TSTP Solution File: HAL004+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : HAL004+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 : n019.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 12:45:38 EDT 2022
% Result : Theorem 70.11s 70.32s
% Output : CNFRefutation 70.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 64
% Syntax : Number of formulae : 434 ( 158 unt; 33 typ; 0 def)
% Number of atoms : 4140 (1564 equ; 0 cnn)
% Maximal formula atoms : 7 ( 10 avg)
% Number of connectives : 11042 (1398 ~;1491 |; 112 &;7991 @)
% ( 4 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 17 con; 0-6 aty)
% Number of variables : 1864 ( 0 ^1844 !; 20 ?;1864 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_alpha,type,
alpha: $i ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_beta,type,
beta: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_commute,type,
commute: $i > $i > $i > $i > $o ).
thf(tp_d,type,
d: $i ).
thf(tp_delta,type,
delta: $i ).
thf(tp_e,type,
e: $i ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_exact,type,
exact: $i > $i > $o ).
thf(tp_f,type,
f: $i ).
thf(tp_g,type,
g: $i ).
thf(tp_gamma,type,
gamma: $i ).
thf(tp_gammma,type,
gammma: $i ).
thf(tp_h,type,
h: $i ).
thf(tp_injection,type,
injection: $i > $o ).
thf(tp_morphism,type,
morphism: $i > $i > $i > $o ).
thf(tp_r,type,
r: $i ).
thf(tp_sK10_SY78,type,
sK10_SY78: $i > $i > $i ).
thf(tp_sK1_E,type,
sK1_E: $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_SY76,type,
sK4_SY76: $i > $i > $i > $i > $i > $i ).
thf(tp_sK5_SY75,type,
sK5_SY75: $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_zero,type,
zero: $i > $i ).
thf(1,axiom,
commute @ beta @ h @ g @ delta,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta_h_g_delta_commute) ).
thf(2,axiom,
commute @ alpha @ g @ f @ gamma,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_g_f_gamma_commute) ).
thf(3,axiom,
exact @ gammma @ delta,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gamma_delta_exact) ).
thf(4,axiom,
exact @ alpha @ beta,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_beta_exact) ).
thf(5,axiom,
surjection @ delta,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',delta_surjection) ).
thf(6,axiom,
surjection @ beta,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta_surjection) ).
thf(7,axiom,
injection @ gamma,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gamma_injection) ).
thf(8,axiom,
injection @ alpha,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_injection) ).
thf(9,axiom,
morphism @ h @ c @ r,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_morphism) ).
thf(10,axiom,
morphism @ g @ b @ e,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_morphism) ).
thf(11,axiom,
morphism @ f @ a @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_morphism) ).
thf(12,axiom,
morphism @ delta @ e @ r,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',delta_morphism) ).
thf(13,axiom,
morphism @ gamma @ d @ e,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gamma_morphism) ).
thf(14,axiom,
morphism @ beta @ b @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta_morphism) ).
thf(15,axiom,
morphism @ alpha @ a @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_morphism) ).
thf(16,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(17,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(18,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(19,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(20,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(21,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(22,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(23,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(24,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(25,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(26,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(27,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(28,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(29,axiom,
surjection @ h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_surjection) ).
thf(30,axiom,
surjection @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_surjection) ).
thf(31,conjecture,
! [E: $i] :
( ( element @ E @ e )
=> ? [R: $i,B1: $i] :
( ( element @ R @ r )
& ( ( apply @ delta @ E )
= R )
& ( element @ B1 @ b )
& ( ( apply @ h @ ( apply @ beta @ B1 ) )
= R )
& ( ( apply @ delta @ ( apply @ g @ B1 ) )
= R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma3) ).
thf(32,negated_conjecture,
( ( ! [E: $i] :
( ( element @ E @ e )
=> ? [R: $i,B1: $i] :
( ( element @ R @ r )
& ( ( apply @ delta @ E )
= R )
& ( element @ B1 @ b )
& ( ( apply @ h @ ( apply @ beta @ B1 ) )
= R )
& ( ( apply @ delta @ ( apply @ g @ B1 ) )
= R ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[31]) ).
thf(33,plain,
( ( ! [E: $i] :
( ( element @ E @ e )
=> ? [R: $i,B1: $i] :
( ( element @ R @ r )
& ( ( apply @ delta @ E )
= R )
& ( element @ B1 @ b )
& ( ( apply @ h @ ( apply @ beta @ B1 ) )
= R )
& ( ( apply @ delta @ ( apply @ g @ B1 ) )
= R ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[32]) ).
