( ( apply @ M2 @ ( apply @ M1 @ ( sK2_ElDom @ DomCod1 @ Dom @ M4 @ M3 @ M2 @ M1 ) ) )
!= ( apply @ M4 @ ( apply @ M3 @ ( sK2_ElDom @ DomCod1 @ Dom @ M4 @ M3 @ M2 @ M1 ) ) ) ) )
| ! [DomCod2: $i,Cod: $i] :
( ~ ( morphism @ M1 @ Dom @ DomCod1 )
| ~ ( morphism @ M2 @ DomCod1 @ Cod )
| ~ ( morphism @ M3 @ Dom @ DomCod2 )
| ~ ( morphism @ M4 @ DomCod2 @ Cod ) )
| ( commute @ M1 @ M2 @ M3 @ M4 ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(399,plain,
( ( ! [Dom: $i,El1: $i,El2: $i] :
( ~ ( element @ El1 @ Dom )
| ~ ( element @ El2 @ Dom )
| ( element @ ( subtract @ Dom @ El1 @ El2 ) @ Dom ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(400,plain,
( ( ! [Dom: $i,El: $i] :
( ~ ( element @ El @ Dom )
| ( ( subtract @ Dom @ El @ El )
= ( zero @ Dom ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(401,plain,
( ( ! [Dom: $i,El1: $i,El2: $i] :
( ~ ( element @ El1 @ Dom )
| ~ ( element @ El2 @ Dom )
| ( ( subtract @ Dom @ El1 @ ( subtract @ Dom @ El1 @ El2 ) )
= El2 ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(402,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ~ ( morphism @ Morphism @ Dom @ Cod )
| ! [El1: $i,El2: $i] :
( ~ ( element @ El1 @ Dom )
| ~ ( element @ El2 @ Dom )
| ( ( apply @ Morphism @ ( subtract @ Dom @ El1 @ El2 ) )
= ( subtract @ Cod @ ( apply @ Morphism @ El1 ) @ ( apply @ Morphism @ El2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(403,plain,
( ( ! [Morphism: $i,Dom: $i,Cod: $i] :
( ~ ( injection_2 @ Morphism )
| ~ ( morphism @ Morphism @ Dom @ Cod )
| ! [El: $i] :
( ( ( apply @ Morphism @ El )
!= ( zero @ Cod ) )
| ~ ( element @ El @ Dom )
| ( El
= ( zero @ Dom ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(404,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i,Cod: $i] :
( ( ( ( apply @ Morphism @ ( sK1_El @ Cod @ Dom @ Morphism ) )
= ( zero @ Cod ) )
& ( element @ ( sK1_El @ Cod @ Dom @ Morphism ) @ Dom )
& ( ( sK1_El @ Cod @ Dom @ Morphism )
!= ( zero @ Dom ) ) )
| ~ ( morphism @ Morphism @ Dom @ Cod ) )
| ( injection_2 @ Morphism ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(405,plain,
( ( ( injection_2 @ x )
& ~ ( injection @ x ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(406,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( morphism @ SX0 @ SX1 @ SX2 )
| ~ ( surjection @ SX0 )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ SX2 )
| ~ ( ( ( apply @ SX0 @ ( sK8_ElDom @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= SX3 )
| ~ ( element @ ( sK8_ElDom @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(407,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ! [SX3: $i,SX4: $i] :
( ~ ( ~ ( ( ( apply @ SX1 @ ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( zero @ SX4 ) )
| ~ ( element @ ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ! [SX5: $i] :
( ( ( apply @ SX0 @ SX5 )
!= ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( element @ SX5 @ SX2 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SX1 @ ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
= ( zero @ SX4 ) )
| ~ ( ( ( apply @ SX0 @ ( sK5_SY78 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( element @ ( sK5_SY78 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ~ ( ( ( apply @ SX0 @ ( sK4_SY79 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( element @ ( sK4_SY79 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) ) )
| ~ ( morphism @ SX0 @ SX2 @ SX3 )
| ~ ( morphism @ SX1 @ SX3 @ SX4 ) )
| ( exact @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(408,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( element @ ( sK7_ElCod @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ! [SX3: $i] :
( ( ( apply @ SX0 @ SX3 )
!= ( sK7_ElCod @ SX2 @ SX1 @ SX0 ) )
| ~ ( element @ SX3 @ SX1 ) ) )
| ~ ( morphism @ SX0 @ SX1 @ SX2 ) )
| ( surjection @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(409,plain,
( ( ~ ( ~ ( injection_2 @ x )
| ~ ~ ( injection @ x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(410,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( morphism @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ SX1 )
| ( element @ ( apply @ SX0 @ SX3 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( morphism @ SX0 @ SX1 @ SX2 )
| ( ( apply @ SX0 @ ( zero @ SX1 ) )
= ( zero @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(411,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 )
| ~ ( ( ( apply @ SX1 @ ( apply @ SX0 @ ( sK2_ElDom @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
!= ( apply @ SX3 @ ( apply @ SX2 @ ( sK2_ElDom @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ! [SX6: $i,SX7: $i] :
( ~ ( morphism @ SX0 @ SX4 @ SX5 )
| ~ ( morphism @ SX1 @ SX5 @ SX7 )
| ~ ( morphism @ SX2 @ SX4 @ SX6 )
| ~ ( morphism @ SX3 @ SX6 @ SX7 ) )
| ( commute @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(412,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( exact @ SX0 @ SX1 )
| ~ ( morphism @ SX0 @ SX2 @ SX3 )
| ~ ( morphism @ SX1 @ SX3 @ SX4 )
| ~ ( ~ ! [SX5: $i] :
( ( ( apply @ SX1 @ SX5 )
!= ( zero @ SX4 ) )
| ~ ( element @ SX5 @ SX3 )
| ~ ( ( ( apply @ SX0 @ ( sK6_ElDom @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= SX5 )
| ~ ( element @ ( sK6_ElDom @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ~ ( ~ ! [SX5: $i] :
( ! [SX6: $i] :
( ( ( apply @ SX0 @ SX6 )
!= SX5 )
| ~ ( element @ SX6 @ SX2 ) )
| ( ( apply @ SX1 @ SX5 )
= ( zero @ SX4 ) ) )
| ~ ! [SX5: $i] :
( ! [SX6: $i] :
( ( ( apply @ SX0 @ SX6 )
!= SX5 )
| ~ ( element @ SX6 @ SX2 ) )
| ( element @ SX5 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(413,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ( ( apply @ SX0 @ ( sK1_El @ SX2 @ SX1 @ SX0 ) )
!= ( zero @ SX2 ) )
| ~ ( element @ ( sK1_El @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK1_El @ SX2 @ SX1 @ SX0 )
!= ( zero @ SX1 ) ) ) )
| ~ ( morphism @ SX0 @ SX1 @ SX2 ) )
| ( injection_2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(414,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SX1 @ SX0 ) @ SX1 )
| ~ ( element @ ( sK10_SY81 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( apply @ SX0 @ ( sK9_El1 @ SX1 @ SX0 ) )
!= ( apply @ SX0 @ ( sK10_SY81 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK9_El1 @ SX1 @ SX0 )
!= ( sK10_SY81 @ SX1 @ SX0 ) ) ) )
| ! [SX2: $i] :
~ ( morphism @ SX0 @ SX1 @ SX2 ) )
| ( injection @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(415,plain,
! [SV81: $i] :
( ( ! [SY255: $i] :
( ~ ( injection @ SV81 )
| ! [SY256: $i] :
~ ( morphism @ SV81 @ SY255 @ SY256 )
| ! [SY257: $i,SY258: $i] :
( ~ ( element @ SY257 @ SY255 )
| ~ ( element @ SY258 @ SY255 )
| ( ( apply @ SV81 @ SY257 )
!= ( apply @ SV81 @ SY258 ) )
| ( SY257 = SY258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(416,plain,
! [SV82: $i] :
( ( ! [SY259: $i,SY260: $i,SY261: $i,SY262: $i,SY263: $i] :
( ! [SY264: $i,SY265: $i] :
( ~ ( commute @ SV82 @ SY259 @ SY260 @ SY261 )
| ~ ( morphism @ SV82 @ SY262 @ SY263 )
| ~ ( morphism @ SY259 @ SY263 @ SY265 )
| ~ ( morphism @ SY260 @ SY262 @ SY264 )
| ~ ( morphism @ SY261 @ SY264 @ SY265 ) )
| ! [SY266: $i] :
( ~ ( element @ SY266 @ SY262 )
| ( ( apply @ SY259 @ ( apply @ SV82 @ SY266 ) )
= ( apply @ SY261 @ ( apply @ SY260 @ SY266 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(417,plain,
! [SV83: $i] :
( ( ! [SY267: $i,SY268: $i] :
( ~ ( element @ SY267 @ SV83 )
| ~ ( element @ SY268 @ SV83 )
| ( element @ ( subtract @ SV83 @ SY267 @ SY268 ) @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(418,plain,
! [SV84: $i] :
( ( ! [SY269: $i] :
( ~ ( element @ SY269 @ SV84 )
| ( ( subtract @ SV84 @ SY269 @ SY269 )
= ( zero @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(419,plain,
! [SV85: $i] :
( ( ! [SY270: $i,SY271: $i] :
( ~ ( element @ SY270 @ SV85 )
| ~ ( element @ SY271 @ SV85 )
| ( ( subtract @ SV85 @ SY270 @ ( subtract @ SV85 @ SY270 @ SY271 ) )
= SY271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(420,plain,
! [SV86: $i] :
( ( ! [SY272: $i,SY273: $i] :
( ~ ( morphism @ SV86 @ SY272 @ SY273 )
| ! [SY274: $i,SY275: $i] :
( ~ ( element @ SY274 @ SY272 )
| ~ ( element @ SY275 @ SY272 )
| ( ( apply @ SV86 @ ( subtract @ SY272 @ SY274 @ SY275 ) )
= ( subtract @ SY273 @ ( apply @ SV86 @ SY274 ) @ ( apply @ SV86 @ SY275 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(421,plain,
! [SV87: $i] :
( ( ! [SY276: $i,SY277: $i] :
( ~ ( injection_2 @ SV87 )
| ~ ( morphism @ SV87 @ SY276 @ SY277 )
| ! [SY278: $i] :
( ( ( apply @ SV87 @ SY278 )
!= ( zero @ SY277 ) )
| ~ ( element @ SY278 @ SY276 )
| ( SY278
= ( zero @ SY276 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(422,plain,
! [SV88: $i] :
( ( ! [SY279: $i,SY280: $i] :
( ~ ( morphism @ SV88 @ SY279 @ SY280 )
| ~ ( surjection @ SV88 )
| ! [SY281: $i] :
( ~ ( element @ SY281 @ SY280 )
| ~ ( ( ( apply @ SV88 @ ( sK8_ElDom @ SY281 @ SY280 @ SY279 @ SV88 ) )
!= SY281 )
| ~ ( element @ ( sK8_ElDom @ SY281 @ SY280 @ SY279 @ SV88 ) @ SY279 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(423,plain,
! [SV89: $i] :
( ( ! [SY282: $i,SY283: $i] :
( ! [SY284: $i,SY285: $i] :
( ~ ( ~ ( ( ( apply @ SY282 @ ( sK3_ElCodDom @ SY285 @ SY284 @ SY283 @ SY282 @ SV89 ) )
!= ( zero @ SY285 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY285 @ SY284 @ SY283 @ SY282 @ SV89 ) @ SY284 )
| ! [SY286: $i] :
( ( ( apply @ SV89 @ SY286 )
!= ( sK3_ElCodDom @ SY285 @ SY284 @ SY283 @ SY282 @ SV89 ) )
| ~ ( element @ SY286 @ SY283 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SY282 @ ( sK3_ElCodDom @ SY285 @ SY284 @ SY283 @ SY282 @ SV89 ) )
= ( zero @ SY285 ) )
| ~ ( ( ( apply @ SV89 @ ( sK5_SY78 @ SY285 @ SY284 @ SY283 @ SY282 @ SV89 ) )
!= ( sK3_ElCodDom @ SY285 @ SY284 @ SY283 @ SY282 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SY285 @ SY284 @ SY283 @ SY282 @ SV89 ) @ SY283 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY285 @ SY284 @ SY283 @ SY282 @ SV89 ) @ SY284 )
| ~ ( ( ( apply @ SV89 @ ( sK4_SY79 @ SY285 @ SY284 @ SY283 @ SY282 @ SV89 ) )
!= ( sK3_ElCodDom @ SY285 @ SY284 @ SY283 @ SY282 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SY285 @ SY284 @ SY283 @ SY282 @ SV89 ) @ SY283 ) ) ) ) )
| ~ ( morphism @ SV89 @ SY283 @ SY284 )
| ~ ( morphism @ SY282 @ SY284 @ SY285 ) )
| ( exact @ SV89 @ SY282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(424,plain,
! [SV90: $i] :
( ( ! [SY287: $i,SY288: $i] :
( ~ ( ~ ( element @ ( sK7_ElCod @ SY288 @ SY287 @ SV90 ) @ SY288 )
| ~ ! [SY289: $i] :
( ( ( apply @ SV90 @ SY289 )
!= ( sK7_ElCod @ SY288 @ SY287 @ SV90 ) )
| ~ ( element @ SY289 @ SY287 ) ) )
| ~ ( morphism @ SV90 @ SY287 @ SY288 ) )
| ( surjection @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(425,plain,
( ( ~ ( injection_2 @ x )
| ~ ~ ( injection @ x ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(426,plain,
! [SV91: $i] :
( ( ~ ( ~ ! [SY290: $i,SY291: $i] :
( ~ ( morphism @ SV91 @ SY290 @ SY291 )
| ! [SY292: $i] :
( ~ ( element @ SY292 @ SY290 )
| ( element @ ( apply @ SV91 @ SY292 ) @ SY291 ) ) )
| ~ ! [SY293: $i,SY294: $i] :
( ~ ( morphism @ SV91 @ SY293 @ SY294 )
| ( ( apply @ SV91 @ ( zero @ SY293 ) )
= ( zero @ SY294 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(427,plain,
! [SV92: $i] :
( ( ! [SY295: $i,SY296: $i,SY297: $i,SY298: $i,SY299: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY299 @ SY298 @ SY297 @ SY296 @ SY295 @ SV92 ) @ SY298 )
| ~ ( ( ( apply @ SY295 @ ( apply @ SV92 @ ( sK2_ElDom @ SY299 @ SY298 @ SY297 @ SY296 @ SY295 @ SV92 ) ) )
!= ( apply @ SY297 @ ( apply @ SY296 @ ( sK2_ElDom @ SY299 @ SY298 @ SY297 @ SY296 @ SY295 @ SV92 ) ) ) ) ) )
| ! [SY300: $i,SY301: $i] :
( ~ ( morphism @ SV92 @ SY298 @ SY299 )
| ~ ( morphism @ SY295 @ SY299 @ SY301 )
| ~ ( morphism @ SY296 @ SY298 @ SY300 )
| ~ ( morphism @ SY297 @ SY300 @ SY301 ) )
| ( commute @ SV92 @ SY295 @ SY296 @ SY297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(428,plain,
! [SV93: $i] :
( ( ! [SY302: $i,SY303: $i,SY304: $i,SY305: $i] :
( ~ ( exact @ SV93 @ SY302 )
| ~ ( morphism @ SV93 @ SY303 @ SY304 )
| ~ ( morphism @ SY302 @ SY304 @ SY305 )
| ~ ( ~ ! [SY306: $i] :
( ( ( apply @ SY302 @ SY306 )
!= ( zero @ SY305 ) )
| ~ ( element @ SY306 @ SY304 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SY306 @ SY305 @ SY304 @ SY303 @ SY302 @ SV93 ) )
!= SY306 )
| ~ ( element @ ( sK6_ElDom @ SY306 @ SY305 @ SY304 @ SY303 @ SY302 @ SV93 ) @ SY303 ) ) )
| ~ ~ ( ~ ! [SY307: $i] :
( ! [SY308: $i] :
( ( ( apply @ SV93 @ SY308 )
!= SY307 )
| ~ ( element @ SY308 @ SY303 ) )
| ( ( apply @ SY302 @ SY307 )
= ( zero @ SY305 ) ) )
| ~ ! [SY309: $i] :
( ! [SY310: $i] :
( ( ( apply @ SV93 @ SY310 )
!= SY309 )
| ~ ( element @ SY310 @ SY303 ) )
| ( element @ SY309 @ SY304 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(429,plain,
! [SV94: $i] :
( ( ! [SY311: $i,SY312: $i] :
( ~ ( ~ ~ ( ( ( apply @ SV94 @ ( sK1_El @ SY312 @ SY311 @ SV94 ) )
!= ( zero @ SY312 ) )
| ~ ( element @ ( sK1_El @ SY312 @ SY311 @ SV94 ) @ SY311 ) )
| ~ ( ( ( sK1_El @ SY312 @ SY311 @ SV94 )
!= ( zero @ SY311 ) ) ) )
| ~ ( morphism @ SV94 @ SY311 @ SY312 ) )
| ( injection_2 @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(430,plain,
! [SV95: $i] :
( ( ! [SY313: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SY313 @ SV95 ) @ SY313 )
| ~ ( element @ ( sK10_SY81 @ SY313 @ SV95 ) @ SY313 ) )
| ( ( apply @ SV95 @ ( sK9_El1 @ SY313 @ SV95 ) )
!= ( apply @ SV95 @ ( sK10_SY81 @ SY313 @ SV95 ) ) ) )
| ~ ( ( ( sK9_El1 @ SY313 @ SV95 )
!= ( sK10_SY81 @ SY313 @ SV95 ) ) ) )
| ! [SY314: $i] :
~ ( morphism @ SV95 @ SY313 @ SY314 ) )
| ( injection @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(431,plain,
! [SV96: $i,SV81: $i] :
( ( ~ ( injection @ SV81 )
| ! [SY315: $i] :
~ ( morphism @ SV81 @ SV96 @ SY315 )
| ! [SY316: $i,SY317: $i] :
( ~ ( element @ SY316 @ SV96 )
| ~ ( element @ SY317 @ SV96 )
| ( ( apply @ SV81 @ SY316 )
!= ( apply @ SV81 @ SY317 ) )
| ( SY316 = SY317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(432,plain,
! [SV97: $i,SV82: $i] :
( ( ! [SY318: $i,SY319: $i,SY320: $i,SY321: $i] :
( ! [SY322: $i,SY323: $i] :
( ~ ( commute @ SV82 @ SV97 @ SY318 @ SY319 )
| ~ ( morphism @ SV82 @ SY320 @ SY321 )
| ~ ( morphism @ SV97 @ SY321 @ SY323 )