thf(34,plain,
( ( commute @ beta @ h @ g @ delta )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(35,plain,
( ( commute @ alpha @ g @ f @ gamma )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(36,plain,
( ( exact @ gammma @ delta )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(37,plain,
( ( exact @ alpha @ beta )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(38,plain,
( ( surjection @ delta )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(39,plain,
( ( surjection @ beta )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(40,plain,
( ( injection @ gamma )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(41,plain,
( ( injection @ alpha )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(42,plain,
( ( morphism @ h @ c @ r )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(43,plain,
( ( morphism @ g @ b @ e )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(44,plain,
( ( morphism @ f @ a @ d )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(45,plain,
( ( morphism @ delta @ e @ r )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(46,plain,
( ( morphism @ gamma @ d @ e )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(47,plain,
( ( morphism @ beta @ b @ c )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(48,plain,
( ( morphism @ alpha @ a @ b )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(49,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)],[16]) ).
thf(50,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)],[17]) ).
thf(51,plain,
( ( ! [Dom: $i,El: $i] :
( ( element @ El @ Dom )
=> ( ( subtract @ Dom @ El @ El )
= ( zero @ Dom ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(52,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)],[19]) ).
thf(53,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)],[20]) ).
thf(54,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)],[21]) ).
thf(55,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)],[22]) ).
thf(56,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)],[23]) ).
thf(57,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)],[24]) ).
thf(58,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)],[25]) ).
thf(59,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)],[26]) ).
thf(60,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)],[27]) ).
thf(61,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)],[28]) ).
thf(62,plain,
( ( surjection @ h )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(63,plain,
( ( surjection @ f )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(64,plain,
( ( ( element @ sK1_E @ e )
=> ? [SY72: $i,SY73: $i] :
( ( element @ SY72 @ r )
& ( ( apply @ delta @ sK1_E )
= SY72 )
& ( element @ SY73 @ b )
& ( ( apply @ h @ ( apply @ beta @ SY73 ) )
= SY72 )
& ( ( apply @ delta @ ( apply @ g @ SY73 ) )
= SY72 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[33]) ).
thf(65,plain,
( ( element @ sK1_E @ e )
= $true ),
inference(standard_cnf,[status(thm)],[64]) ).
thf(66,plain,
( ( ? [SY72: $i,SY73: $i] :
( ( element @ SY72 @ r )
& ( ( apply @ delta @ sK1_E )
= SY72 )
& ( element @ SY73 @ b )
& ( ( apply @ h @ ( apply @ beta @ SY73 ) )
= SY72 )
& ( ( apply @ delta @ ( apply @ g @ SY73 ) )
= SY72 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[64]) ).
thf(67,plain,
( ( ~ ? [SY72: $i,SY73: $i] :
( ( element @ SY72 @ r )
& ( ( apply @ delta @ sK1_E )
= SY72 )
& ( element @ SY73 @ b )
& ( ( apply @ h @ ( apply @ beta @ SY73 ) )
= SY72 )
& ( ( apply @ delta @ ( apply @ g @ SY73 ) )
= SY72 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[66]) ).
thf(68,plain,
( ( ! [SY72: $i,SY73: $i] :
( ( ( apply @ delta @ sK1_E )
!= SY72 )
| ~ ( element @ SY72 @ r )
| ~ ( element @ SY73 @ b )
| ( ( apply @ h @ ( apply @ beta @ SY73 ) )
!= SY72 )
| ( ( apply @ delta @ ( apply @ g @ SY73 ) )
!= SY72 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(69,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)],[49]) ).
thf(70,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)],[50]) ).
thf(71,plain,
( ( ! [Dom: $i,El: $i] :
( ~ ( element @ El @ Dom )
| ( ( subtract @ Dom @ El @ El )
= ( zero @ Dom ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(72,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)],[52]) ).
thf(73,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)],[53]) ).
thf(74,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)],[54]) ).
thf(75,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 )
| ! [SY74: $i] :
( ( ( apply @ Morphism1 @ SY74 )
!= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
| ~ ( element @ SY74 @ Dom ) ) )
& ( ( ( apply @ Morphism2 @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( zero @ Cod ) )
| ( ( ( apply @ Morphism1 @ ( sK5_SY75 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
& ( element @ ( sK5_SY75 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ Dom ) ) )
& ( ( element @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ CodDom )
| ( ( ( apply @ Morphism1 @ ( sK4_SY76 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
& ( element @ ( sK4_SY76 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ Dom ) ) ) )
| ~ ( morphism @ Morphism1 @ Dom @ CodDom )
| ~ ( morphism @ Morphism2 @ CodDom @ Cod ) )
| ( exact @ Morphism1 @ Morphism2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(76,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)],[56]) ).
thf(77,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i,Cod: $i] :
( ( ( element @ ( sK7_ElCod @ Cod @ Dom @ Morphism ) @ Cod )
& ! [SY77: $i] :
( ( ( apply @ Morphism @ SY77 )
!= ( sK7_ElCod @ Cod @ Dom @ Morphism ) )
| ~ ( element @ SY77 @ Dom ) ) )
| ~ ( morphism @ Morphism @ Dom @ Cod ) )
| ( surjection @ Morphism ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(78,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)],[58]) ).