| ~ ( morphism @ SY318 @ SY320 @ SY322 )
| ~ ( morphism @ SY319 @ SY322 @ SY323 ) )
| ! [SY324: $i] :
( ~ ( element @ SY324 @ SY320 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY324 ) )
= ( apply @ SY319 @ ( apply @ SY318 @ SY324 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(433,plain,
! [SV83: $i,SV98: $i] :
( ( ! [SY325: $i] :
( ~ ( element @ SV98 @ SV83 )
| ~ ( element @ SY325 @ SV83 )
| ( element @ ( subtract @ SV83 @ SV98 @ SY325 ) @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(434,plain,
! [SV84: $i,SV99: $i] :
( ( ~ ( element @ SV99 @ SV84 )
| ( ( subtract @ SV84 @ SV99 @ SV99 )
= ( zero @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(435,plain,
! [SV85: $i,SV100: $i] :
( ( ! [SY326: $i] :
( ~ ( element @ SV100 @ SV85 )
| ~ ( element @ SY326 @ SV85 )
| ( ( subtract @ SV85 @ SV100 @ ( subtract @ SV85 @ SV100 @ SY326 ) )
= SY326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(436,plain,
! [SV101: $i,SV86: $i] :
( ( ! [SY327: $i] :
( ~ ( morphism @ SV86 @ SV101 @ SY327 )
| ! [SY328: $i,SY329: $i] :
( ~ ( element @ SY328 @ SV101 )
| ~ ( element @ SY329 @ SV101 )
| ( ( apply @ SV86 @ ( subtract @ SV101 @ SY328 @ SY329 ) )
= ( subtract @ SY327 @ ( apply @ SV86 @ SY328 ) @ ( apply @ SV86 @ SY329 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(437,plain,
! [SV102: $i,SV87: $i] :
( ( ! [SY330: $i] :
( ~ ( injection_2 @ SV87 )
| ~ ( morphism @ SV87 @ SV102 @ SY330 )
| ! [SY331: $i] :
( ( ( apply @ SV87 @ SY331 )
!= ( zero @ SY330 ) )
| ~ ( element @ SY331 @ SV102 )
| ( SY331
= ( zero @ SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(438,plain,
! [SV103: $i,SV88: $i] :
( ( ! [SY332: $i] :
( ~ ( morphism @ SV88 @ SV103 @ SY332 )
| ~ ( surjection @ SV88 )
| ! [SY333: $i] :
( ~ ( element @ SY333 @ SY332 )
| ~ ( ( ( apply @ SV88 @ ( sK8_ElDom @ SY333 @ SY332 @ SV103 @ SV88 ) )
!= SY333 )
| ~ ( element @ ( sK8_ElDom @ SY333 @ SY332 @ SV103 @ SV88 ) @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(439,plain,
! [SV89: $i,SV104: $i] :
( ( ! [SY334: $i] :
( ! [SY335: $i,SY336: $i] :
( ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SY336 @ SY335 @ SY334 @ SV104 @ SV89 ) )
!= ( zero @ SY336 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY336 @ SY335 @ SY334 @ SV104 @ SV89 ) @ SY335 )
| ! [SY337: $i] :
( ( ( apply @ SV89 @ SY337 )
!= ( sK3_ElCodDom @ SY336 @ SY335 @ SY334 @ SV104 @ SV89 ) )
| ~ ( element @ SY337 @ SY334 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SY336 @ SY335 @ SY334 @ SV104 @ SV89 ) )
= ( zero @ SY336 ) )
| ~ ( ( ( apply @ SV89 @ ( sK5_SY78 @ SY336 @ SY335 @ SY334 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SY336 @ SY335 @ SY334 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SY336 @ SY335 @ SY334 @ SV104 @ SV89 ) @ SY334 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY336 @ SY335 @ SY334 @ SV104 @ SV89 ) @ SY335 )
| ~ ( ( ( apply @ SV89 @ ( sK4_SY79 @ SY336 @ SY335 @ SY334 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SY336 @ SY335 @ SY334 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SY336 @ SY335 @ SY334 @ SV104 @ SV89 ) @ SY334 ) ) ) ) )
| ~ ( morphism @ SV89 @ SY334 @ SY335 )
| ~ ( morphism @ SV104 @ SY335 @ SY336 ) )
| ( exact @ SV89 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(440,plain,
! [SV90: $i] :
( ( ( ! [SY287: $i,SY288: $i] :
( ~ ( ~ ( element @ ( sK7_ElCod @ SY288 @ SY287 @ SV90 ) @ SY288 )
| ~ ! [SY289: $i] :
( ( ( apply @ SV90 @ SY289 )
!= ( sK7_ElCod @ SY288 @ SY287 @ SV90 ) )
| ~ ( element @ SY289 @ SY287 ) ) )
| ~ ( morphism @ SV90 @ SY287 @ SY288 ) ) )
= $true )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(441,plain,
( ( ~ ( injection_2 @ x ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(442,plain,
( ( ~ ~ ( injection @ x ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(443,plain,
! [SV91: $i] :
( ( ~ ! [SY290: $i,SY291: $i] :
( ~ ( morphism @ SV91 @ SY290 @ SY291 )
| ! [SY292: $i] :
( ~ ( element @ SY292 @ SY290 )
| ( element @ ( apply @ SV91 @ SY292 ) @ SY291 ) ) )
| ~ ! [SY293: $i,SY294: $i] :
( ~ ( morphism @ SV91 @ SY293 @ SY294 )
| ( ( apply @ SV91 @ ( zero @ SY293 ) )
= ( zero @ SY294 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(444,plain,
! [SV92: $i,SV105: $i] :
( ( ! [SY338: $i,SY339: $i,SY340: $i,SY341: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY341 @ SY340 @ SY339 @ SY338 @ SV105 @ SV92 ) @ SY340 )
| ~ ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SY341 @ SY340 @ SY339 @ SY338 @ SV105 @ SV92 ) ) )
!= ( apply @ SY339 @ ( apply @ SY338 @ ( sK2_ElDom @ SY341 @ SY340 @ SY339 @ SY338 @ SV105 @ SV92 ) ) ) ) ) )
| ! [SY342: $i,SY343: $i] :
( ~ ( morphism @ SV92 @ SY340 @ SY341 )
| ~ ( morphism @ SV105 @ SY341 @ SY343 )
| ~ ( morphism @ SY338 @ SY340 @ SY342 )
| ~ ( morphism @ SY339 @ SY342 @ SY343 ) )
| ( commute @ SV92 @ SV105 @ SY338 @ SY339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(445,plain,
! [SV106: $i,SV93: $i] :
( ( ! [SY344: $i,SY345: $i,SY346: $i] :
( ~ ( exact @ SV93 @ SV106 )
| ~ ( morphism @ SV93 @ SY344 @ SY345 )
| ~ ( morphism @ SV106 @ SY345 @ SY346 )
| ~ ( ~ ! [SY347: $i] :
( ( ( apply @ SV106 @ SY347 )
!= ( zero @ SY346 ) )
| ~ ( element @ SY347 @ SY345 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SY347 @ SY346 @ SY345 @ SY344 @ SV106 @ SV93 ) )
!= SY347 )
| ~ ( element @ ( sK6_ElDom @ SY347 @ SY346 @ SY345 @ SY344 @ SV106 @ SV93 ) @ SY344 ) ) )
| ~ ~ ( ~ ! [SY348: $i] :
( ! [SY308: $i] :
( ( ( apply @ SV93 @ SY308 )
!= SY348 )
| ~ ( element @ SY308 @ SY344 ) )
| ( ( apply @ SV106 @ SY348 )
= ( zero @ SY346 ) ) )
| ~ ! [SY309: $i] :
( ! [SY310: $i] :
( ( ( apply @ SV93 @ SY310 )
!= SY309 )
| ~ ( element @ SY310 @ SY344 ) )
| ( element @ SY309 @ SY345 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(446,plain,
! [SV94: $i] :
( ( ( ! [SY311: $i,SY312: $i] :
( ~ ( ~ ~ ( ( ( apply @ SV94 @ ( sK1_El @ SY312 @ SY311 @ SV94 ) )
!= ( zero @ SY312 ) )
| ~ ( element @ ( sK1_El @ SY312 @ SY311 @ SV94 ) @ SY311 ) )
| ~ ( ( ( sK1_El @ SY312 @ SY311 @ SV94 )
!= ( zero @ SY311 ) ) ) )
| ~ ( morphism @ SV94 @ SY311 @ SY312 ) ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(447,plain,
! [SV95: $i] :
( ( ( ! [SY313: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SY313 @ SV95 ) @ SY313 )
| ~ ( element @ ( sK10_SY81 @ SY313 @ SV95 ) @ SY313 ) )
| ( ( apply @ SV95 @ ( sK9_El1 @ SY313 @ SV95 ) )
!= ( apply @ SV95 @ ( sK10_SY81 @ SY313 @ SV95 ) ) ) )
| ~ ( ( ( sK9_El1 @ SY313 @ SV95 )
!= ( sK10_SY81 @ SY313 @ SV95 ) ) ) )
| ! [SY314: $i] :
~ ( morphism @ SV95 @ SY313 @ SY314 ) ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(448,plain,
! [SV96: $i,SV81: $i] :
( ( ( ~ ( injection @ SV81 )
| ! [SY315: $i] :
~ ( morphism @ SV81 @ SV96 @ SY315 ) )
= $true )
| ( ( ! [SY316: $i,SY317: $i] :
( ~ ( element @ SY316 @ SV96 )
| ~ ( element @ SY317 @ SV96 )
| ( ( apply @ SV81 @ SY316 )
!= ( apply @ SV81 @ SY317 ) )
| ( SY316 = SY317 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(449,plain,
! [SV107: $i,SV97: $i,SV82: $i] :
( ( ! [SY352: $i,SY353: $i,SY354: $i] :
( ! [SY355: $i,SY356: $i] :
( ~ ( commute @ SV82 @ SV97 @ SV107 @ SY352 )
| ~ ( morphism @ SV82 @ SY353 @ SY354 )
| ~ ( morphism @ SV97 @ SY354 @ SY356 )
| ~ ( morphism @ SV107 @ SY353 @ SY355 )
| ~ ( morphism @ SY352 @ SY355 @ SY356 ) )
| ! [SY357: $i] :
( ~ ( element @ SY357 @ SY353 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY357 ) )
= ( apply @ SY352 @ ( apply @ SV107 @ SY357 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(450,plain,
! [SV108: $i,SV83: $i,SV98: $i] :
( ( ~ ( element @ SV98 @ SV83 )
| ~ ( element @ SV108 @ SV83 )
| ( element @ ( subtract @ SV83 @ SV98 @ SV108 ) @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(451,plain,
! [SV84: $i,SV99: $i] :
( ( ( ~ ( element @ SV99 @ SV84 ) )
= $true )
| ( ( ( subtract @ SV84 @ SV99 @ SV99 )
= ( zero @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(452,plain,
! [SV109: $i,SV85: $i,SV100: $i] :
( ( ~ ( element @ SV100 @ SV85 )
| ~ ( element @ SV109 @ SV85 )
| ( ( subtract @ SV85 @ SV100 @ ( subtract @ SV85 @ SV100 @ SV109 ) )
= SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(453,plain,
! [SV110: $i,SV101: $i,SV86: $i] :
( ( ~ ( morphism @ SV86 @ SV101 @ SV110 )
| ! [SY358: $i,SY359: $i] :
( ~ ( element @ SY358 @ SV101 )
| ~ ( element @ SY359 @ SV101 )
| ( ( apply @ SV86 @ ( subtract @ SV101 @ SY358 @ SY359 ) )
= ( subtract @ SV110 @ ( apply @ SV86 @ SY358 ) @ ( apply @ SV86 @ SY359 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(454,plain,
! [SV111: $i,SV102: $i,SV87: $i] :
( ( ~ ( injection_2 @ SV87 )
| ~ ( morphism @ SV87 @ SV102 @ SV111 )
| ! [SY360: $i] :
( ( ( apply @ SV87 @ SY360 )
!= ( zero @ SV111 ) )
| ~ ( element @ SY360 @ SV102 )
| ( SY360
= ( zero @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(455,plain,
! [SV112: $i,SV103: $i,SV88: $i] :
( ( ~ ( morphism @ SV88 @ SV103 @ SV112 )
| ~ ( surjection @ SV88 )
| ! [SY361: $i] :
( ~ ( element @ SY361 @ SV112 )
| ~ ( ( ( apply @ SV88 @ ( sK8_ElDom @ SY361 @ SV112 @ SV103 @ SV88 ) )
!= SY361 )
| ~ ( element @ ( sK8_ElDom @ SY361 @ SV112 @ SV103 @ SV88 ) @ SV103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(456,plain,
! [SV89: $i,SV113: $i,SV104: $i] :
( ( ! [SY362: $i,SY363: $i] :
( ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) )
!= ( zero @ SY363 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) @ SY362 )
| ! [SY364: $i] :
( ( ( apply @ SV89 @ SY364 )
!= ( sK3_ElCodDom @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ SY364 @ SV113 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SY363 ) )
| ~ ( ( ( apply @ SV89 @ ( sK5_SY78 @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) @ SY362 )
| ~ ( ( ( apply @ SV89 @ ( sK4_SY79 @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) ) ) )
| ~ ( morphism @ SV89 @ SV113 @ SY362 )
| ~ ( morphism @ SV104 @ SY362 @ SY363 ) )
| ( exact @ SV89 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(457,plain,
! [SV90: $i,SV114: $i] :
( ( ( ! [SY365: $i] :
( ~ ( ~ ( element @ ( sK7_ElCod @ SY365 @ SV114 @ SV90 ) @ SY365 )
| ~ ! [SY366: $i] :
( ( ( apply @ SV90 @ SY366 )
!= ( sK7_ElCod @ SY365 @ SV114 @ SV90 ) )
| ~ ( element @ SY366 @ SV114 ) ) )
| ~ ( morphism @ SV90 @ SV114 @ SY365 ) ) )
= $true )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(458,plain,
( ( injection_2 @ x )
= $true ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(459,plain,
( ( ~ ( injection @ x ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(460,plain,
! [SV91: $i] :
( ( ~ ! [SY290: $i,SY291: $i] :
( ~ ( morphism @ SV91 @ SY290 @ SY291 )
| ! [SY292: $i] :
( ~ ( element @ SY292 @ SY290 )
| ( element @ ( apply @ SV91 @ SY292 ) @ SY291 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(461,plain,
! [SV91: $i] :
( ( ~ ! [SY293: $i,SY294: $i] :
( ~ ( morphism @ SV91 @ SY293 @ SY294 )
| ( ( apply @ SV91 @ ( zero @ SY293 ) )
= ( zero @ SY294 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(462,plain,
! [SV92: $i,SV105: $i,SV115: $i] :
( ( ! [SY367: $i,SY368: $i,SY369: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY369 @ SY368 @ SY367 @ SV115 @ SV105 @ SV92 ) @ SY368 )
| ~ ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SY369 @ SY368 @ SY367 @ SV115 @ SV105 @ SV92 ) ) )
!= ( apply @ SY367 @ ( apply @ SV115 @ ( sK2_ElDom @ SY369 @ SY368 @ SY367 @ SV115 @ SV105 @ SV92 ) ) ) ) ) )
| ! [SY370: $i,SY371: $i] :
( ~ ( morphism @ SV92 @ SY368 @ SY369 )
| ~ ( morphism @ SV105 @ SY369 @ SY371 )
| ~ ( morphism @ SV115 @ SY368 @ SY370 )
| ~ ( morphism @ SY367 @ SY370 @ SY371 ) )
| ( commute @ SV92 @ SV105 @ SV115 @ SY367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(463,plain,
! [SV116: $i,SV106: $i,SV93: $i] :
( ( ! [SY372: $i,SY373: $i] :
( ~ ( exact @ SV93 @ SV106 )
| ~ ( morphism @ SV93 @ SV116 @ SY372 )
| ~ ( morphism @ SV106 @ SY372 @ SY373 )
| ~ ( ~ ! [SY374: $i] :
( ( ( apply @ SV106 @ SY374 )
!= ( zero @ SY373 ) )
| ~ ( element @ SY374 @ SY372 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SY374 @ SY373 @ SY372 @ SV116 @ SV106 @ SV93 ) )
!= SY374 )
| ~ ( element @ ( sK6_ElDom @ SY374 @ SY373 @ SY372 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
| ~ ~ ( ~ ! [SY375: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY375 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY375 )
= ( zero @ SY373 ) ) )
| ~ ! [SY377: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY377 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY377 @ SY372 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(464,plain,
! [SV117: $i,SV94: $i] :
( ( ( ! [SY379: $i] :
( ~ ( ~ ~ ( ( ( apply @ SV94 @ ( sK1_El @ SY379 @ SV117 @ SV94 ) )
!= ( zero @ SY379 ) )
| ~ ( element @ ( sK1_El @ SY379 @ SV117 @ SV94 ) @ SV117 ) )
| ~ ( ( ( sK1_El @ SY379 @ SV117 @ SV94 )
!= ( zero @ SV117 ) ) ) )
| ~ ( morphism @ SV94 @ SV117 @ SY379 ) ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(465,plain,
! [SV95: $i,SV118: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV118 @ SV95 ) @ SV118 )
| ~ ( element @ ( sK10_SY81 @ SV118 @ SV95 ) @ SV118 ) )
| ( ( apply @ SV95 @ ( sK9_El1 @ SV118 @ SV95 ) )
!= ( apply @ SV95 @ ( sK10_SY81 @ SV118 @ SV95 ) ) ) )
| ~ ( ( ( sK9_El1 @ SV118 @ SV95 )
!= ( sK10_SY81 @ SV118 @ SV95 ) ) ) )
| ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(466,plain,
! [SV96: $i,SV81: $i] :
( ( ( ~ ( injection @ SV81 ) )
= $true )
| ( ( ! [SY315: $i] :
~ ( morphism @ SV81 @ SV96 @ SY315 ) )
= $true )
| ( ( ! [SY316: $i,SY317: $i] :
( ~ ( element @ SY316 @ SV96 )
| ~ ( element @ SY317 @ SV96 )
| ( ( apply @ SV81 @ SY316 )
!= ( apply @ SV81 @ SY317 ) )
| ( SY316 = SY317 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(467,plain,
! [SV119: $i,SV107: $i,SV97: $i,SV82: $i] :
( ( ! [SY381: $i,SY382: $i] :
( ! [SY383: $i,SY384: $i] :
( ~ ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
| ~ ( morphism @ SV82 @ SY381 @ SY382 )
| ~ ( morphism @ SV97 @ SY382 @ SY384 )
| ~ ( morphism @ SV107 @ SY381 @ SY383 )
| ~ ( morphism @ SV119 @ SY383 @ SY384 ) )
| ! [SY385: $i] :
( ~ ( element @ SY385 @ SY381 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY385 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY385 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(468,plain,
! [SV108: $i,SV83: $i,SV98: $i] :
( ( ( ~ ( element @ SV98 @ SV83 )
| ~ ( element @ SV108 @ SV83 ) )
= $true )
| ( ( element @ ( subtract @ SV83 @ SV98 @ SV108 ) @ SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(469,plain,
! [SV84: $i,SV99: $i] :
( ( ( element @ SV99 @ SV84 )
= $false )
| ( ( ( subtract @ SV84 @ SV99 @ SV99 )
= ( zero @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(470,plain,
! [SV109: $i,SV85: $i,SV100: $i] :
( ( ( ~ ( element @ SV100 @ SV85 )
| ~ ( element @ SV109 @ SV85 ) )
= $true )
| ( ( ( subtract @ SV85 @ SV100 @ ( subtract @ SV85 @ SV100 @ SV109 ) )
= SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(471,plain,
! [SV110: $i,SV101: $i,SV86: $i] :
( ( ( ~ ( morphism @ SV86 @ SV101 @ SV110 ) )
= $true )
| ( ( ! [SY358: $i,SY359: $i] :
( ~ ( element @ SY358 @ SV101 )
| ~ ( element @ SY359 @ SV101 )
| ( ( apply @ SV86 @ ( subtract @ SV101 @ SY358 @ SY359 ) )
= ( subtract @ SV110 @ ( apply @ SV86 @ SY358 ) @ ( apply @ SV86 @ SY359 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(472,plain,
! [SV111: $i,SV102: $i,SV87: $i] :
( ( ( ~ ( injection_2 @ SV87 )
| ~ ( morphism @ SV87 @ SV102 @ SV111 ) )
= $true )
| ( ( ! [SY360: $i] :
( ( ( apply @ SV87 @ SY360 )
!= ( zero @ SV111 ) )
| ~ ( element @ SY360 @ SV102 )
| ( SY360
= ( zero @ SV102 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(473,plain,
! [SV112: $i,SV103: $i,SV88: $i] :
( ( ( ~ ( morphism @ SV88 @ SV103 @ SV112 )
| ~ ( surjection @ SV88 ) )
= $true )
| ( ( ! [SY361: $i] :
( ~ ( element @ SY361 @ SV112 )
| ~ ( ( ( apply @ SV88 @ ( sK8_ElDom @ SY361 @ SV112 @ SV103 @ SV88 ) )
!= SY361 )
| ~ ( element @ ( sK8_ElDom @ SY361 @ SV112 @ SV103 @ SV88 ) @ SV103 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(474,plain,
! [SV89: $i,SV113: $i,SV104: $i] :
( ( ( ! [SY362: $i,SY363: $i] :
( ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) )
!= ( zero @ SY363 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) @ SY362 )
| ! [SY364: $i] :
( ( ( apply @ SV89 @ SY364 )
!= ( sK3_ElCodDom @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ SY364 @ SV113 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SY363 ) )
| ~ ( ( ( apply @ SV89 @ ( sK5_SY78 @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) @ SY362 )
| ~ ( ( ( apply @ SV89 @ ( sK4_SY79 @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SY363 @ SY362 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) ) ) )
| ~ ( morphism @ SV89 @ SV113 @ SY362 )
| ~ ( morphism @ SV104 @ SY362 @ SY363 ) ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(475,plain,
! [SV90: $i,SV114: $i,SV120: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) @ SV120 )
| ~ ! [SY386: $i] :
( ( ( apply @ SV90 @ SY386 )
!= ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) )
| ~ ( element @ SY386 @ SV114 ) ) )
| ~ ( morphism @ SV90 @ SV114 @ SV120 ) )
= $true )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(476,plain,
( ( injection @ x )
= $false ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(477,plain,
! [SV91: $i] :
( ( ! [SY290: $i,SY291: $i] :
( ~ ( morphism @ SV91 @ SY290 @ SY291 )
| ! [SY292: $i] :
( ~ ( element @ SY292 @ SY290 )
| ( element @ ( apply @ SV91 @ SY292 ) @ SY291 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(478,plain,
! [SV91: $i] :
( ( ! [SY293: $i,SY294: $i] :
( ~ ( morphism @ SV91 @ SY293 @ SY294 )
| ( ( apply @ SV91 @ ( zero @ SY293 ) )
= ( zero @ SY294 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(479,plain,
! [SV92: $i,SV105: $i,SV115: $i,SV121: $i] :
( ( ! [SY387: $i,SY388: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY388 @ SY387 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SY387 )
| ~ ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SY388 @ SY387 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
!= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SY388 @ SY387 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) ) ) )
| ! [SY389: $i,SY390: $i] :
( ~ ( morphism @ SV92 @ SY387 @ SY388 )
| ~ ( morphism @ SV105 @ SY388 @ SY390 )
| ~ ( morphism @ SV115 @ SY387 @ SY389 )
| ~ ( morphism @ SV121 @ SY389 @ SY390 ) )
| ( commute @ SV92 @ SV105 @ SV115 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(480,plain,
! [SV122: $i,SV116: $i,SV106: $i,SV93: $i] :
( ( ! [SY391: $i] :
( ~ ( exact @ SV93 @ SV106 )
| ~ ( morphism @ SV93 @ SV116 @ SV122 )
| ~ ( morphism @ SV106 @ SV122 @ SY391 )
| ~ ( ~ ! [SY392: $i] :
( ( ( apply @ SV106 @ SY392 )
!= ( zero @ SY391 ) )
| ~ ( element @ SY392 @ SV122 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SY392 @ SY391 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SY392 )
| ~ ( element @ ( sK6_ElDom @ SY392 @ SY391 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
| ~ ~ ( ~ ! [SY375: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY375 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY375 )
= ( zero @ SY391 ) ) )
| ~ ! [SY395: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY395 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY395 @ SV122 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(481,plain,
! [SV117: $i,SV123: $i,SV94: $i] :
( ( ( ~ ( ~ ~ ( ( ( apply @ SV94 @ ( sK1_El @ SV123 @ SV117 @ SV94 ) )
!= ( zero @ SV123 ) )
| ~ ( element @ ( sK1_El @ SV123 @ SV117 @ SV94 ) @ SV117 ) )
| ~ ( ( ( sK1_El @ SV123 @ SV117 @ SV94 )
!= ( zero @ SV117 ) ) ) )
| ~ ( morphism @ SV94 @ SV117 @ SV123 ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(482,plain,
! [SV95: $i,SV118: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV118 @ SV95 ) @ SV118 )
| ~ ( element @ ( sK10_SY81 @ SV118 @ SV95 ) @ SV118 ) )
| ( ( apply @ SV95 @ ( sK9_El1 @ SV118 @ SV95 ) )
!= ( apply @ SV95 @ ( sK10_SY81 @ SV118 @ SV95 ) ) ) )
| ~ ( ( ( sK9_El1 @ SV118 @ SV95 )
!= ( sK10_SY81 @ SV118 @ SV95 ) ) ) ) )
= $true )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(483,plain,
! [SV96: $i,SV81: $i] :
( ( ( injection @ SV81 )
= $false )
| ( ( ! [SY315: $i] :
~ ( morphism @ SV81 @ SV96 @ SY315 ) )
= $true )
| ( ( ! [SY316: $i,SY317: $i] :
( ~ ( element @ SY316 @ SV96 )
| ~ ( element @ SY317 @ SV96 )
| ( ( apply @ SV81 @ SY316 )
!= ( apply @ SV81 @ SY317 ) )
| ( SY316 = SY317 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(484,plain,
! [SV124: $i,SV119: $i,SV107: $i,SV97: $i,SV82: $i] :
( ( ! [SY397: $i] :
( ! [SY398: $i,SY399: $i] :
( ~ ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
| ~ ( morphism @ SV82 @ SV124 @ SY397 )
| ~ ( morphism @ SV97 @ SY397 @ SY399 )
| ~ ( morphism @ SV107 @ SV124 @ SY398 )
| ~ ( morphism @ SV119 @ SY398 @ SY399 ) )
| ! [SY400: $i] :
( ~ ( element @ SY400 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY400 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY400 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(485,plain,
! [SV108: $i,SV83: $i,SV98: $i] :
( ( ( ~ ( element @ SV98 @ SV83 ) )
= $true )
| ( ( ~ ( element @ SV108 @ SV83 ) )
= $true )
| ( ( element @ ( subtract @ SV83 @ SV98 @ SV108 ) @ SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(486,plain,
! [SV109: $i,SV85: $i,SV100: $i] :
( ( ( ~ ( element @ SV100 @ SV85 ) )
= $true )
| ( ( ~ ( element @ SV109 @ SV85 ) )
= $true )
| ( ( ( subtract @ SV85 @ SV100 @ ( subtract @ SV85 @ SV100 @ SV109 ) )
= SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(487,plain,
! [SV110: $i,SV101: $i,SV86: $i] :
( ( ( morphism @ SV86 @ SV101 @ SV110 )
= $false )
| ( ( ! [SY358: $i,SY359: $i] :
( ~ ( element @ SY358 @ SV101 )
| ~ ( element @ SY359 @ SV101 )
| ( ( apply @ SV86 @ ( subtract @ SV101 @ SY358 @ SY359 ) )
= ( subtract @ SV110 @ ( apply @ SV86 @ SY358 ) @ ( apply @ SV86 @ SY359 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(488,plain,
! [SV111: $i,SV102: $i,SV87: $i] :
( ( ( ~ ( injection_2 @ SV87 ) )
= $true )
| ( ( ~ ( morphism @ SV87 @ SV102 @ SV111 ) )
= $true )
| ( ( ! [SY360: $i] :
( ( ( apply @ SV87 @ SY360 )
!= ( zero @ SV111 ) )
| ~ ( element @ SY360 @ SV102 )
| ( SY360
= ( zero @ SV102 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(489,plain,
! [SV112: $i,SV103: $i,SV88: $i] :
( ( ( ~ ( morphism @ SV88 @ SV103 @ SV112 ) )
= $true )
| ( ( ~ ( surjection @ SV88 ) )
= $true )
| ( ( ! [SY361: $i] :
( ~ ( element @ SY361 @ SV112 )
| ~ ( ( ( apply @ SV88 @ ( sK8_ElDom @ SY361 @ SV112 @ SV103 @ SV88 ) )
!= SY361 )
| ~ ( element @ ( sK8_ElDom @ SY361 @ SV112 @ SV103 @ SV88 ) @ SV103 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(490,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV104: $i] :
( ( ( ! [SY401: $i] :
( ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SY401 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( zero @ SY401 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY401 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ! [SY402: $i] :
( ( ( apply @ SV89 @ SY402 )
!= ( sK3_ElCodDom @ SY401 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ SY402 @ SV113 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SY401 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SY401 ) )
| ~ ( ( ( apply @ SV89 @ ( sK5_SY78 @ SY401 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SY401 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SY401 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY401 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ~ ( ( ( apply @ SV89 @ ( sK4_SY79 @ SY401 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SY401 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SY401 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) ) ) )
| ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SY401 ) ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(491,plain,
! [SV90: $i,SV114: $i,SV120: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) @ SV120 )
| ~ ! [SY386: $i] :
( ( ( apply @ SV90 @ SY386 )
!= ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) )
| ~ ( element @ SY386 @ SV114 ) ) ) )
= $true )
| ( ( ~ ( morphism @ SV90 @ SV114 @ SV120 ) )
= $true )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(492,plain,
! [SV126: $i,SV91: $i] :
( ( ! [SY403: $i] :
( ~ ( morphism @ SV91 @ SV126 @ SY403 )
| ! [SY404: $i] :
( ~ ( element @ SY404 @ SV126 )
| ( element @ ( apply @ SV91 @ SY404 ) @ SY403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(493,plain,
! [SV127: $i,SV91: $i] :
( ( ! [SY405: $i] :
( ~ ( morphism @ SV91 @ SV127 @ SY405 )
| ( ( apply @ SV91 @ ( zero @ SV127 ) )
= ( zero @ SY405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(494,plain,
! [SV92: $i,SV105: $i,SV115: $i,SV121: $i,SV128: $i] :
( ( ! [SY406: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY406 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
| ~ ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SY406 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
!= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SY406 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) ) ) )
| ! [SY407: $i,SY408: $i] :
( ~ ( morphism @ SV92 @ SV128 @ SY406 )
| ~ ( morphism @ SV105 @ SY406 @ SY408 )
| ~ ( morphism @ SV115 @ SV128 @ SY407 )
| ~ ( morphism @ SV121 @ SY407 @ SY408 ) )
| ( commute @ SV92 @ SV105 @ SV115 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(495,plain,
! [SV129: $i,SV122: $i,SV116: $i,SV106: $i,SV93: $i] :
( ( ~ ( exact @ SV93 @ SV106 )
| ~ ( morphism @ SV93 @ SV116 @ SV122 )
| ~ ( morphism @ SV106 @ SV122 @ SV129 )
| ~ ( ~ ! [SY409: $i] :
( ( ( apply @ SV106 @ SY409 )
!= ( zero @ SV129 ) )
| ~ ( element @ SY409 @ SV122 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SY409 )
| ~ ( element @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
| ~ ~ ( ~ ! [SY410: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY410 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY410 )
= ( zero @ SV129 ) ) )
| ~ ! [SY395: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY395 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY395 @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(496,plain,
! [SV117: $i,SV123: $i,SV94: $i] :
( ( ( ~ ( ~ ~ ( ( ( apply @ SV94 @ ( sK1_El @ SV123 @ SV117 @ SV94 ) )
!= ( zero @ SV123 ) )
| ~ ( element @ ( sK1_El @ SV123 @ SV117 @ SV94 ) @ SV117 ) )
| ~ ( ( ( sK1_El @ SV123 @ SV117 @ SV94 )
!= ( zero @ SV117 ) ) ) ) )
= $true )
| ( ( ~ ( morphism @ SV94 @ SV117 @ SV123 ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(497,plain,
! [SV95: $i,SV118: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV118 @ SV95 ) @ SV118 )
| ~ ( element @ ( sK10_SY81 @ SV118 @ SV95 ) @ SV118 ) )
| ( ( apply @ SV95 @ ( sK9_El1 @ SV118 @ SV95 ) )
!= ( apply @ SV95 @ ( sK10_SY81 @ SV118 @ SV95 ) ) ) )
| ~ ( ( ( sK9_El1 @ SV118 @ SV95 )
!= ( sK10_SY81 @ SV118 @ SV95 ) ) ) )
= $false )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(498,plain,
! [SV130: $i,SV96: $i,SV81: $i] :
( ( ( ~ ( morphism @ SV81 @ SV96 @ SV130 ) )
= $true )
| ( ( injection @ SV81 )
= $false )
| ( ( ! [SY316: $i,SY317: $i] :
( ~ ( element @ SY316 @ SV96 )
| ~ ( element @ SY317 @ SV96 )
| ( ( apply @ SV81 @ SY316 )
!= ( apply @ SV81 @ SY317 ) )
| ( SY316 = SY317 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(499,plain,
! [SV131: $i,SV124: $i,SV119: $i,SV107: $i,SV97: $i,SV82: $i] :
( ( ! [SY414: $i,SY415: $i] :
( ~ ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
| ~ ( morphism @ SV82 @ SV124 @ SV131 )
| ~ ( morphism @ SV97 @ SV131 @ SY415 )
| ~ ( morphism @ SV107 @ SV124 @ SY414 )
| ~ ( morphism @ SV119 @ SY414 @ SY415 ) )
| ! [SY400: $i] :
( ~ ( element @ SY400 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY400 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY400 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(500,plain,
! [SV108: $i,SV83: $i,SV98: $i] :
( ( ( element @ SV98 @ SV83 )
= $false )
| ( ( ~ ( element @ SV108 @ SV83 ) )
= $true )
| ( ( element @ ( subtract @ SV83 @ SV98 @ SV108 ) @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(501,plain,
! [SV109: $i,SV85: $i,SV100: $i] :
( ( ( element @ SV100 @ SV85 )
= $false )
| ( ( ~ ( element @ SV109 @ SV85 ) )
= $true )
| ( ( ( subtract @ SV85 @ SV100 @ ( subtract @ SV85 @ SV100 @ SV109 ) )
= SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(502,plain,