thf(79,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i] :
( ( ( element @ ( sK9_El1 @ Dom @ Morphism ) @ Dom )
& ( element @ ( sK10_SY78 @ Dom @ Morphism ) @ Dom )
& ( ( apply @ Morphism @ ( sK9_El1 @ Dom @ Morphism ) )
= ( apply @ Morphism @ ( sK10_SY78 @ Dom @ Morphism ) ) )
& ( ( sK9_El1 @ Dom @ Morphism )
!= ( sK10_SY78 @ Dom @ Morphism ) ) )
| ! [Cod: $i] :
~ ( morphism @ Morphism @ Dom @ Cod ) )
| ( injection @ Morphism ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(80,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)],[60]) ).
thf(81,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)],[61]) ).
thf(82,plain,
( ( surjection @ f )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(83,plain,
( ( surjection @ h )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(84,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)],[81]) ).
thf(85,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)],[80]) ).
thf(86,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i] :
( ( ( element @ ( sK9_El1 @ Dom @ Morphism ) @ Dom )
& ( element @ ( sK10_SY78 @ Dom @ Morphism ) @ Dom )
& ( ( apply @ Morphism @ ( sK9_El1 @ Dom @ Morphism ) )
= ( apply @ Morphism @ ( sK10_SY78 @ Dom @ Morphism ) ) )
& ( ( sK9_El1 @ Dom @ Morphism )
!= ( sK10_SY78 @ Dom @ Morphism ) ) )
| ! [Cod: $i] :
~ ( morphism @ Morphism @ Dom @ Cod ) )
| ( injection @ Morphism ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(87,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)],[78]) ).
thf(88,plain,
( ( ! [Morphism: $i] :
( ! [Dom: $i,Cod: $i] :
( ( ( element @ ( sK7_ElCod @ Cod @ Dom @ Morphism ) @ Cod )
& ! [SY77: $i] :
( ( ( apply @ Morphism @ SY77 )
!= ( sK7_ElCod @ Cod @ Dom @ Morphism ) )
| ~ ( element @ SY77 @ Dom ) ) )
| ~ ( morphism @ Morphism @ Dom @ Cod ) )
| ( surjection @ Morphism ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(89,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)],[76]) ).
thf(90,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 )
| ! [SY74: $i] :
( ( ( apply @ Morphism1 @ SY74 )
!= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
| ~ ( element @ SY74 @ Dom ) ) )
& ( ( ( apply @ Morphism2 @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( zero @ Cod ) )
| ( ( ( apply @ Morphism1 @ ( sK5_SY75 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
& ( element @ ( sK5_SY75 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ Dom ) ) )
& ( ( element @ ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ CodDom )
| ( ( ( apply @ Morphism1 @ ( sK4_SY76 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
= ( sK3_ElCodDom @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) )
& ( element @ ( sK4_SY76 @ Cod @ CodDom @ Dom @ Morphism2 @ Morphism1 ) @ Dom ) ) ) )
| ~ ( morphism @ Morphism1 @ Dom @ CodDom )
| ~ ( morphism @ Morphism2 @ CodDom @ Cod ) )
| ( exact @ Morphism1 @ Morphism2 ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(91,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)],[74]) ).
thf(92,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)],[73]) ).
thf(93,plain,
( ( ! [Dom: $i,El1: $i,El2: $i] :
( ~ ( element @ El1 @ Dom )
| ~ ( element @ El2 @ Dom )
| ( element @ ( subtract @ Dom @ El1 @ El2 ) @ Dom ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(94,plain,
( ( ! [Dom: $i,El: $i] :
( ~ ( element @ El @ Dom )
| ( ( subtract @ Dom @ El @ El )
= ( zero @ Dom ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(95,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)],[70]) ).
thf(96,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)],[69]) ).
thf(97,plain,
( ( morphism @ alpha @ a @ b )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(98,plain,
( ( morphism @ beta @ b @ c )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(99,plain,
( ( morphism @ gamma @ d @ e )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(100,plain,
( ( morphism @ delta @ e @ r )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(101,plain,
( ( morphism @ f @ a @ d )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(102,plain,
( ( morphism @ g @ b @ e )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(103,plain,
( ( morphism @ h @ c @ r )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(104,plain,
( ( injection @ alpha )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(105,plain,
( ( injection @ gamma )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(106,plain,
( ( surjection @ beta )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(107,plain,
( ( surjection @ delta )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(108,plain,
( ( exact @ alpha @ beta )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(109,plain,
( ( exact @ gammma @ delta )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(110,plain,
( ( commute @ alpha @ g @ f @ gamma )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(111,plain,
( ( commute @ beta @ h @ g @ delta )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(112,plain,
( ( element @ sK1_E @ e )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(113,plain,
( ( ! [SY72: $i,SY73: $i] :
( ( ( apply @ delta @ sK1_E )
!= SY72 )
| ~ ( element @ SY72 @ r )
| ~ ( element @ SY73 @ b )
| ( ( apply @ h @ ( apply @ beta @ SY73 ) )
!= SY72 )
| ( ( apply @ delta @ ( apply @ g @ SY73 ) )
!= SY72 ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(114,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SX1 @ SX0 ) @ SX1 )
| ~ ( element @ ( sK10_SY78 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( apply @ SX0 @ ( sK9_El1 @ SX1 @ SX0 ) )
!= ( apply @ SX0 @ ( sK10_SY78 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK9_El1 @ SX1 @ SX0 )
!= ( sK10_SY78 @ SX1 @ SX0 ) ) ) )
| ! [SX2: $i] :
~ ( morphism @ SX0 @ SX1 @ SX2 ) )
| ( injection @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(115,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)],[88]) ).