! [SV110: $i,SV86: $i,SV101: $i,SV132: $i] :
( ( ( ! [SY417: $i] :
( ~ ( element @ SV132 @ SV101 )
| ~ ( element @ SY417 @ SV101 )
| ( ( apply @ SV86 @ ( subtract @ SV101 @ SV132 @ SY417 ) )
= ( subtract @ SV110 @ ( apply @ SV86 @ SV132 ) @ ( apply @ SV86 @ SY417 ) ) ) ) )
= $true )
| ( ( morphism @ SV86 @ SV101 @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(503,plain,
! [SV111: $i,SV102: $i,SV87: $i] :
( ( ( injection_2 @ SV87 )
= $false )
| ( ( ~ ( morphism @ SV87 @ SV102 @ SV111 ) )
= $true )
| ( ( ! [SY360: $i] :
( ( ( apply @ SV87 @ SY360 )
!= ( zero @ SV111 ) )
| ~ ( element @ SY360 @ SV102 )
| ( SY360
= ( zero @ SV102 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(504,plain,
! [SV112: $i,SV103: $i,SV88: $i] :
( ( ( morphism @ SV88 @ SV103 @ SV112 )
= $false )
| ( ( ~ ( surjection @ SV88 ) )
= $true )
| ( ( ! [SY361: $i] :
( ~ ( element @ SY361 @ SV112 )
| ~ ( ( ( apply @ SV88 @ ( sK8_ElDom @ SY361 @ SV112 @ SV103 @ SV88 ) )
!= SY361 )
| ~ ( element @ ( sK8_ElDom @ SY361 @ SV112 @ SV103 @ SV88 ) @ SV103 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(505,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV133: $i,SV104: $i] :
( ( ( ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( zero @ SV133 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ! [SY418: $i] :
( ( ( apply @ SV89 @ SY418 )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ SY418 @ SV113 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
| ~ ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ~ ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) ) ) )
| ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(506,plain,
! [SV90: $i,SV114: $i,SV120: $i] :
( ( ( ~ ( element @ ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) @ SV120 )
| ~ ! [SY386: $i] :
( ( ( apply @ SV90 @ SY386 )
!= ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) )
| ~ ( element @ SY386 @ SV114 ) ) )
= $false )
| ( ( ~ ( morphism @ SV90 @ SV114 @ SV120 ) )
= $true )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(507,plain,
! [SV134: $i,SV126: $i,SV91: $i] :
( ( ~ ( morphism @ SV91 @ SV126 @ SV134 )
| ! [SY419: $i] :
( ~ ( element @ SY419 @ SV126 )
| ( element @ ( apply @ SV91 @ SY419 ) @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(508,plain,
! [SV135: $i,SV127: $i,SV91: $i] :
( ( ~ ( morphism @ SV91 @ SV127 @ SV135 )
| ( ( apply @ SV91 @ ( zero @ SV127 ) )
= ( zero @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(509,plain,
! [SV92: $i,SV105: $i,SV115: $i,SV121: $i,SV128: $i,SV136: $i] :
( ( ~ ( ~ ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
| ~ ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
!= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) ) ) )
| ! [SY420: $i,SY421: $i] :
( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SY421 )
| ~ ( morphism @ SV115 @ SV128 @ SY420 )
| ~ ( morphism @ SV121 @ SY420 @ SY421 ) )
| ( commute @ SV92 @ SV105 @ SV115 @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(510,plain,
! [SV129: $i,SV122: $i,SV116: $i,SV106: $i,SV93: $i] :
( ( ( ~ ( exact @ SV93 @ SV106 )
| ~ ( morphism @ SV93 @ SV116 @ SV122 )
| ~ ( morphism @ SV106 @ SV122 @ SV129 ) )
= $true )
| ( ( ~ ( ~ ! [SY409: $i] :
( ( ( apply @ SV106 @ SY409 )
!= ( zero @ SV129 ) )
| ~ ( element @ SY409 @ SV122 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SY409 )
| ~ ( element @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
| ~ ~ ( ~ ! [SY410: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY410 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY410 )
= ( zero @ SV129 ) ) )
| ~ ! [SY395: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY395 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY395 @ SV122 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(511,plain,
! [SV117: $i,SV123: $i,SV94: $i] :
( ( ( ~ ~ ( ( ( apply @ SV94 @ ( sK1_El @ SV123 @ SV117 @ SV94 ) )
!= ( zero @ SV123 ) )
| ~ ( element @ ( sK1_El @ SV123 @ SV117 @ SV94 ) @ SV117 ) )
| ~ ( ( ( sK1_El @ SV123 @ SV117 @ SV94 )
!= ( zero @ SV117 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV94 @ SV117 @ SV123 ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(512,plain,
! [SV95: $i,SV118: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV118 @ SV95 ) @ SV118 )
| ~ ( element @ ( sK10_SY81 @ SV118 @ SV95 ) @ SV118 ) )
| ( ( apply @ SV95 @ ( sK9_El1 @ SV118 @ SV95 ) )
!= ( apply @ SV95 @ ( sK10_SY81 @ SV118 @ SV95 ) ) ) ) )
= $false )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[497]) ).
thf(513,plain,
! [SV95: $i,SV118: $i] :
( ( ( ~ ( ( ( sK9_El1 @ SV118 @ SV95 )
!= ( sK10_SY81 @ SV118 @ SV95 ) ) ) )
= $false )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[497]) ).
thf(514,plain,
! [SV130: $i,SV96: $i,SV81: $i] :
( ( ( morphism @ SV81 @ SV96 @ SV130 )
= $false )
| ( ( injection @ SV81 )
= $false )
| ( ( ! [SY316: $i,SY317: $i] :
( ~ ( element @ SY316 @ SV96 )
| ~ ( element @ SY317 @ SV96 )
| ( ( apply @ SV81 @ SY316 )
!= ( apply @ SV81 @ SY317 ) )
| ( SY316 = SY317 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(515,plain,
! [SV131: $i,SV124: $i,SV119: $i,SV107: $i,SV97: $i,SV82: $i] :
( ( ( ! [SY414: $i,SY415: $i] :
( ~ ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
| ~ ( morphism @ SV82 @ SV124 @ SV131 )
| ~ ( morphism @ SV97 @ SV131 @ SY415 )
| ~ ( morphism @ SV107 @ SV124 @ SY414 )
| ~ ( morphism @ SV119 @ SY414 @ SY415 ) ) )
= $true )
| ( ( ! [SY400: $i] :
( ~ ( element @ SY400 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY400 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY400 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(516,plain,
! [SV98: $i,SV83: $i,SV108: $i] :
( ( ( element @ SV108 @ SV83 )
= $false )
| ( ( element @ SV98 @ SV83 )
= $false )
| ( ( element @ ( subtract @ SV83 @ SV98 @ SV108 ) @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(517,plain,
! [SV100: $i,SV85: $i,SV109: $i] :
( ( ( element @ SV109 @ SV85 )
= $false )
| ( ( element @ SV100 @ SV85 )
= $false )
| ( ( ( subtract @ SV85 @ SV100 @ ( subtract @ SV85 @ SV100 @ SV109 ) )
= SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(518,plain,
! [SV110: $i,SV86: $i,SV137: $i,SV101: $i,SV132: $i] :
( ( ( ~ ( element @ SV132 @ SV101 )
| ~ ( element @ SV137 @ SV101 )
| ( ( apply @ SV86 @ ( subtract @ SV101 @ SV132 @ SV137 ) )
= ( subtract @ SV110 @ ( apply @ SV86 @ SV132 ) @ ( apply @ SV86 @ SV137 ) ) ) )
= $true )
| ( ( morphism @ SV86 @ SV101 @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(519,plain,
! [SV111: $i,SV102: $i,SV87: $i] :
( ( ( morphism @ SV87 @ SV102 @ SV111 )
= $false )
| ( ( injection_2 @ SV87 )
= $false )
| ( ( ! [SY360: $i] :
( ( ( apply @ SV87 @ SY360 )
!= ( zero @ SV111 ) )
| ~ ( element @ SY360 @ SV102 )
| ( SY360
= ( zero @ SV102 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(520,plain,
! [SV112: $i,SV103: $i,SV88: $i] :
( ( ( surjection @ SV88 )
= $false )
| ( ( morphism @ SV88 @ SV103 @ SV112 )
= $false )
| ( ( ! [SY361: $i] :
( ~ ( element @ SY361 @ SV112 )
| ~ ( ( ( apply @ SV88 @ ( sK8_ElDom @ SY361 @ SV112 @ SV103 @ SV88 ) )
!= SY361 )
| ~ ( element @ ( sK8_ElDom @ SY361 @ SV112 @ SV103 @ SV88 ) @ SV103 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(521,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV133: $i,SV104: $i] :
( ( ( ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( zero @ SV133 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ! [SY418: $i] :
( ( ( apply @ SV89 @ SY418 )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ SY418 @ SV113 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
| ~ ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ~ ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) ) ) ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(522,plain,
! [SV90: $i,SV114: $i,SV120: $i] :
( ( ( ~ ( element @ ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) @ SV120 ) )
= $false )
| ( ( ~ ( morphism @ SV90 @ SV114 @ SV120 ) )
= $true )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[506]) ).
thf(523,plain,
! [SV114: $i,SV120: $i,SV90: $i] :
( ( ( ~ ! [SY386: $i] :
( ( ( apply @ SV90 @ SY386 )
!= ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) )
| ~ ( element @ SY386 @ SV114 ) ) )
= $false )
| ( ( ~ ( morphism @ SV90 @ SV114 @ SV120 ) )
= $true )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[506]) ).
thf(524,plain,
! [SV134: $i,SV126: $i,SV91: $i] :
( ( ( ~ ( morphism @ SV91 @ SV126 @ SV134 ) )
= $true )
| ( ( ! [SY419: $i] :
( ~ ( element @ SY419 @ SV126 )
| ( element @ ( apply @ SV91 @ SY419 ) @ SV134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(525,plain,
! [SV135: $i,SV127: $i,SV91: $i] :
( ( ( ~ ( morphism @ SV91 @ SV127 @ SV135 ) )
= $true )
| ( ( ( apply @ SV91 @ ( zero @ SV127 ) )
= ( zero @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(526,plain,
! [SV92: $i,SV105: $i,SV115: $i,SV121: $i,SV128: $i,SV136: $i] :
( ( ( ~ ( ~ ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
| ~ ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
!= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) ) ) )
| ! [SY420: $i,SY421: $i] :
( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SY421 )
| ~ ( morphism @ SV115 @ SV128 @ SY420 )
| ~ ( morphism @ SV121 @ SY420 @ SY421 ) ) )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(527,plain,
! [SV129: $i,SV122: $i,SV116: $i,SV106: $i,SV93: $i] :
( ( ( ~ ( exact @ SV93 @ SV106 )
| ~ ( morphism @ SV93 @ SV116 @ SV122 ) )
= $true )
| ( ( ~ ( morphism @ SV106 @ SV122 @ SV129 ) )
= $true )
| ( ( ~ ( ~ ! [SY409: $i] :
( ( ( apply @ SV106 @ SY409 )
!= ( zero @ SV129 ) )
| ~ ( element @ SY409 @ SV122 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SY409 )
| ~ ( element @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
| ~ ~ ( ~ ! [SY410: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY410 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY410 )
= ( zero @ SV129 ) ) )
| ~ ! [SY395: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY395 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY395 @ SV122 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(528,plain,
! [SV117: $i,SV123: $i,SV94: $i] :
( ( ( ~ ~ ( ( ( apply @ SV94 @ ( sK1_El @ SV123 @ SV117 @ SV94 ) )
!= ( zero @ SV123 ) )
| ~ ( element @ ( sK1_El @ SV123 @ SV117 @ SV94 ) @ SV117 ) ) )
= $false )
| ( ( ~ ( morphism @ SV94 @ SV117 @ SV123 ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(529,plain,
! [SV94: $i,SV117: $i,SV123: $i] :
( ( ( ~ ( ( ( sK1_El @ SV123 @ SV117 @ SV94 )
!= ( zero @ SV117 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV94 @ SV117 @ SV123 ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(530,plain,
! [SV95: $i,SV118: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV118 @ SV95 ) @ SV118 )
| ~ ( element @ ( sK10_SY81 @ SV118 @ SV95 ) @ SV118 ) )
| ( ( apply @ SV95 @ ( sK9_El1 @ SV118 @ SV95 ) )
!= ( apply @ SV95 @ ( sK10_SY81 @ SV118 @ SV95 ) ) ) ) )
= $true )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(531,plain,
! [SV95: $i,SV118: $i] :
( ( ( ( ( sK9_El1 @ SV118 @ SV95 )
!= ( sK10_SY81 @ SV118 @ SV95 ) ) )
= $true )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(532,plain,
! [SV130: $i,SV81: $i,SV96: $i,SV138: $i] :
( ( ( ! [SY422: $i] :
( ~ ( element @ SV138 @ SV96 )
| ~ ( element @ SY422 @ SV96 )
| ( ( apply @ SV81 @ SV138 )
!= ( apply @ SV81 @ SY422 ) )
| ( SV138 = SY422 ) ) )
= $true )
| ( ( injection @ SV81 )
= $false )
| ( ( morphism @ SV81 @ SV96 @ SV130 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(533,plain,
! [SV139: $i,SV131: $i,SV124: $i,SV119: $i,SV107: $i,SV97: $i,SV82: $i] :
( ( ( ! [SY423: $i] :
( ~ ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
| ~ ( morphism @ SV82 @ SV124 @ SV131 )
| ~ ( morphism @ SV97 @ SV131 @ SY423 )
| ~ ( morphism @ SV107 @ SV124 @ SV139 )
| ~ ( morphism @ SV119 @ SV139 @ SY423 ) ) )
= $true )
| ( ( ! [SY400: $i] :
( ~ ( element @ SY400 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY400 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY400 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(534,plain,
! [SV110: $i,SV86: $i,SV137: $i,SV101: $i,SV132: $i] :
( ( ( ~ ( element @ SV132 @ SV101 )
| ~ ( element @ SV137 @ SV101 ) )
= $true )
| ( ( ( apply @ SV86 @ ( subtract @ SV101 @ SV132 @ SV137 ) )
= ( subtract @ SV110 @ ( apply @ SV86 @ SV132 ) @ ( apply @ SV86 @ SV137 ) ) )
= $true )
| ( ( morphism @ SV86 @ SV101 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(535,plain,
! [SV102: $i,SV111: $i,SV140: $i,SV87: $i] :
( ( ( ( ( apply @ SV87 @ SV140 )
!= ( zero @ SV111 ) )
| ~ ( element @ SV140 @ SV102 )
| ( SV140
= ( zero @ SV102 ) ) )
= $true )
| ( ( injection_2 @ SV87 )
= $false )
| ( ( morphism @ SV87 @ SV102 @ SV111 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(536,plain,
! [SV103: $i,SV88: $i,SV112: $i,SV141: $i] :
( ( ( ~ ( element @ SV141 @ SV112 )
| ~ ( ( ( apply @ SV88 @ ( sK8_ElDom @ SV141 @ SV112 @ SV103 @ SV88 ) )
!= SV141 )
| ~ ( element @ ( sK8_ElDom @ SV141 @ SV112 @ SV103 @ SV88 ) @ SV103 ) ) )
= $true )
| ( ( morphism @ SV88 @ SV103 @ SV112 )
= $false )
| ( ( surjection @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(537,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV133: $i,SV104: $i] :
( ( ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( zero @ SV133 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ! [SY418: $i] :
( ( ( apply @ SV89 @ SY418 )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ SY418 @ SV113 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
| ~ ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ~ ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(538,plain,
! [SV90: $i,SV114: $i,SV120: $i] :
( ( ( element @ ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) @ SV120 )
= $true )
| ( ( ~ ( morphism @ SV90 @ SV114 @ SV120 ) )
= $true )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(539,plain,
! [SV114: $i,SV120: $i,SV90: $i] :
( ( ( ! [SY386: $i] :
( ( ( apply @ SV90 @ SY386 )
!= ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) )
| ~ ( element @ SY386 @ SV114 ) ) )
= $true )
| ( ( ~ ( morphism @ SV90 @ SV114 @ SV120 ) )
= $true )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(540,plain,
! [SV134: $i,SV126: $i,SV91: $i] :
( ( ( morphism @ SV91 @ SV126 @ SV134 )
= $false )
| ( ( ! [SY419: $i] :
( ~ ( element @ SY419 @ SV126 )
| ( element @ ( apply @ SV91 @ SY419 ) @ SV134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(541,plain,
! [SV135: $i,SV127: $i,SV91: $i] :
( ( ( morphism @ SV91 @ SV127 @ SV135 )
= $false )
| ( ( ( apply @ SV91 @ ( zero @ SV127 ) )
= ( zero @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(542,plain,
! [SV92: $i,SV105: $i,SV115: $i,SV121: $i,SV128: $i,SV136: $i] :
( ( ( ~ ( ~ ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
| ~ ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
!= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY420: $i,SY421: $i] :
( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SY421 )
| ~ ( morphism @ SV115 @ SV128 @ SY420 )
| ~ ( morphism @ SV121 @ SY420 @ SY421 ) ) )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(543,plain,
! [SV129: $i,SV122: $i,SV116: $i,SV106: $i,SV93: $i] :
( ( ( ~ ( exact @ SV93 @ SV106 ) )
= $true )
| ( ( ~ ( morphism @ SV93 @ SV116 @ SV122 ) )
= $true )
| ( ( ~ ( morphism @ SV106 @ SV122 @ SV129 ) )
= $true )
| ( ( ~ ( ~ ! [SY409: $i] :
( ( ( apply @ SV106 @ SY409 )
!= ( zero @ SV129 ) )
| ~ ( element @ SY409 @ SV122 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SY409 )
| ~ ( element @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
| ~ ~ ( ~ ! [SY410: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY410 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY410 )
= ( zero @ SV129 ) ) )
| ~ ! [SY395: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY395 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY395 @ SV122 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(544,plain,
! [SV117: $i,SV123: $i,SV94: $i] :
( ( ( ~ ( ( ( apply @ SV94 @ ( sK1_El @ SV123 @ SV117 @ SV94 ) )
!= ( zero @ SV123 ) )
| ~ ( element @ ( sK1_El @ SV123 @ SV117 @ SV94 ) @ SV117 ) ) )
= $true )
| ( ( ~ ( morphism @ SV94 @ SV117 @ SV123 ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(545,plain,
! [SV94: $i,SV117: $i,SV123: $i] :
( ( ( ( ( sK1_El @ SV123 @ SV117 @ SV94 )
!= ( zero @ SV117 ) ) )
= $true )
| ( ( ~ ( morphism @ SV94 @ SV117 @ SV123 ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(546,plain,
! [SV95: $i,SV118: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV118 @ SV95 ) @ SV118 )
| ~ ( element @ ( sK10_SY81 @ SV118 @ SV95 ) @ SV118 ) )
| ( ( apply @ SV95 @ ( sK9_El1 @ SV118 @ SV95 ) )
!= ( apply @ SV95 @ ( sK10_SY81 @ SV118 @ SV95 ) ) ) )
= $false )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(547,plain,
! [SV95: $i,SV118: $i] :
( ( ( ( sK9_El1 @ SV118 @ SV95 )
= ( sK10_SY81 @ SV118 @ SV95 ) )
= $false )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(548,plain,
! [SV130: $i,SV81: $i,SV142: $i,SV96: $i,SV138: $i] :
( ( ( ~ ( element @ SV138 @ SV96 )
| ~ ( element @ SV142 @ SV96 )
| ( ( apply @ SV81 @ SV138 )
!= ( apply @ SV81 @ SV142 ) )
| ( SV138 = SV142 ) )
= $true )
| ( ( injection @ SV81 )
= $false )
| ( ( morphism @ SV81 @ SV96 @ SV130 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(549,plain,
! [SV139: $i,SV143: $i,SV131: $i,SV124: $i,SV119: $i,SV107: $i,SV97: $i,SV82: $i] :
( ( ( ~ ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
| ~ ( morphism @ SV82 @ SV124 @ SV131 )
| ~ ( morphism @ SV97 @ SV131 @ SV143 )
| ~ ( morphism @ SV107 @ SV124 @ SV139 )
| ~ ( morphism @ SV119 @ SV139 @ SV143 ) )
= $true )
| ( ( ! [SY400: $i] :
( ~ ( element @ SY400 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY400 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY400 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(550,plain,
! [SV110: $i,SV86: $i,SV137: $i,SV101: $i,SV132: $i] :
( ( ( ~ ( element @ SV132 @ SV101 ) )
= $true )
| ( ( ~ ( element @ SV137 @ SV101 ) )
= $true )
| ( ( ( apply @ SV86 @ ( subtract @ SV101 @ SV132 @ SV137 ) )
= ( subtract @ SV110 @ ( apply @ SV86 @ SV132 ) @ ( apply @ SV86 @ SV137 ) ) )
= $true )
| ( ( morphism @ SV86 @ SV101 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(551,plain,
! [SV102: $i,SV111: $i,SV140: $i,SV87: $i] :
( ( ( ( ( apply @ SV87 @ SV140 )
!= ( zero @ SV111 ) )
| ~ ( element @ SV140 @ SV102 ) )
= $true )
| ( ( SV140
= ( zero @ SV102 ) )
= $true )
| ( ( injection_2 @ SV87 )
= $false )
| ( ( morphism @ SV87 @ SV102 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(552,plain,
! [SV103: $i,SV88: $i,SV112: $i,SV141: $i] :
( ( ( ~ ( element @ SV141 @ SV112 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV88 @ ( sK8_ElDom @ SV141 @ SV112 @ SV103 @ SV88 ) )
!= SV141 )
| ~ ( element @ ( sK8_ElDom @ SV141 @ SV112 @ SV103 @ SV88 ) @ SV103 ) ) )
= $true )
| ( ( morphism @ SV88 @ SV103 @ SV112 )
= $false )
| ( ( surjection @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(553,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV133: $i,SV104: $i] :
( ( ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( zero @ SV133 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ! [SY418: $i] :
( ( ( apply @ SV89 @ SY418 )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ SY418 @ SV113 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(554,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV133: $i,SV104: $i] :
( ( ( ~ ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
| ~ ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ~ ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(555,plain,
! [SV120: $i,SV114: $i,SV90: $i] :
( ( ( morphism @ SV90 @ SV114 @ SV120 )
= $false )
| ( ( element @ ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) @ SV120 )
= $true )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(556,plain,
! [SV114: $i,SV120: $i,SV144: $i,SV90: $i] :
( ( ( ( ( apply @ SV90 @ SV144 )
!= ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) )
| ~ ( element @ SV144 @ SV114 ) )
= $true )
| ( ( ~ ( morphism @ SV90 @ SV114 @ SV120 ) )
= $true )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(557,plain,
! [SV134: $i,SV91: $i,SV126: $i,SV145: $i] :
( ( ( ~ ( element @ SV145 @ SV126 )
| ( element @ ( apply @ SV91 @ SV145 ) @ SV134 ) )
= $true )
| ( ( morphism @ SV91 @ SV126 @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(558,plain,
! [SV92: $i,SV105: $i,SV115: $i,SV121: $i,SV128: $i,SV136: $i] :
( ( ( ~ ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
| ~ ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
!= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) ) ) )
= $false )
| ( ( ! [SY420: $i,SY421: $i] :
( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SY421 )
| ~ ( morphism @ SV115 @ SV128 @ SY420 )
| ~ ( morphism @ SV121 @ SY420 @ SY421 ) ) )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(559,plain,
! [SV129: $i,SV122: $i,SV116: $i,SV106: $i,SV93: $i] :
( ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( ~ ( morphism @ SV93 @ SV116 @ SV122 ) )
= $true )
| ( ( ~ ( morphism @ SV106 @ SV122 @ SV129 ) )
= $true )
| ( ( ~ ( ~ ! [SY409: $i] :
( ( ( apply @ SV106 @ SY409 )
!= ( zero @ SV129 ) )
| ~ ( element @ SY409 @ SV122 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SY409 )
| ~ ( element @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
| ~ ~ ( ~ ! [SY410: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY410 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY410 )
= ( zero @ SV129 ) ) )
| ~ ! [SY395: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY395 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY395 @ SV122 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(560,plain,
! [SV117: $i,SV123: $i,SV94: $i] :
( ( ( ( ( apply @ SV94 @ ( sK1_El @ SV123 @ SV117 @ SV94 ) )
!= ( zero @ SV123 ) )
| ~ ( element @ ( sK1_El @ SV123 @ SV117 @ SV94 ) @ SV117 ) )
= $false )
| ( ( ~ ( morphism @ SV94 @ SV117 @ SV123 ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(561,plain,
! [SV94: $i,SV117: $i,SV123: $i] :
( ( ( ( sK1_El @ SV123 @ SV117 @ SV94 )
= ( zero @ SV117 ) )
= $false )
| ( ( ~ ( morphism @ SV94 @ SV117 @ SV123 ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(562,plain,
! [SV95: $i,SV118: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV118 @ SV95 ) @ SV118 )
| ~ ( element @ ( sK10_SY81 @ SV118 @ SV95 ) @ SV118 ) ) )
= $false )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(563,plain,
! [SV118: $i,SV95: $i] :
( ( ( ( ( apply @ SV95 @ ( sK9_El1 @ SV118 @ SV95 ) )
!= ( apply @ SV95 @ ( sK10_SY81 @ SV118 @ SV95 ) ) ) )
= $false )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(564,plain,
! [SV146: $i,SV118: $i,SV95: $i] :
( ( ( ~ ( morphism @ SV95 @ SV118 @ SV146 ) )
= $true )
| ( ( ( sK9_El1 @ SV118 @ SV95 )
= ( sK10_SY81 @ SV118 @ SV95 ) )
= $false )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(565,plain,
! [SV130: $i,SV81: $i,SV142: $i,SV96: $i,SV138: $i] :
( ( ( ~ ( element @ SV138 @ SV96 )
| ~ ( element @ SV142 @ SV96 )
| ( ( apply @ SV81 @ SV138 )
!= ( apply @ SV81 @ SV142 ) ) )
= $true )
| ( ( SV138 = SV142 )
= $true )
| ( ( injection @ SV81 )
= $false )
| ( ( morphism @ SV81 @ SV96 @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(566,plain,
! [SV139: $i,SV143: $i,SV131: $i,SV124: $i,SV119: $i,SV107: $i,SV97: $i,SV82: $i] :
( ( ( ~ ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
| ~ ( morphism @ SV82 @ SV124 @ SV131 )
| ~ ( morphism @ SV97 @ SV131 @ SV143 )
| ~ ( morphism @ SV107 @ SV124 @ SV139 ) )
= $true )
| ( ( ~ ( morphism @ SV119 @ SV139 @ SV143 ) )
= $true )
| ( ( ! [SY400: $i] :
( ~ ( element @ SY400 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY400 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY400 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(567,plain,
! [SV110: $i,SV86: $i,SV137: $i,SV101: $i,SV132: $i] :
( ( ( element @ SV132 @ SV101 )
= $false )
| ( ( ~ ( element @ SV137 @ SV101 ) )
= $true )
| ( ( ( apply @ SV86 @ ( subtract @ SV101 @ SV132 @ SV137 ) )
= ( subtract @ SV110 @ ( apply @ SV86 @ SV132 ) @ ( apply @ SV86 @ SV137 ) ) )
= $true )
| ( ( morphism @ SV86 @ SV101 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(568,plain,
! [SV102: $i,SV111: $i,SV140: $i,SV87: $i] :
( ( ( ( ( apply @ SV87 @ SV140 )
!= ( zero @ SV111 ) ) )
= $true )
| ( ( ~ ( element @ SV140 @ SV102 ) )
= $true )
| ( ( SV140
= ( zero @ SV102 ) )
= $true )
| ( ( injection_2 @ SV87 )
= $false )
| ( ( morphism @ SV87 @ SV102 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(569,plain,
! [SV103: $i,SV88: $i,SV112: $i,SV141: $i] :
( ( ( element @ SV141 @ SV112 )
= $false )
| ( ( ~ ( ( ( apply @ SV88 @ ( sK8_ElDom @ SV141 @ SV112 @ SV103 @ SV88 ) )
!= SV141 )
| ~ ( element @ ( sK8_ElDom @ SV141 @ SV112 @ SV103 @ SV88 ) @ SV103 ) ) )
= $true )
| ( ( morphism @ SV88 @ SV103 @ SV112 )
= $false )
| ( ( surjection @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(570,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV133: $i,SV104: $i] :
( ( ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( zero @ SV133 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ! [SY418: $i] :
( ( ( apply @ SV89 @ SY418 )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ SY418 @ SV113 ) ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(571,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV133: $i,SV104: $i] :
( ( ( ~ ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
| ~ ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ~ ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) ) ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(572,plain,
! [SV114: $i,SV120: $i,SV144: $i,SV90: $i] :
( ( ( ( ( apply @ SV90 @ SV144 )
!= ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) ) )
= $true )
| ( ( ~ ( element @ SV144 @ SV114 ) )
= $true )
| ( ( ~ ( morphism @ SV90 @ SV114 @ SV120 ) )
= $true )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(573,plain,
! [SV134: $i,SV91: $i,SV126: $i,SV145: $i] :
( ( ( ~ ( element @ SV145 @ SV126 ) )
= $true )
| ( ( element @ ( apply @ SV91 @ SV145 ) @ SV134 )
= $true )
| ( ( morphism @ SV91 @ SV126 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(574,plain,
! [SV92: $i,SV105: $i,SV115: $i,SV121: $i,SV128: $i,SV136: $i] :
( ( ( ~ ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 ) )
= $false )
| ( ( ! [SY420: $i,SY421: $i] :
( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SY421 )
| ~ ( morphism @ SV115 @ SV128 @ SY420 )
| ~ ( morphism @ SV121 @ SY420 @ SY421 ) ) )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[558]) ).
thf(575,plain,
! [SV115: $i,SV121: $i,SV128: $i,SV136: $i,SV92: $i,SV105: $i] :
( ( ( ~ ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
!= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) ) ) )
= $false )
| ( ( ! [SY420: $i,SY421: $i] :
( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SY421 )
| ~ ( morphism @ SV115 @ SV128 @ SY420 )
| ~ ( morphism @ SV121 @ SY420 @ SY421 ) ) )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[558]) ).
thf(576,plain,
! [SV129: $i,SV106: $i,SV122: $i,SV116: $i,SV93: $i] :
( ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( ~ ( morphism @ SV106 @ SV122 @ SV129 ) )
= $true )
| ( ( ~ ( ~ ! [SY409: $i] :
( ( ( apply @ SV106 @ SY409 )
!= ( zero @ SV129 ) )
| ~ ( element @ SY409 @ SV122 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SY409 )
| ~ ( element @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
| ~ ~ ( ~ ! [SY410: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY410 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY410 )
= ( zero @ SV129 ) ) )
| ~ ! [SY395: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY395 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY395 @ SV122 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(577,plain,
! [SV117: $i,SV123: $i,SV94: $i] :
( ( ( ( ( apply @ SV94 @ ( sK1_El @ SV123 @ SV117 @ SV94 ) )
!= ( zero @ SV123 ) ) )
= $false )
| ( ( ~ ( morphism @ SV94 @ SV117 @ SV123 ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[560]) ).
thf(578,plain,
! [SV94: $i,SV117: $i,SV123: $i] :
( ( ( ~ ( element @ ( sK1_El @ SV123 @ SV117 @ SV94 ) @ SV117 ) )
= $false )
| ( ( ~ ( morphism @ SV94 @ SV117 @ SV123 ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[560]) ).