thf(116,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)],[92]) ).
thf(117,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)],[84]) ).
thf(118,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)],[87]) ).
thf(119,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_SY75 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( element @ ( sK5_SY75 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ~ ( ( ( apply @ SX0 @ ( sK4_SY76 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( sK3_ElCodDom @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( element @ ( sK4_SY76 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) ) )
| ~ ( morphism @ SX0 @ SX2 @ SX3 )
| ~ ( morphism @ SX1 @ SX3 @ SX4 ) )
| ( exact @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(120,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)],[89]) ).
thf(121,plain,
! [SV1: $i] :
( ( ! [SY79: $i] :
( ~ ( injection @ SV1 )
| ! [SY80: $i] :
~ ( morphism @ SV1 @ SY79 @ SY80 )
| ! [SY81: $i,SY82: $i] :
( ~ ( element @ SY81 @ SY79 )
| ~ ( element @ SY82 @ SY79 )
| ( ( apply @ SV1 @ SY81 )
!= ( apply @ SV1 @ SY82 ) )
| ( SY81 = SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(122,plain,
! [SV2: $i] :
( ( ! [SY83: $i,SY84: $i,SY85: $i,SY86: $i,SY87: $i] :
( ! [SY88: $i,SY89: $i] :
( ~ ( commute @ SV2 @ SY83 @ SY84 @ SY85 )
| ~ ( morphism @ SV2 @ SY86 @ SY87 )
| ~ ( morphism @ SY83 @ SY87 @ SY89 )
| ~ ( morphism @ SY84 @ SY86 @ SY88 )
| ~ ( morphism @ SY85 @ SY88 @ SY89 ) )
| ! [SY90: $i] :
( ~ ( element @ SY90 @ SY86 )
| ( ( apply @ SY83 @ ( apply @ SV2 @ SY90 ) )
= ( apply @ SY85 @ ( apply @ SY84 @ SY90 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(123,plain,
! [SV3: $i] :
( ( ! [SY91: $i,SY92: $i] :
( ~ ( element @ SY91 @ SV3 )
| ~ ( element @ SY92 @ SV3 )
| ( element @ ( subtract @ SV3 @ SY91 @ SY92 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(124,plain,
! [SV4: $i] :
( ( ! [SY93: $i] :
( ~ ( element @ SY93 @ SV4 )
| ( ( subtract @ SV4 @ SY93 @ SY93 )
= ( zero @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(125,plain,
! [SV5: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ~ ( element @ SY94 @ SV5 )
| ~ ( element @ SY95 @ SV5 )
| ( ( subtract @ SV5 @ SY94 @ ( subtract @ SV5 @ SY94 @ SY95 ) )
= SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(126,plain,
! [SV6: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ( morphism @ SV6 @ SY96 @ SY97 )
| ! [SY98: $i,SY99: $i] :
( ~ ( element @ SY98 @ SY96 )
| ~ ( element @ SY99 @ SY96 )
| ( ( apply @ SV6 @ ( subtract @ SY96 @ SY98 @ SY99 ) )
= ( subtract @ SY97 @ ( apply @ SV6 @ SY98 ) @ ( apply @ SV6 @ SY99 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(127,plain,
! [SV7: $i] :
( ( ! [SY100: $i] :
( ( ( apply @ delta @ sK1_E )
!= SV7 )
| ~ ( element @ SV7 @ r )
| ~ ( element @ SY100 @ b )
| ( ( apply @ h @ ( apply @ beta @ SY100 ) )
!= SV7 )
| ( ( apply @ delta @ ( apply @ g @ SY100 ) )
!= SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(128,plain,
! [SV8: $i] :
( ( ! [SY101: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SY101 @ SV8 ) @ SY101 )
| ~ ( element @ ( sK10_SY78 @ SY101 @ SV8 ) @ SY101 ) )
| ( ( apply @ SV8 @ ( sK9_El1 @ SY101 @ SV8 ) )
!= ( apply @ SV8 @ ( sK10_SY78 @ SY101 @ SV8 ) ) ) )
| ~ ( ( ( sK9_El1 @ SY101 @ SV8 )
!= ( sK10_SY78 @ SY101 @ SV8 ) ) ) )
| ! [SY102: $i] :
~ ( morphism @ SV8 @ SY101 @ SY102 ) )
| ( injection @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(129,plain,
! [SV9: $i] :
( ( ! [SY103: $i,SY104: $i] :
( ~ ( ~ ( element @ ( sK7_ElCod @ SY104 @ SY103 @ SV9 ) @ SY104 )
| ~ ! [SY105: $i] :
( ( ( apply @ SV9 @ SY105 )
!= ( sK7_ElCod @ SY104 @ SY103 @ SV9 ) )
| ~ ( element @ SY105 @ SY103 ) ) )
| ~ ( morphism @ SV9 @ SY103 @ SY104 ) )
| ( surjection @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(130,plain,
! [SV10: $i] :
( ( ! [SY106: $i,SY107: $i,SY108: $i,SY109: $i,SY110: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY110 @ SY109 @ SY108 @ SY107 @ SY106 @ SV10 ) @ SY109 )
| ~ ( ( ( apply @ SY106 @ ( apply @ SV10 @ ( sK2_ElDom @ SY110 @ SY109 @ SY108 @ SY107 @ SY106 @ SV10 ) ) )
!= ( apply @ SY108 @ ( apply @ SY107 @ ( sK2_ElDom @ SY110 @ SY109 @ SY108 @ SY107 @ SY106 @ SV10 ) ) ) ) ) )
| ! [SY111: $i,SY112: $i] :
( ~ ( morphism @ SV10 @ SY109 @ SY110 )
| ~ ( morphism @ SY106 @ SY110 @ SY112 )
| ~ ( morphism @ SY107 @ SY109 @ SY111 )
| ~ ( morphism @ SY108 @ SY111 @ SY112 ) )
| ( commute @ SV10 @ SY106 @ SY107 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(131,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( morphism @ SV11 @ SY113 @ SY114 )
| ! [SY115: $i] :
( ~ ( element @ SY115 @ SY113 )
| ( element @ ( apply @ SV11 @ SY115 ) @ SY114 ) ) )
| ~ ! [SY116: $i,SY117: $i] :
( ~ ( morphism @ SV11 @ SY116 @ SY117 )
| ( ( apply @ SV11 @ ( zero @ SY116 ) )
= ( zero @ SY117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(132,plain,
! [SV12: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ~ ( morphism @ SV12 @ SY118 @ SY119 )
| ~ ( surjection @ SV12 )
| ! [SY120: $i] :
( ~ ( element @ SY120 @ SY119 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SY120 @ SY119 @ SY118 @ SV12 ) )
!= SY120 )
| ~ ( element @ ( sK8_ElDom @ SY120 @ SY119 @ SY118 @ SV12 ) @ SY118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV13: $i] :
( ( ! [SY121: $i,SY122: $i] :
( ! [SY123: $i,SY124: $i] :
( ~ ( ~ ( ( ( apply @ SY121 @ ( sK3_ElCodDom @ SY124 @ SY123 @ SY122 @ SY121 @ SV13 ) )
!= ( zero @ SY124 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY124 @ SY123 @ SY122 @ SY121 @ SV13 ) @ SY123 )
| ! [SY125: $i] :
( ( ( apply @ SV13 @ SY125 )
!= ( sK3_ElCodDom @ SY124 @ SY123 @ SY122 @ SY121 @ SV13 ) )
| ~ ( element @ SY125 @ SY122 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SY121 @ ( sK3_ElCodDom @ SY124 @ SY123 @ SY122 @ SY121 @ SV13 ) )
= ( zero @ SY124 ) )
| ~ ( ( ( apply @ SV13 @ ( sK5_SY75 @ SY124 @ SY123 @ SY122 @ SY121 @ SV13 ) )
!= ( sK3_ElCodDom @ SY124 @ SY123 @ SY122 @ SY121 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SY124 @ SY123 @ SY122 @ SY121 @ SV13 ) @ SY122 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY124 @ SY123 @ SY122 @ SY121 @ SV13 ) @ SY123 )
| ~ ( ( ( apply @ SV13 @ ( sK4_SY76 @ SY124 @ SY123 @ SY122 @ SY121 @ SV13 ) )
!= ( sK3_ElCodDom @ SY124 @ SY123 @ SY122 @ SY121 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SY124 @ SY123 @ SY122 @ SY121 @ SV13 ) @ SY122 ) ) ) ) )
| ~ ( morphism @ SV13 @ SY122 @ SY123 )
| ~ ( morphism @ SY121 @ SY123 @ SY124 ) )
| ( exact @ SV13 @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV14: $i] :
( ( ! [SY126: $i,SY127: $i,SY128: $i,SY129: $i] :
( ~ ( exact @ SV14 @ SY126 )
| ~ ( morphism @ SV14 @ SY127 @ SY128 )
| ~ ( morphism @ SY126 @ SY128 @ SY129 )
| ~ ( ~ ! [SY130: $i] :
( ( ( apply @ SY126 @ SY130 )