thf(579,plain,
! [SV123: $i,SV117: $i,SV94: $i] :
( ( ( morphism @ SV94 @ SV117 @ SV123 )
= $false )
| ( ( ( sK1_El @ SV123 @ SV117 @ SV94 )
= ( zero @ SV117 ) )
= $false )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(580,plain,
! [SV95: $i,SV118: $i] :
( ( ( ~ ( ~ ( element @ ( sK9_El1 @ SV118 @ SV95 ) @ SV118 )
| ~ ( element @ ( sK10_SY81 @ SV118 @ SV95 ) @ SV118 ) ) )
= $true )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(581,plain,
! [SV118: $i,SV95: $i] :
( ( ( ( apply @ SV95 @ ( sK9_El1 @ SV118 @ SV95 ) )
= ( apply @ SV95 @ ( sK10_SY81 @ SV118 @ SV95 ) ) )
= $true )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(582,plain,
! [SV146: $i,SV118: $i,SV95: $i] :
( ( ( morphism @ SV95 @ SV118 @ SV146 )
= $false )
| ( ( ( sK9_El1 @ SV118 @ SV95 )
= ( sK10_SY81 @ SV118 @ SV95 ) )
= $false )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(583,plain,
! [SV130: $i,SV81: $i,SV142: $i,SV96: $i,SV138: $i] :
( ( ( ~ ( element @ SV138 @ SV96 )
| ~ ( element @ SV142 @ SV96 ) )
= $true )
| ( ( ( ( apply @ SV81 @ SV138 )
!= ( apply @ SV81 @ SV142 ) ) )
= $true )
| ( ( SV138 = SV142 )
= $true )
| ( ( injection @ SV81 )
= $false )
| ( ( morphism @ SV81 @ SV96 @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(584,plain,
! [SV139: $i,SV143: $i,SV131: $i,SV124: $i,SV119: $i,SV107: $i,SV97: $i,SV82: $i] :
( ( ( ~ ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
| ~ ( morphism @ SV82 @ SV124 @ SV131 )
| ~ ( morphism @ SV97 @ SV131 @ SV143 ) )
= $true )
| ( ( ~ ( morphism @ SV107 @ SV124 @ SV139 ) )
= $true )
| ( ( ~ ( morphism @ SV119 @ SV139 @ SV143 ) )
= $true )
| ( ( ! [SY400: $i] :
( ~ ( element @ SY400 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY400 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY400 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(585,plain,
! [SV110: $i,SV86: $i,SV132: $i,SV101: $i,SV137: $i] :
( ( ( element @ SV137 @ SV101 )
= $false )
| ( ( element @ SV132 @ SV101 )
= $false )
| ( ( ( apply @ SV86 @ ( subtract @ SV101 @ SV132 @ SV137 ) )
= ( subtract @ SV110 @ ( apply @ SV86 @ SV132 ) @ ( apply @ SV86 @ SV137 ) ) )
= $true )
| ( ( morphism @ SV86 @ SV101 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(586,plain,
! [SV102: $i,SV111: $i,SV140: $i,SV87: $i] :
( ( ( ( apply @ SV87 @ SV140 )
= ( zero @ SV111 ) )
= $false )
| ( ( ~ ( element @ SV140 @ SV102 ) )
= $true )
| ( ( SV140
= ( zero @ SV102 ) )
= $true )
| ( ( injection_2 @ SV87 )
= $false )
| ( ( morphism @ SV87 @ SV102 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(587,plain,
! [SV103: $i,SV112: $i,SV141: $i,SV88: $i] :
( ( ( ( ( apply @ SV88 @ ( sK8_ElDom @ SV141 @ SV112 @ SV103 @ SV88 ) )
!= SV141 )
| ~ ( element @ ( sK8_ElDom @ SV141 @ SV112 @ SV103 @ SV88 ) @ SV103 ) )
= $false )
| ( ( element @ SV141 @ SV112 )
= $false )
| ( ( morphism @ SV88 @ SV103 @ SV112 )
= $false )
| ( ( surjection @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(588,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV133: $i,SV104: $i] :
( ( ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( zero @ SV133 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 ) )
= $true )
| ( ( ! [SY418: $i] :
( ( ( apply @ SV89 @ SY418 )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ SY418 @ SV113 ) ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(589,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV133: $i,SV104: $i] :
( ( ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
| ~ ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ~ ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(590,plain,
! [SV114: $i,SV120: $i,SV144: $i,SV90: $i] :
( ( ( ( apply @ SV90 @ SV144 )
= ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) )
= $false )
| ( ( ~ ( element @ SV144 @ SV114 ) )
= $true )
| ( ( ~ ( morphism @ SV90 @ SV114 @ SV120 ) )
= $true )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(591,plain,
! [SV134: $i,SV91: $i,SV126: $i,SV145: $i] :
( ( ( element @ SV145 @ SV126 )
= $false )
| ( ( element @ ( apply @ SV91 @ SV145 ) @ SV134 )
= $true )
| ( ( morphism @ SV91 @ SV126 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(592,plain,
! [SV92: $i,SV105: $i,SV115: $i,SV121: $i,SV128: $i,SV136: $i] :
( ( ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
= $true )
| ( ( ! [SY420: $i,SY421: $i] :
( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SY421 )
| ~ ( morphism @ SV115 @ SV128 @ SY420 )
| ~ ( morphism @ SV121 @ SY420 @ SY421 ) ) )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(593,plain,
! [SV115: $i,SV121: $i,SV128: $i,SV136: $i,SV92: $i,SV105: $i] :
( ( ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
!= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) ) )
= $true )
| ( ( ! [SY420: $i,SY421: $i] :
( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SY421 )
| ~ ( morphism @ SV115 @ SV128 @ SY420 )
| ~ ( morphism @ SV121 @ SY420 @ SY421 ) ) )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(594,plain,
! [SV116: $i,SV93: $i,SV129: $i,SV122: $i,SV106: $i] :
( ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( ~ ( ~ ! [SY409: $i] :
( ( ( apply @ SV106 @ SY409 )
!= ( zero @ SV129 ) )
| ~ ( element @ SY409 @ SV122 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SY409 )
| ~ ( element @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
| ~ ~ ( ~ ! [SY410: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY410 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY410 )
= ( zero @ SV129 ) ) )
| ~ ! [SY395: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY395 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY395 @ SV122 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(595,plain,
! [SV117: $i,SV123: $i,SV94: $i] :
( ( ( ( apply @ SV94 @ ( sK1_El @ SV123 @ SV117 @ SV94 ) )
= ( zero @ SV123 ) )
= $true )
| ( ( ~ ( morphism @ SV94 @ SV117 @ SV123 ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(596,plain,
! [SV94: $i,SV117: $i,SV123: $i] :
( ( ( element @ ( sK1_El @ SV123 @ SV117 @ SV94 ) @ SV117 )
= $true )
| ( ( ~ ( morphism @ SV94 @ SV117 @ SV123 ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(597,plain,
! [SV95: $i,SV118: $i] :
( ( ( ~ ( element @ ( sK9_El1 @ SV118 @ SV95 ) @ SV118 )
| ~ ( element @ ( sK10_SY81 @ SV118 @ SV95 ) @ SV118 ) )
= $false )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(598,plain,
! [SV147: $i,SV118: $i,SV95: $i] :
( ( ( ~ ( morphism @ SV95 @ SV118 @ SV147 ) )
= $true )
| ( ( ( apply @ SV95 @ ( sK9_El1 @ SV118 @ SV95 ) )
= ( apply @ SV95 @ ( sK10_SY81 @ SV118 @ SV95 ) ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(599,plain,
! [SV130: $i,SV81: $i,SV142: $i,SV96: $i,SV138: $i] :
( ( ( ~ ( element @ SV138 @ SV96 ) )
= $true )
| ( ( ~ ( element @ SV142 @ SV96 ) )
= $true )
| ( ( ( ( apply @ SV81 @ SV138 )
!= ( apply @ SV81 @ SV142 ) ) )
= $true )
| ( ( SV138 = SV142 )
= $true )
| ( ( injection @ SV81 )
= $false )
| ( ( morphism @ SV81 @ SV96 @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(600,plain,
! [SV139: $i,SV143: $i,SV131: $i,SV124: $i,SV119: $i,SV107: $i,SV97: $i,SV82: $i] :
( ( ( ~ ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
| ~ ( morphism @ SV82 @ SV124 @ SV131 ) )
= $true )
| ( ( ~ ( morphism @ SV97 @ SV131 @ SV143 ) )
= $true )
| ( ( ~ ( morphism @ SV107 @ SV124 @ SV139 ) )
= $true )
| ( ( ~ ( morphism @ SV119 @ SV139 @ SV143 ) )
= $true )
| ( ( ! [SY400: $i] :
( ~ ( element @ SY400 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY400 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY400 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(601,plain,
! [SV111: $i,SV87: $i,SV102: $i,SV140: $i] :
( ( ( element @ SV140 @ SV102 )
= $false )
| ( ( ( apply @ SV87 @ SV140 )
= ( zero @ SV111 ) )
= $false )
| ( ( SV140
= ( zero @ SV102 ) )
= $true )
| ( ( injection_2 @ SV87 )
= $false )
| ( ( morphism @ SV87 @ SV102 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(602,plain,
! [SV103: $i,SV112: $i,SV141: $i,SV88: $i] :
( ( ( ( ( apply @ SV88 @ ( sK8_ElDom @ SV141 @ SV112 @ SV103 @ SV88 ) )
!= SV141 ) )
= $false )
| ( ( element @ SV141 @ SV112 )
= $false )
| ( ( morphism @ SV88 @ SV103 @ SV112 )
= $false )
| ( ( surjection @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[587]) ).
thf(603,plain,
! [SV88: $i,SV103: $i,SV112: $i,SV141: $i] :
( ( ( ~ ( element @ ( sK8_ElDom @ SV141 @ SV112 @ SV103 @ SV88 ) @ SV103 ) )
= $false )
| ( ( element @ SV141 @ SV112 )
= $false )
| ( ( morphism @ SV88 @ SV103 @ SV112 )
= $false )
| ( ( surjection @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[587]) ).
thf(604,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV133: $i,SV104: $i] :
( ( ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( zero @ SV133 ) ) )
= $true )
| ( ( ~ ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 ) )
= $true )
| ( ( ! [SY418: $i] :
( ( ( apply @ SV89 @ SY418 )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ SY418 @ SV113 ) ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(605,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV133: $i,SV104: $i] :
( ( ( ~ ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
| ~ ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(606,plain,
! [SV89: $i,SV104: $i,SV113: $i,SV125: $i,SV133: $i] :
( ( ( ~ ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ~ ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(607,plain,
! [SV120: $i,SV90: $i,SV114: $i,SV144: $i] :
( ( ( element @ SV144 @ SV114 )
= $false )
| ( ( ( apply @ SV90 @ SV144 )
= ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) )
= $false )
| ( ( ~ ( morphism @ SV90 @ SV114 @ SV120 ) )
= $true )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(608,plain,
! [SV121: $i,SV148: $i,SV115: $i,SV105: $i,SV136: $i,SV128: $i,SV92: $i] :
( ( ( ! [SY424: $i] :
( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SY424 )
| ~ ( morphism @ SV115 @ SV128 @ SV148 )
| ~ ( morphism @ SV121 @ SV148 @ SY424 ) ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(609,plain,
! [SV115: $i,SV121: $i,SV128: $i,SV136: $i,SV92: $i,SV105: $i] :
( ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) )
= $false )
| ( ( ! [SY420: $i,SY421: $i] :
( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SY421 )
| ~ ( morphism @ SV115 @ SV128 @ SY420 )
| ~ ( morphism @ SV121 @ SY420 @ SY421 ) ) )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(610,plain,
! [SV116: $i,SV93: $i,SV122: $i,SV129: $i,SV106: $i] :
( ( ( ~ ! [SY409: $i] :
( ( ( apply @ SV106 @ SY409 )
!= ( zero @ SV129 ) )
| ~ ( element @ SY409 @ SV122 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SY409 )
| ~ ( element @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
| ~ ~ ( ~ ! [SY410: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY410 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY410 )
= ( zero @ SV129 ) ) )
| ~ ! [SY395: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY395 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY395 @ SV122 ) ) ) )
= $false )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(611,plain,
! [SV123: $i,SV117: $i,SV94: $i] :
( ( ( morphism @ SV94 @ SV117 @ SV123 )
= $false )
| ( ( ( apply @ SV94 @ ( sK1_El @ SV123 @ SV117 @ SV94 ) )
= ( zero @ SV123 ) )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(612,plain,
! [SV123: $i,SV117: $i,SV94: $i] :
( ( ( morphism @ SV94 @ SV117 @ SV123 )
= $false )
| ( ( element @ ( sK1_El @ SV123 @ SV117 @ SV94 ) @ SV117 )
= $true )
| ( ( injection_2 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(613,plain,
! [SV95: $i,SV118: $i] :
( ( ( ~ ( element @ ( sK9_El1 @ SV118 @ SV95 ) @ SV118 ) )
= $false )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(614,plain,
! [SV95: $i,SV118: $i] :
( ( ( ~ ( element @ ( sK10_SY81 @ SV118 @ SV95 ) @ SV118 ) )
= $false )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(615,plain,
! [SV147: $i,SV118: $i,SV95: $i] :
( ( ( morphism @ SV95 @ SV118 @ SV147 )
= $false )
| ( ( ( apply @ SV95 @ ( sK9_El1 @ SV118 @ SV95 ) )
= ( apply @ SV95 @ ( sK10_SY81 @ SV118 @ SV95 ) ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(616,plain,
! [SV130: $i,SV81: $i,SV142: $i,SV96: $i,SV138: $i] :
( ( ( element @ SV138 @ SV96 )
= $false )
| ( ( ~ ( element @ SV142 @ SV96 ) )
= $true )
| ( ( ( ( apply @ SV81 @ SV138 )
!= ( apply @ SV81 @ SV142 ) ) )
= $true )
| ( ( SV138 = SV142 )
= $true )
| ( ( injection @ SV81 )
= $false )
| ( ( morphism @ SV81 @ SV96 @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(617,plain,
! [SV139: $i,SV143: $i,SV131: $i,SV124: $i,SV119: $i,SV107: $i,SV97: $i,SV82: $i] :
( ( ( ~ ( commute @ SV82 @ SV97 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( morphism @ SV82 @ SV124 @ SV131 ) )
= $true )
| ( ( ~ ( morphism @ SV97 @ SV131 @ SV143 ) )
= $true )
| ( ( ~ ( morphism @ SV107 @ SV124 @ SV139 ) )
= $true )
| ( ( ~ ( morphism @ SV119 @ SV139 @ SV143 ) )
= $true )
| ( ( ! [SY400: $i] :
( ~ ( element @ SY400 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY400 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY400 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(618,plain,
! [SV103: $i,SV112: $i,SV141: $i,SV88: $i] :
( ( ( ( apply @ SV88 @ ( sK8_ElDom @ SV141 @ SV112 @ SV103 @ SV88 ) )
= SV141 )
= $true )
| ( ( element @ SV141 @ SV112 )
= $false )
| ( ( morphism @ SV88 @ SV103 @ SV112 )
= $false )
| ( ( surjection @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[602]) ).
thf(619,plain,
! [SV88: $i,SV103: $i,SV112: $i,SV141: $i] :
( ( ( element @ ( sK8_ElDom @ SV141 @ SV112 @ SV103 @ SV88 ) @ SV103 )
= $true )
| ( ( element @ SV141 @ SV112 )
= $false )
| ( ( morphism @ SV88 @ SV103 @ SV112 )
= $false )
| ( ( surjection @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[603]) ).
thf(620,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV133: $i,SV104: $i] :
( ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $false )
| ( ( ~ ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 ) )
= $true )
| ( ( ! [SY418: $i] :
( ( ( apply @ SV89 @ SY418 )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ SY418 @ SV113 ) ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(621,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV133: $i,SV104: $i] :
( ( ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
| ~ ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[605]) ).
thf(622,plain,
! [SV89: $i,SV104: $i,SV113: $i,SV125: $i,SV133: $i] :
( ( ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
| ~ ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(623,plain,
! [SV144: $i,SV120: $i,SV114: $i,SV90: $i] :
( ( ( morphism @ SV90 @ SV114 @ SV120 )
= $false )
| ( ( ( apply @ SV90 @ SV144 )
= ( sK7_ElCod @ SV120 @ SV114 @ SV90 ) )
= $false )
| ( ( element @ SV144 @ SV114 )
= $false )
| ( ( surjection @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(624,plain,
! [SV121: $i,SV148: $i,SV115: $i,SV149: $i,SV105: $i,SV136: $i,SV128: $i,SV92: $i] :
( ( ( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SV149 )
| ~ ( morphism @ SV115 @ SV128 @ SV148 )
| ~ ( morphism @ SV121 @ SV148 @ SV149 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(625,plain,
! [SV121: $i,SV150: $i,SV115: $i,SV105: $i,SV136: $i,SV128: $i,SV92: $i] :
( ( ( ! [SY425: $i] :
( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SY425 )
| ~ ( morphism @ SV115 @ SV128 @ SV150 )
| ~ ( morphism @ SV121 @ SV150 @ SY425 ) ) )
= $true )
| ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) )
= $false )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(626,plain,
! [SV116: $i,SV93: $i,SV122: $i,SV129: $i,SV106: $i] :
( ( ( ~ ! [SY409: $i] :
( ( ( apply @ SV106 @ SY409 )
!= ( zero @ SV129 ) )
| ~ ( element @ SY409 @ SV122 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SY409 )
| ~ ( element @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) ) )
= $false )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(627,plain,
! [SV122: $i,SV129: $i,SV106: $i,SV116: $i,SV93: $i] :
( ( ( ~ ~ ( ~ ! [SY410: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY410 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY410 )
= ( zero @ SV129 ) ) )
| ~ ! [SY395: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY395 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY395 @ SV122 ) ) ) )
= $false )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(628,plain,
! [SV95: $i,SV118: $i] :
( ( ( element @ ( sK9_El1 @ SV118 @ SV95 ) @ SV118 )
= $true )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[613]) ).
thf(629,plain,
! [SV95: $i,SV118: $i] :
( ( ( element @ ( sK10_SY81 @ SV118 @ SV95 ) @ SV118 )
= $true )
| ( ( ! [SY380: $i] :
~ ( morphism @ SV95 @ SV118 @ SY380 ) )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[614]) ).