!= ( zero @ SY129 ) )
| ~ ( element @ SY130 @ SY128 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY130 @ SY129 @ SY128 @ SY127 @ SY126 @ SV14 ) )
!= SY130 )
| ~ ( element @ ( sK6_ElDom @ SY130 @ SY129 @ SY128 @ SY127 @ SY126 @ SV14 ) @ SY127 ) ) )
| ~ ~ ( ~ ! [SY131: $i] :
( ! [SY132: $i] :
( ( ( apply @ SV14 @ SY132 )
!= SY131 )
| ~ ( element @ SY132 @ SY127 ) )
| ( ( apply @ SY126 @ SY131 )
= ( zero @ SY129 ) ) )
| ~ ! [SY133: $i] :
( ! [SY134: $i] :
( ( ( apply @ SV14 @ SY134 )
!= SY133 )
| ~ ( element @ SY134 @ SY127 ) )
| ( element @ SY133 @ SY128 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV15: $i,SV1: $i] :
( ( ~ ( injection @ SV1 )
| ! [SY135: $i] :
~ ( morphism @ SV1 @ SV15 @ SY135 )
| ! [SY136: $i,SY137: $i] :
( ~ ( element @ SY136 @ SV15 )
| ~ ( element @ SY137 @ SV15 )
| ( ( apply @ SV1 @ SY136 )
!= ( apply @ SV1 @ SY137 ) )
| ( SY136 = SY137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV16: $i,SV2: $i] :
( ( ! [SY138: $i,SY139: $i,SY140: $i,SY141: $i] :
( ! [SY142: $i,SY143: $i] :
( ~ ( commute @ SV2 @ SV16 @ SY138 @ SY139 )
| ~ ( morphism @ SV2 @ SY140 @ SY141 )
| ~ ( morphism @ SV16 @ SY141 @ SY143 )
| ~ ( morphism @ SY138 @ SY140 @ SY142 )
| ~ ( morphism @ SY139 @ SY142 @ SY143 ) )
| ! [SY144: $i] :
( ~ ( element @ SY144 @ SY140 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY144 ) )
= ( apply @ SY139 @ ( apply @ SY138 @ SY144 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV3: $i,SV17: $i] :
( ( ! [SY145: $i] :
( ~ ( element @ SV17 @ SV3 )
| ~ ( element @ SY145 @ SV3 )
| ( element @ ( subtract @ SV3 @ SV17 @ SY145 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV4: $i,SV18: $i] :
( ( ~ ( element @ SV18 @ SV4 )
| ( ( subtract @ SV4 @ SV18 @ SV18 )
= ( zero @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(139,plain,
! [SV5: $i,SV19: $i] :
( ( ! [SY146: $i] :
( ~ ( element @ SV19 @ SV5 )
| ~ ( element @ SY146 @ SV5 )
| ( ( subtract @ SV5 @ SV19 @ ( subtract @ SV5 @ SV19 @ SY146 ) )
= SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(140,plain,
! [SV20: $i,SV6: $i] :
( ( ! [SY147: $i] :
( ~ ( morphism @ SV6 @ SV20 @ SY147 )
| ! [SY148: $i,SY149: $i] :
( ~ ( element @ SY148 @ SV20 )
| ~ ( element @ SY149 @ SV20 )
| ( ( apply @ SV6 @ ( subtract @ SV20 @ SY148 @ SY149 ) )
= ( subtract @ SY147 @ ( apply @ SV6 @ SY148 ) @ ( apply @ SV6 @ SY149 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(141,plain,
! [SV21: $i,SV7: $i] :
( ( ( ( apply @ delta @ sK1_E )
!= SV7 )
| ~ ( element @ SV7 @ r )
| ~ ( element @ SV21 @ b )
| ( ( apply @ h @ ( apply @ beta @ SV21 ) )
!= SV7 )
| ( ( apply @ delta @ ( apply @ g @ SV21 ) )
!= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(142,plain,
! [SV8: $i] :
( ( ( ! [SY101: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SY101 @ SV8 ) @ SY101 )
| ~ ( element @ ( sK10_SY78 @ SY101 @ SV8 ) @ SY101 ) )
| ( ( apply @ SV8 @ ( sK9_El1 @ SY101 @ SV8 ) )
!= ( apply @ SV8 @ ( sK10_SY78 @ SY101 @ SV8 ) ) ) )
| ~ ( ( ( sK9_El1 @ SY101 @ SV8 )
!= ( sK10_SY78 @ SY101 @ SV8 ) ) ) )
| ! [SY102: $i] :
~ ( morphism @ SV8 @ SY101 @ SY102 ) ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(143,plain,
! [SV9: $i] :
( ( ( ! [SY103: $i,SY104: $i] :
( ~ ( ~ ( element @ ( sK7_ElCod @ SY104 @ SY103 @ SV9 ) @ SY104 )
| ~ ! [SY105: $i] :
( ( ( apply @ SV9 @ SY105 )
!= ( sK7_ElCod @ SY104 @ SY103 @ SV9 ) )
| ~ ( element @ SY105 @ SY103 ) ) )