thf(630,plain,
! [SV130: $i,SV81: $i,SV138: $i,SV96: $i,SV142: $i] :
( ( ( element @ SV142 @ SV96 )
= $false )
| ( ( element @ SV138 @ SV96 )
= $false )
| ( ( ( ( apply @ SV81 @ SV138 )
!= ( apply @ SV81 @ SV142 ) ) )
= $true )
| ( ( SV138 = SV142 )
= $true )
| ( ( injection @ SV81 )
= $false )
| ( ( morphism @ SV81 @ SV96 @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(631,plain,
! [SV139: $i,SV143: $i,SV131: $i,SV124: $i,SV119: $i,SV107: $i,SV97: $i,SV82: $i] :
( ( ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
= $false )
| ( ( ~ ( morphism @ SV82 @ SV124 @ SV131 ) )
= $true )
| ( ( ~ ( morphism @ SV97 @ SV131 @ SV143 ) )
= $true )
| ( ( ~ ( morphism @ SV107 @ SV124 @ SV139 ) )
= $true )
| ( ( ~ ( morphism @ SV119 @ SV139 @ SV143 ) )
= $true )
| ( ( ! [SY400: $i] :
( ~ ( element @ SY400 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY400 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY400 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(632,plain,
! [SV89: $i,SV104: $i,SV113: $i,SV125: $i,SV133: $i] :
( ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $false )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $false )
| ( ( ! [SY418: $i] :
( ( ( apply @ SV89 @ SY418 )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ SY418 @ SV113 ) ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(633,plain,
! [SV89: $i,SV113: $i,SV125: $i,SV133: $i,SV104: $i] :
( ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(634,plain,
! [SV89: $i,SV104: $i,SV113: $i,SV125: $i,SV133: $i] :
( ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $true )
| ( ( ~ ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(635,plain,
! [SV121: $i,SV148: $i,SV115: $i,SV149: $i,SV105: $i,SV136: $i,SV128: $i,SV92: $i] :
( ( ( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SV149 )
| ~ ( morphism @ SV115 @ SV128 @ SV148 ) )
= $true )
| ( ( ~ ( morphism @ SV121 @ SV148 @ SV149 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(636,plain,
! [SV121: $i,SV150: $i,SV115: $i,SV151: $i,SV105: $i,SV136: $i,SV128: $i,SV92: $i] :
( ( ( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SV151 )
| ~ ( morphism @ SV115 @ SV128 @ SV150 )
| ~ ( morphism @ SV121 @ SV150 @ SV151 ) )
= $true )
| ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) )
= $false )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(637,plain,
! [SV116: $i,SV93: $i,SV122: $i,SV129: $i,SV106: $i] :
( ( ( ! [SY409: $i] :
( ( ( apply @ SV106 @ SY409 )
!= ( zero @ SV129 ) )
| ~ ( element @ SY409 @ SV122 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SY409 )
| ~ ( element @ ( sK6_ElDom @ SY409 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(638,plain,
! [SV122: $i,SV129: $i,SV106: $i,SV116: $i,SV93: $i] :
( ( ( ~ ( ~ ! [SY410: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY410 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY410 )
= ( zero @ SV129 ) ) )
| ~ ! [SY395: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY395 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY395 @ SV122 ) ) ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[627]) ).
thf(639,plain,
! [SV152: $i,SV118: $i,SV95: $i] :
( ( ( ~ ( morphism @ SV95 @ SV118 @ SV152 ) )
= $true )
| ( ( element @ ( sK9_El1 @ SV118 @ SV95 ) @ SV118 )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(640,plain,
! [SV153: $i,SV118: $i,SV95: $i] :
( ( ( ~ ( morphism @ SV95 @ SV118 @ SV153 ) )
= $true )
| ( ( element @ ( sK10_SY81 @ SV118 @ SV95 ) @ SV118 )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(641,plain,
! [SV130: $i,SV96: $i,SV142: $i,SV138: $i,SV81: $i] :
( ( ( ( apply @ SV81 @ SV138 )
= ( apply @ SV81 @ SV142 ) )
= $false )
| ( ( element @ SV138 @ SV96 )
= $false )
| ( ( element @ SV142 @ SV96 )
= $false )
| ( ( SV138 = SV142 )
= $true )
| ( ( injection @ SV81 )
= $false )
| ( ( morphism @ SV81 @ SV96 @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(642,plain,
! [SV139: $i,SV143: $i,SV119: $i,SV107: $i,SV97: $i,SV131: $i,SV124: $i,SV82: $i] :
( ( ( morphism @ SV82 @ SV124 @ SV131 )
= $false )
| ( ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
= $false )
| ( ( ~ ( morphism @ SV97 @ SV131 @ SV143 ) )
= $true )
| ( ( ~ ( morphism @ SV107 @ SV124 @ SV139 ) )
= $true )
| ( ( ~ ( morphism @ SV119 @ SV139 @ SV143 ) )
= $true )
| ( ( ! [SY400: $i] :
( ~ ( element @ SY400 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY400 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY400 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(643,plain,
! [SV104: $i,SV113: $i,SV125: $i,SV133: $i,SV154: $i,SV89: $i] :
( ( ( ( ( apply @ SV89 @ SV154 )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ SV154 @ SV113 ) )
= $true )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $false )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(644,plain,
! [SV104: $i,SV113: $i,SV125: $i,SV133: $i,SV89: $i] :
( ( ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) )
= $false )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(645,plain,
! [SV104: $i,SV113: $i,SV125: $i,SV133: $i,SV89: $i] :
( ( ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
| ~ ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(646,plain,
! [SV121: $i,SV148: $i,SV115: $i,SV149: $i,SV105: $i,SV136: $i,SV128: $i,SV92: $i] :
( ( ( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SV149 ) )
= $true )
| ( ( ~ ( morphism @ SV115 @ SV128 @ SV148 ) )
= $true )
| ( ( ~ ( morphism @ SV121 @ SV148 @ SV149 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(647,plain,
! [SV121: $i,SV150: $i,SV115: $i,SV151: $i,SV105: $i,SV136: $i,SV128: $i,SV92: $i] :
( ( ( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SV151 )
| ~ ( morphism @ SV115 @ SV128 @ SV150 ) )
= $true )
| ( ( ~ ( morphism @ SV121 @ SV150 @ SV151 ) )
= $true )
| ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) )
= $false )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(648,plain,
! [SV116: $i,SV93: $i,SV122: $i,SV129: $i,SV155: $i,SV106: $i] :
( ( ( ( ( apply @ SV106 @ SV155 )
!= ( zero @ SV129 ) )
| ~ ( element @ SV155 @ SV122 )
| ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SV155 )
| ~ ( element @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(649,plain,
! [SV122: $i,SV129: $i,SV106: $i,SV116: $i,SV93: $i] :
( ( ( ~ ! [SY410: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY410 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY410 )
= ( zero @ SV129 ) ) )
| ~ ! [SY395: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY395 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY395 @ SV122 ) ) )
= $false )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(650,plain,
! [SV152: $i,SV118: $i,SV95: $i] :
( ( ( morphism @ SV95 @ SV118 @ SV152 )
= $false )
| ( ( element @ ( sK9_El1 @ SV118 @ SV95 ) @ SV118 )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(651,plain,
! [SV153: $i,SV118: $i,SV95: $i] :
( ( ( morphism @ SV95 @ SV118 @ SV153 )
= $false )
| ( ( element @ ( sK10_SY81 @ SV118 @ SV95 ) @ SV118 )
= $true )
| ( ( injection @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(652,plain,
! [SV139: $i,SV124: $i,SV119: $i,SV107: $i,SV82: $i,SV143: $i,SV131: $i,SV97: $i] :
( ( ( morphism @ SV97 @ SV131 @ SV143 )
= $false )
| ( ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
= $false )
| ( ( morphism @ SV82 @ SV124 @ SV131 )
= $false )
| ( ( ~ ( morphism @ SV107 @ SV124 @ SV139 ) )
= $true )
| ( ( ~ ( morphism @ SV119 @ SV139 @ SV143 ) )
= $true )
| ( ( ! [SY400: $i] :
( ~ ( element @ SY400 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY400 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY400 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(653,plain,
! [SV104: $i,SV113: $i,SV125: $i,SV133: $i,SV154: $i,SV89: $i] :
( ( ( ( ( apply @ SV89 @ SV154 )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) ) )
= $true )
| ( ( ~ ( element @ SV154 @ SV113 ) )
= $true )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $false )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(654,plain,
! [SV104: $i,SV113: $i,SV125: $i,SV133: $i,SV89: $i] :
( ( ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) ) )
= $false )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[644]) ).
thf(655,plain,
! [SV89: $i,SV104: $i,SV113: $i,SV125: $i,SV133: $i] :
( ( ( ~ ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) )
= $false )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[644]) ).
thf(656,plain,
! [SV104: $i,SV113: $i,SV125: $i,SV133: $i,SV89: $i] :
( ( ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
!= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(657,plain,
! [SV89: $i,SV104: $i,SV113: $i,SV125: $i,SV133: $i] :
( ( ( ~ ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(658,plain,
! [SV121: $i,SV148: $i,SV115: $i,SV149: $i,SV105: $i,SV136: $i,SV128: $i,SV92: $i] :
( ( ( ~ ( morphism @ SV92 @ SV128 @ SV136 ) )
= $true )
| ( ( ~ ( morphism @ SV105 @ SV136 @ SV149 ) )
= $true )
| ( ( ~ ( morphism @ SV115 @ SV128 @ SV148 ) )
= $true )
| ( ( ~ ( morphism @ SV121 @ SV148 @ SV149 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(659,plain,
! [SV121: $i,SV150: $i,SV115: $i,SV151: $i,SV105: $i,SV136: $i,SV128: $i,SV92: $i] :
( ( ( ~ ( morphism @ SV92 @ SV128 @ SV136 )
| ~ ( morphism @ SV105 @ SV136 @ SV151 ) )
= $true )
| ( ( ~ ( morphism @ SV115 @ SV128 @ SV150 ) )
= $true )
| ( ( ~ ( morphism @ SV121 @ SV150 @ SV151 ) )
= $true )
| ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) )
= $false )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(660,plain,
! [SV116: $i,SV93: $i,SV122: $i,SV129: $i,SV155: $i,SV106: $i] :
( ( ( ( ( apply @ SV106 @ SV155 )
!= ( zero @ SV129 ) )
| ~ ( element @ SV155 @ SV122 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SV155 )
| ~ ( element @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(661,plain,
! [SV122: $i,SV129: $i,SV106: $i,SV116: $i,SV93: $i] :
( ( ( ~ ! [SY410: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY410 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY410 )
= ( zero @ SV129 ) ) ) )
= $false )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[649]) ).
thf(662,plain,
! [SV129: $i,SV106: $i,SV122: $i,SV116: $i,SV93: $i] :
( ( ( ~ ! [SY395: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY395 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY395 @ SV122 ) ) )
= $false )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[649]) ).
thf(663,plain,
! [SV143: $i,SV119: $i,SV97: $i,SV131: $i,SV82: $i,SV139: $i,SV124: $i,SV107: $i] :
( ( ( morphism @ SV107 @ SV124 @ SV139 )
= $false )
| ( ( morphism @ SV82 @ SV124 @ SV131 )
= $false )
| ( ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
= $false )
| ( ( morphism @ SV97 @ SV131 @ SV143 )
= $false )
| ( ( ~ ( morphism @ SV119 @ SV139 @ SV143 ) )
= $true )
| ( ( ! [SY400: $i] :
( ~ ( element @ SY400 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY400 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY400 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(664,plain,
! [SV104: $i,SV113: $i,SV125: $i,SV133: $i,SV154: $i,SV89: $i] :
( ( ( ( apply @ SV89 @ SV154 )
= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= $false )
| ( ( ~ ( element @ SV154 @ SV113 ) )
= $true )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $false )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(665,plain,
! [SV104: $i,SV113: $i,SV125: $i,SV133: $i,SV89: $i] :
( ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= $true )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[654]) ).
thf(666,plain,
! [SV89: $i,SV104: $i,SV113: $i,SV125: $i,SV133: $i] :
( ( ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 )
= $true )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[655]) ).
thf(667,plain,
! [SV104: $i,SV113: $i,SV125: $i,SV133: $i,SV89: $i] :
( ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[656]) ).
thf(668,plain,
! [SV89: $i,SV104: $i,SV113: $i,SV125: $i,SV133: $i] :
( ( ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $true )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[657]) ).
thf(669,plain,
! [SV121: $i,SV148: $i,SV115: $i,SV149: $i,SV105: $i,SV136: $i,SV128: $i,SV92: $i] :
( ( ( morphism @ SV92 @ SV128 @ SV136 )
= $false )
| ( ( ~ ( morphism @ SV105 @ SV136 @ SV149 ) )
= $true )
| ( ( ~ ( morphism @ SV115 @ SV128 @ SV148 ) )
= $true )
| ( ( ~ ( morphism @ SV121 @ SV148 @ SV149 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(670,plain,
! [SV121: $i,SV150: $i,SV115: $i,SV151: $i,SV105: $i,SV136: $i,SV128: $i,SV92: $i] :
( ( ( ~ ( morphism @ SV92 @ SV128 @ SV136 ) )
= $true )
| ( ( ~ ( morphism @ SV105 @ SV136 @ SV151 ) )
= $true )
| ( ( ~ ( morphism @ SV115 @ SV128 @ SV150 ) )
= $true )
| ( ( ~ ( morphism @ SV121 @ SV150 @ SV151 ) )
= $true )
| ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) )
= $false )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(671,plain,
! [SV116: $i,SV93: $i,SV122: $i,SV129: $i,SV155: $i,SV106: $i] :
( ( ( ( ( apply @ SV106 @ SV155 )
!= ( zero @ SV129 ) ) )
= $true )
| ( ( ~ ( element @ SV155 @ SV122 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SV155 )
| ~ ( element @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(672,plain,
! [SV122: $i,SV129: $i,SV106: $i,SV116: $i,SV93: $i] :
( ( ( ! [SY410: $i] :
( ! [SY376: $i] :
( ( ( apply @ SV93 @ SY376 )
!= SY410 )
| ~ ( element @ SY376 @ SV116 ) )
| ( ( apply @ SV106 @ SY410 )
= ( zero @ SV129 ) ) ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[661]) ).
thf(673,plain,
! [SV129: $i,SV106: $i,SV122: $i,SV116: $i,SV93: $i] :
( ( ( ! [SY395: $i] :
( ! [SY378: $i] :
( ( ( apply @ SV93 @ SY378 )
!= SY395 )
| ~ ( element @ SY378 @ SV116 ) )
| ( element @ SY395 @ SV122 ) ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[662]) ).
thf(674,plain,
! [SV124: $i,SV107: $i,SV82: $i,SV131: $i,SV97: $i,SV143: $i,SV139: $i,SV119: $i] :
( ( ( morphism @ SV119 @ SV139 @ SV143 )
= $false )
| ( ( morphism @ SV97 @ SV131 @ SV143 )
= $false )
| ( ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
= $false )
| ( ( morphism @ SV82 @ SV124 @ SV131 )
= $false )
| ( ( morphism @ SV107 @ SV124 @ SV139 )
= $false )
| ( ( ! [SY400: $i] :
( ~ ( element @ SY400 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SY400 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SY400 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(675,plain,
! [SV104: $i,SV125: $i,SV133: $i,SV89: $i,SV113: $i,SV154: $i] :
( ( ( element @ SV154 @ SV113 )
= $false )
| ( ( ( apply @ SV89 @ SV154 )
= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= $false )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $false )
| ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 )
| ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(676,plain,
! [SV133: $i,SV104: $i,SV125: $i,SV113: $i,SV89: $i] :
( ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 ) )
= $true )
| ( ( ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $true )
| ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(677,plain,
! [SV133: $i,SV104: $i,SV125: $i,SV113: $i,SV89: $i] :
( ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 ) )
= $true )
| ( ( ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $true )
| ( ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(678,plain,
! [SV133: $i,SV104: $i,SV125: $i,SV113: $i,SV89: $i] :
( ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 ) )
= $true )
| ( ( ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $true )
| ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[667]) ).