| ~ ( morphism @ SV9 @ SY103 @ SY104 ) ) )
= $true )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(144,plain,
! [SV10: $i,SV22: $i] :
( ( ! [SY150: $i,SY151: $i,SY152: $i,SY153: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY153 @ SY152 @ SY151 @ SY150 @ SV22 @ SV10 ) @ SY152 )
| ~ ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SY153 @ SY152 @ SY151 @ SY150 @ SV22 @ SV10 ) ) )
!= ( apply @ SY151 @ ( apply @ SY150 @ ( sK2_ElDom @ SY153 @ SY152 @ SY151 @ SY150 @ SV22 @ SV10 ) ) ) ) ) )
| ! [SY154: $i,SY155: $i] :
( ~ ( morphism @ SV10 @ SY152 @ SY153 )
| ~ ( morphism @ SV22 @ SY153 @ SY155 )
| ~ ( morphism @ SY150 @ SY152 @ SY154 )
| ~ ( morphism @ SY151 @ SY154 @ SY155 ) )
| ( commute @ SV10 @ SV22 @ SY150 @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(145,plain,
! [SV11: $i] :
( ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( morphism @ SV11 @ SY113 @ SY114 )
| ! [SY115: $i] :
( ~ ( element @ SY115 @ SY113 )
| ( element @ ( apply @ SV11 @ SY115 ) @ SY114 ) ) )
| ~ ! [SY116: $i,SY117: $i] :
( ~ ( morphism @ SV11 @ SY116 @ SY117 )
| ( ( apply @ SV11 @ ( zero @ SY116 ) )
= ( zero @ SY117 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(146,plain,
! [SV23: $i,SV12: $i] :
( ( ! [SY156: $i] :
( ~ ( morphism @ SV12 @ SV23 @ SY156 )
| ~ ( surjection @ SV12 )
| ! [SY157: $i] :
( ~ ( element @ SY157 @ SY156 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SY157 @ SY156 @ SV23 @ SV12 ) )
!= SY157 )
| ~ ( element @ ( sK8_ElDom @ SY157 @ SY156 @ SV23 @ SV12 ) @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV13: $i,SV24: $i] :
( ( ! [SY158: $i] :
( ! [SY159: $i,SY160: $i] :
( ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY160 @ SY159 @ SY158 @ SV24 @ SV13 ) )
!= ( zero @ SY160 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY160 @ SY159 @ SY158 @ SV24 @ SV13 ) @ SY159 )
| ! [SY161: $i] :
( ( ( apply @ SV13 @ SY161 )
!= ( sK3_ElCodDom @ SY160 @ SY159 @ SY158 @ SV24 @ SV13 ) )
| ~ ( element @ SY161 @ SY158 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY160 @ SY159 @ SY158 @ SV24 @ SV13 ) )
= ( zero @ SY160 ) )
| ~ ( ( ( apply @ SV13 @ ( sK5_SY75 @ SY160 @ SY159 @ SY158 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SY160 @ SY159 @ SY158 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SY160 @ SY159 @ SY158 @ SV24 @ SV13 ) @ SY158 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY160 @ SY159 @ SY158 @ SV24 @ SV13 ) @ SY159 )
| ~ ( ( ( apply @ SV13 @ ( sK4_SY76 @ SY160 @ SY159 @ SY158 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SY160 @ SY159 @ SY158 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SY160 @ SY159 @ SY158 @ SV24 @ SV13 ) @ SY158 ) ) ) ) )
| ~ ( morphism @ SV13 @ SY158 @ SY159 )
| ~ ( morphism @ SV24 @ SY159 @ SY160 ) )
| ( exact @ SV13 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV25: $i,SV14: $i] :
( ( ! [SY162: $i,SY163: $i,SY164: $i] :
( ~ ( exact @ SV14 @ SV25 )
| ~ ( morphism @ SV14 @ SY162 @ SY163 )
| ~ ( morphism @ SV25 @ SY163 @ SY164 )
| ~ ( ~ ! [SY165: $i] :
( ( ( apply @ SV25 @ SY165 )
!= ( zero @ SY164 ) )
| ~ ( element @ SY165 @ SY163 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY165 @ SY164 @ SY163 @ SY162 @ SV25 @ SV14 ) )
!= SY165 )
| ~ ( element @ ( sK6_ElDom @ SY165 @ SY164 @ SY163 @ SY162 @ SV25 @ SV14 ) @ SY162 ) ) )
| ~ ~ ( ~ ! [SY166: $i] :
( ! [SY132: $i] :
( ( ( apply @ SV14 @ SY132 )
!= SY166 )
| ~ ( element @ SY132 @ SY162 ) )