thf(679,plain,
! [SV133: $i,SV104: $i,SV125: $i,SV113: $i,SV89: $i] :
( ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 ) )
= $true )
| ( ( ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $true )
| ( ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(680,plain,
! [SV121: $i,SV148: $i,SV115: $i,SV128: $i,SV92: $i,SV149: $i,SV136: $i,SV105: $i] :
( ( ( morphism @ SV105 @ SV136 @ SV149 )
= $false )
| ( ( morphism @ SV92 @ SV128 @ SV136 )
= $false )
| ( ( ~ ( morphism @ SV115 @ SV128 @ SV148 ) )
= $true )
| ( ( ~ ( morphism @ SV121 @ SV148 @ SV149 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(681,plain,
! [SV121: $i,SV150: $i,SV115: $i,SV151: $i,SV105: $i,SV136: $i,SV128: $i,SV92: $i] :
( ( ( morphism @ SV92 @ SV128 @ SV136 )
= $false )
| ( ( ~ ( morphism @ SV105 @ SV136 @ SV151 ) )
= $true )
| ( ( ~ ( morphism @ SV115 @ SV128 @ SV150 ) )
= $true )
| ( ( ~ ( morphism @ SV121 @ SV150 @ SV151 ) )
= $true )
| ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) )
= $false )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(682,plain,
! [SV116: $i,SV93: $i,SV122: $i,SV129: $i,SV155: $i,SV106: $i] :
( ( ( ( apply @ SV106 @ SV155 )
= ( zero @ SV129 ) )
= $false )
| ( ( ~ ( element @ SV155 @ SV122 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SV155 )
| ~ ( element @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(683,plain,
! [SV122: $i,SV129: $i,SV106: $i,SV116: $i,SV156: $i,SV93: $i] :
( ( ( ! [SY426: $i] :
( ( ( apply @ SV93 @ SY426 )
!= SV156 )
| ~ ( element @ SY426 @ SV116 ) )
| ( ( apply @ SV106 @ SV156 )
= ( zero @ SV129 ) ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(684,plain,
! [SV129: $i,SV106: $i,SV122: $i,SV116: $i,SV157: $i,SV93: $i] :
( ( ( ! [SY427: $i] :
( ( ( apply @ SV93 @ SY427 )
!= SV157 )
| ~ ( element @ SY427 @ SV116 ) )
| ( element @ SV157 @ SV122 ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(685,plain,
! [SV143: $i,SV131: $i,SV139: $i,SV107: $i,SV119: $i,SV82: $i,SV97: $i,SV124: $i,SV158: $i] :
( ( ( ~ ( element @ SV158 @ SV124 )
| ( ( apply @ SV97 @ ( apply @ SV82 @ SV158 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SV158 ) ) ) )
= $true )
| ( ( morphism @ SV107 @ SV124 @ SV139 )
= $false )
| ( ( morphism @ SV82 @ SV124 @ SV131 )
= $false )
| ( ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
= $false )
| ( ( morphism @ SV97 @ SV131 @ SV143 )
= $false )
| ( ( morphism @ SV119 @ SV139 @ SV143 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(686,plain,
! [SV154: $i,SV133: $i,SV104: $i,SV125: $i,SV113: $i,SV89: $i] :
( ( ( ~ ( morphism @ SV89 @ SV113 @ SV125 ) )
= $true )
| ( ( ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $false )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $false )
| ( ( ( apply @ SV89 @ SV154 )
= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= $false )
| ( ( element @ SV154 @ SV113 )
= $false )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(687,plain,
! [SV133: $i,SV104: $i,SV125: $i,SV113: $i,SV89: $i] :
( ( ( morphism @ SV89 @ SV113 @ SV125 )
= $false )
| ( ( ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $true )
| ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(688,plain,
! [SV133: $i,SV104: $i,SV125: $i,SV113: $i,SV89: $i] :
( ( ( morphism @ SV89 @ SV113 @ SV125 )
= $false )
| ( ( ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $true )
| ( ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(689,plain,
! [SV133: $i,SV104: $i,SV125: $i,SV113: $i,SV89: $i] :
( ( ( morphism @ SV89 @ SV113 @ SV125 )
= $false )
| ( ( ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $true )
| ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(690,plain,
! [SV133: $i,SV104: $i,SV125: $i,SV113: $i,SV89: $i] :
( ( ( morphism @ SV89 @ SV113 @ SV125 )
= $false )
| ( ( ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $true )
| ( ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(691,plain,
! [SV121: $i,SV149: $i,SV105: $i,SV136: $i,SV92: $i,SV148: $i,SV128: $i,SV115: $i] :
( ( ( morphism @ SV115 @ SV128 @ SV148 )
= $false )
| ( ( morphism @ SV92 @ SV128 @ SV136 )
= $false )
| ( ( morphism @ SV105 @ SV136 @ SV149 )
= $false )
| ( ( ~ ( morphism @ SV121 @ SV148 @ SV149 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(692,plain,
! [SV121: $i,SV150: $i,SV115: $i,SV128: $i,SV92: $i,SV151: $i,SV136: $i,SV105: $i] :
( ( ( morphism @ SV105 @ SV136 @ SV151 )
= $false )
| ( ( morphism @ SV92 @ SV128 @ SV136 )
= $false )
| ( ( ~ ( morphism @ SV115 @ SV128 @ SV150 ) )
= $true )
| ( ( ~ ( morphism @ SV121 @ SV150 @ SV151 ) )
= $true )
| ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) )
= $false )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(693,plain,
! [SV116: $i,SV93: $i,SV129: $i,SV106: $i,SV122: $i,SV155: $i] :
( ( ( element @ SV155 @ SV122 )
= $false )
| ( ( ( apply @ SV106 @ SV155 )
= ( zero @ SV129 ) )
= $false )
| ( ( ~ ( ( ( apply @ SV93 @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SV155 )
| ~ ( element @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(694,plain,
! [SV122: $i,SV129: $i,SV106: $i,SV116: $i,SV156: $i,SV93: $i] :
( ( ( ! [SY426: $i] :
( ( ( apply @ SV93 @ SY426 )
!= SV156 )
| ~ ( element @ SY426 @ SV116 ) ) )
= $true )
| ( ( ( apply @ SV106 @ SV156 )
= ( zero @ SV129 ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(695,plain,
! [SV129: $i,SV106: $i,SV122: $i,SV116: $i,SV157: $i,SV93: $i] :
( ( ( ! [SY427: $i] :
( ( ( apply @ SV93 @ SY427 )
!= SV157 )
| ~ ( element @ SY427 @ SV116 ) ) )
= $true )
| ( ( element @ SV157 @ SV122 )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[684]) ).
thf(696,plain,
! [SV143: $i,SV131: $i,SV139: $i,SV107: $i,SV119: $i,SV82: $i,SV97: $i,SV124: $i,SV158: $i] :
( ( ( ~ ( element @ SV158 @ SV124 ) )
= $true )
| ( ( ( apply @ SV97 @ ( apply @ SV82 @ SV158 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SV158 ) ) )
= $true )
| ( ( morphism @ SV107 @ SV124 @ SV139 )
= $false )
| ( ( morphism @ SV82 @ SV124 @ SV131 )
= $false )
| ( ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
= $false )
| ( ( morphism @ SV97 @ SV131 @ SV143 )
= $false )
| ( ( morphism @ SV119 @ SV139 @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(697,plain,
! [SV154: $i,SV133: $i,SV104: $i,SV125: $i,SV113: $i,SV89: $i] :
( ( ( morphism @ SV89 @ SV113 @ SV125 )
= $false )
| ( ( ~ ( morphism @ SV104 @ SV125 @ SV133 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $false )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $false )
| ( ( ( apply @ SV89 @ SV154 )
= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= $false )
| ( ( element @ SV154 @ SV113 )
= $false )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(698,plain,
! [SV113: $i,SV89: $i,SV133: $i,SV125: $i,SV104: $i] :
( ( ( morphism @ SV104 @ SV125 @ SV133 )
= $false )
| ( ( morphism @ SV89 @ SV113 @ SV125 )
= $false )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $true )
| ( ( ( apply @ SV89 @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(699,plain,
! [SV113: $i,SV89: $i,SV133: $i,SV125: $i,SV104: $i] :
( ( ( morphism @ SV104 @ SV125 @ SV133 )
= $false )
| ( ( morphism @ SV89 @ SV113 @ SV125 )
= $false )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $true )
| ( ( element @ ( sK5_SY78 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(700,plain,
! [SV113: $i,SV89: $i,SV133: $i,SV125: $i,SV104: $i] :
( ( ( morphism @ SV104 @ SV125 @ SV133 )
= $false )
| ( ( morphism @ SV89 @ SV113 @ SV125 )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $true )
| ( ( ( apply @ SV89 @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(701,plain,
! [SV113: $i,SV89: $i,SV133: $i,SV125: $i,SV104: $i] :
( ( ( morphism @ SV104 @ SV125 @ SV133 )
= $false )
| ( ( morphism @ SV89 @ SV113 @ SV125 )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $true )
| ( ( element @ ( sK4_SY79 @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV113 )
= $true )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(702,plain,
! [SV115: $i,SV128: $i,SV92: $i,SV136: $i,SV105: $i,SV149: $i,SV148: $i,SV121: $i] :
( ( ( morphism @ SV121 @ SV148 @ SV149 )
= $false )
| ( ( morphism @ SV105 @ SV136 @ SV149 )
= $false )
| ( ( morphism @ SV92 @ SV128 @ SV136 )
= $false )
| ( ( morphism @ SV115 @ SV128 @ SV148 )
= $false )
| ( ( element @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) @ SV128 )
= $true )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(703,plain,
! [SV121: $i,SV151: $i,SV105: $i,SV136: $i,SV92: $i,SV150: $i,SV128: $i,SV115: $i] :
( ( ( morphism @ SV115 @ SV128 @ SV150 )
= $false )
| ( ( morphism @ SV92 @ SV128 @ SV136 )
= $false )
| ( ( morphism @ SV105 @ SV136 @ SV151 )
= $false )
| ( ( ~ ( morphism @ SV121 @ SV150 @ SV151 ) )
= $true )
| ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) )
= $false )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(704,plain,
! [SV106: $i,SV116: $i,SV122: $i,SV129: $i,SV155: $i,SV93: $i] :
( ( ( ( ( apply @ SV93 @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SV155 )
| ~ ( element @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) )
= $false )
| ( ( ( apply @ SV106 @ SV155 )
= ( zero @ SV129 ) )
= $false )
| ( ( element @ SV155 @ SV122 )
= $false )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(705,plain,
! [SV122: $i,SV129: $i,SV106: $i,SV116: $i,SV156: $i,SV159: $i,SV93: $i] :
( ( ( ( ( apply @ SV93 @ SV159 )
!= SV156 )
| ~ ( element @ SV159 @ SV116 ) )
= $true )
| ( ( ( apply @ SV106 @ SV156 )
= ( zero @ SV129 ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(706,plain,
! [SV129: $i,SV106: $i,SV122: $i,SV116: $i,SV157: $i,SV160: $i,SV93: $i] :
( ( ( ( ( apply @ SV93 @ SV160 )
!= SV157 )
| ~ ( element @ SV160 @ SV116 ) )
= $true )
| ( ( element @ SV157 @ SV122 )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(707,plain,
! [SV143: $i,SV131: $i,SV139: $i,SV107: $i,SV119: $i,SV82: $i,SV97: $i,SV124: $i,SV158: $i] :
( ( ( element @ SV158 @ SV124 )
= $false )
| ( ( ( apply @ SV97 @ ( apply @ SV82 @ SV158 ) )
= ( apply @ SV119 @ ( apply @ SV107 @ SV158 ) ) )
= $true )
| ( ( morphism @ SV107 @ SV124 @ SV139 )
= $false )
| ( ( morphism @ SV82 @ SV124 @ SV131 )
= $false )
| ( ( commute @ SV82 @ SV97 @ SV107 @ SV119 )
= $false )
| ( ( morphism @ SV97 @ SV131 @ SV143 )
= $false )
| ( ( morphism @ SV119 @ SV139 @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(708,plain,
! [SV154: $i,SV113: $i,SV89: $i,SV133: $i,SV125: $i,SV104: $i] :
( ( ( morphism @ SV104 @ SV125 @ SV133 )
= $false )
| ( ( morphism @ SV89 @ SV113 @ SV125 )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) @ SV125 )
= $false )
| ( ( ( apply @ SV104 @ ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= ( zero @ SV133 ) )
= $false )
| ( ( ( apply @ SV89 @ SV154 )
= ( sK3_ElCodDom @ SV133 @ SV125 @ SV113 @ SV104 @ SV89 ) )
= $false )
| ( ( element @ SV154 @ SV113 )
= $false )
| ( ( exact @ SV89 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(709,plain,
! [SV115: $i,SV128: $i,SV92: $i,SV136: $i,SV105: $i,SV151: $i,SV150: $i,SV121: $i] :
( ( ( morphism @ SV121 @ SV150 @ SV151 )
= $false )
| ( ( morphism @ SV105 @ SV136 @ SV151 )
= $false )
| ( ( morphism @ SV92 @ SV128 @ SV136 )
= $false )
| ( ( morphism @ SV115 @ SV128 @ SV150 )
= $false )
| ( ( ( apply @ SV105 @ ( apply @ SV92 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) )
= ( apply @ SV121 @ ( apply @ SV115 @ ( sK2_ElDom @ SV136 @ SV128 @ SV121 @ SV115 @ SV105 @ SV92 ) ) ) )
= $false )
| ( ( commute @ SV92 @ SV105 @ SV115 @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(710,plain,
! [SV106: $i,SV116: $i,SV122: $i,SV129: $i,SV155: $i,SV93: $i] :
( ( ( ( ( apply @ SV93 @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
!= SV155 ) )
= $false )
| ( ( ( apply @ SV106 @ SV155 )
= ( zero @ SV129 ) )
= $false )
| ( ( element @ SV155 @ SV122 )
= $false )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(711,plain,
! [SV93: $i,SV106: $i,SV116: $i,SV122: $i,SV129: $i,SV155: $i] :
( ( ( ~ ( element @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 ) )
= $false )
| ( ( ( apply @ SV106 @ SV155 )
= ( zero @ SV129 ) )
= $false )
| ( ( element @ SV155 @ SV122 )
= $false )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(712,plain,
! [SV122: $i,SV129: $i,SV106: $i,SV116: $i,SV156: $i,SV159: $i,SV93: $i] :
( ( ( ( ( apply @ SV93 @ SV159 )
!= SV156 ) )
= $true )
| ( ( ~ ( element @ SV159 @ SV116 ) )
= $true )
| ( ( ( apply @ SV106 @ SV156 )
= ( zero @ SV129 ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(713,plain,
! [SV129: $i,SV106: $i,SV122: $i,SV116: $i,SV157: $i,SV160: $i,SV93: $i] :
( ( ( ( ( apply @ SV93 @ SV160 )
!= SV157 ) )
= $true )
| ( ( ~ ( element @ SV160 @ SV116 ) )
= $true )
| ( ( element @ SV157 @ SV122 )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(714,plain,
! [SV106: $i,SV116: $i,SV122: $i,SV129: $i,SV155: $i,SV93: $i] :
( ( ( ( apply @ SV93 @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) )
= SV155 )
= $true )
| ( ( ( apply @ SV106 @ SV155 )
= ( zero @ SV129 ) )
= $false )
| ( ( element @ SV155 @ SV122 )
= $false )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(715,plain,
! [SV93: $i,SV106: $i,SV116: $i,SV122: $i,SV129: $i,SV155: $i] :
( ( ( element @ ( sK6_ElDom @ SV155 @ SV129 @ SV122 @ SV116 @ SV106 @ SV93 ) @ SV116 )
= $true )
| ( ( ( apply @ SV106 @ SV155 )
= ( zero @ SV129 ) )
= $false )
| ( ( element @ SV155 @ SV122 )
= $false )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[711]) ).
thf(716,plain,
! [SV122: $i,SV129: $i,SV106: $i,SV116: $i,SV156: $i,SV159: $i,SV93: $i] :
( ( ( ( apply @ SV93 @ SV159 )
= SV156 )
= $false )
| ( ( ~ ( element @ SV159 @ SV116 ) )
= $true )
| ( ( ( apply @ SV106 @ SV156 )
= ( zero @ SV129 ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(717,plain,
! [SV129: $i,SV106: $i,SV122: $i,SV116: $i,SV157: $i,SV160: $i,SV93: $i] :
( ( ( ( apply @ SV93 @ SV160 )
= SV157 )
= $false )
| ( ( ~ ( element @ SV160 @ SV116 ) )
= $true )
| ( ( element @ SV157 @ SV122 )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(718,plain,
! [SV122: $i,SV129: $i,SV106: $i,SV156: $i,SV93: $i,SV116: $i,SV159: $i] :
( ( ( element @ SV159 @ SV116 )
= $false )
| ( ( ( apply @ SV93 @ SV159 )
= SV156 )
= $false )
| ( ( ( apply @ SV106 @ SV156 )
= ( zero @ SV129 ) )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(719,plain,
! [SV129: $i,SV106: $i,SV122: $i,SV157: $i,SV93: $i,SV116: $i,SV160: $i] :
( ( ( element @ SV160 @ SV116 )
= $false )
| ( ( ( apply @ SV93 @ SV160 )
= SV157 )
= $false )
| ( ( element @ SV157 @ SV122 )
= $true )
| ( ( morphism @ SV93 @ SV116 @ SV122 )
= $false )
| ( ( exact @ SV93 @ SV106 )
= $false )
| ( ( morphism @ SV106 @ SV122 @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(720,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[389,719,718,715,714,709,708,707,702,701,700,699,698,651,650,641,623,619,618,615,612,611,601,591,585,582,579,555,541,517,516,476,469,458]) ).
thf(721,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[720,388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : HAL002+1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 7 21:42:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.40
% 0.12/0.40 No.of.Axioms: 16
% 0.12/0.40
% 0.12/0.40 Length.of.Defs: 0
% 0.12/0.40
% 0.12/0.40 Contains.Choice.Funs: false
% 0.12/0.41 .
% 0.19/0.46 (rf:0,axioms:16,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:18,loop_count:0,foatp_calls:0,translation:fof_full)...........................................................
% 1.36/1.61
% 1.36/1.61 ********************************
% 1.36/1.61 * All subproblems solved! *
% 1.36/1.61 ********************************
% 1.36/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:720,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.74/1.90
% 1.74/1.90 %**** Beginning of derivation protocol ****
% 1.74/1.90 % SZS output start CNFRefutation
% See solution above
% 1.74/1.91
% 1.74/1.91 %**** End of derivation protocol ****
% 1.74/1.91 %**** no. of clauses in derivation: 721 ****
% 1.74/1.91 %**** clause counter: 720 ****
% 1.74/1.91
% 1.74/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:720,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------