| ( ( apply @ SV25 @ SY166 )
= ( zero @ SY164 ) ) )
| ~ ! [SY133: $i] :
( ! [SY134: $i] :
( ( ( apply @ SV14 @ SY134 )
!= SY133 )
| ~ ( element @ SY134 @ SY162 ) )
| ( element @ SY133 @ SY163 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV15: $i,SV1: $i] :
( ( ( ~ ( injection @ SV1 )
| ! [SY135: $i] :
~ ( morphism @ SV1 @ SV15 @ SY135 ) )
= $true )
| ( ( ! [SY136: $i,SY137: $i] :
( ~ ( element @ SY136 @ SV15 )
| ~ ( element @ SY137 @ SV15 )
| ( ( apply @ SV1 @ SY136 )
!= ( apply @ SV1 @ SY137 ) )
| ( SY136 = SY137 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV26: $i,SV16: $i,SV2: $i] :
( ( ! [SY170: $i,SY171: $i,SY172: $i] :
( ! [SY173: $i,SY174: $i] :
( ~ ( commute @ SV2 @ SV16 @ SV26 @ SY170 )
| ~ ( morphism @ SV2 @ SY171 @ SY172 )
| ~ ( morphism @ SV16 @ SY172 @ SY174 )
| ~ ( morphism @ SV26 @ SY171 @ SY173 )
| ~ ( morphism @ SY170 @ SY173 @ SY174 ) )
| ! [SY175: $i] :
( ~ ( element @ SY175 @ SY171 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY175 ) )
= ( apply @ SY170 @ ( apply @ SV26 @ SY175 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(151,plain,
! [SV27: $i,SV3: $i,SV17: $i] :
( ( ~ ( element @ SV17 @ SV3 )
| ~ ( element @ SV27 @ SV3 )
| ( element @ ( subtract @ SV3 @ SV17 @ SV27 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(152,plain,
! [SV4: $i,SV18: $i] :
( ( ( ~ ( element @ SV18 @ SV4 ) )
= $true )
| ( ( ( subtract @ SV4 @ SV18 @ SV18 )
= ( zero @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(153,plain,
! [SV28: $i,SV5: $i,SV19: $i] :
( ( ~ ( element @ SV19 @ SV5 )
| ~ ( element @ SV28 @ SV5 )
| ( ( subtract @ SV5 @ SV19 @ ( subtract @ SV5 @ SV19 @ SV28 ) )
= SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(154,plain,
! [SV29: $i,SV20: $i,SV6: $i] :
( ( ~ ( morphism @ SV6 @ SV20 @ SV29 )
| ! [SY176: $i,SY177: $i] :
( ~ ( element @ SY176 @ SV20 )
| ~ ( element @ SY177 @ SV20 )
| ( ( apply @ SV6 @ ( subtract @ SV20 @ SY176 @ SY177 ) )
= ( subtract @ SV29 @ ( apply @ SV6 @ SY176 ) @ ( apply @ SV6 @ SY177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(155,plain,
! [SV21: $i,SV7: $i] :
( ( ( ( ( apply @ delta @ sK1_E )
!= SV7 )
| ~ ( element @ SV7 @ r )
| ~ ( element @ SV21 @ b )
| ( ( apply @ h @ ( apply @ beta @ SV21 ) )
!= SV7 ) )
= $true )
| ( ( ( ( apply @ delta @ ( apply @ g @ SV21 ) )
!= SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(156,plain,
! [SV8: $i,SV30: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV30 @ SV8 ) @ SV30 )
| ~ ( element @ ( sK10_SY78 @ SV30 @ SV8 ) @ SV30 ) )
| ( ( apply @ SV8 @ ( sK9_El1 @ SV30 @ SV8 ) )
!= ( apply @ SV8 @ ( sK10_SY78 @ SV30 @ SV8 ) ) ) )
| ~ ( ( ( sK9_El1 @ SV30 @ SV8 )
!= ( sK10_SY78 @ SV30 @ SV8 ) ) ) )
| ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(157,plain,
! [SV9: $i,SV31: $i] :
( ( ( ! [SY179: $i] :
( ~ ( ~ ( element @ ( sK7_ElCod @ SY179 @ SV31 @ SV9 ) @ SY179 )
| ~ ! [SY180: $i] :
( ( ( apply @ SV9 @ SY180 )
!= ( sK7_ElCod @ SY179 @ SV31 @ SV9 ) )
| ~ ( element @ SY180 @ SV31 ) ) )
| ~ ( morphism @ SV9 @ SV31 @ SY179 ) ) )
= $true )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(158,plain,
! [SV10: $i,SV22: $i,SV32: $i] :
( ( ! [SY181: $i,SY182: $i,SY183: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY183 @ SY182 @ SY181 @ SV32 @ SV22 @ SV10 ) @ SY182 )
| ~ ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SY183 @ SY182 @ SY181 @ SV32 @ SV22 @ SV10 ) ) )
!= ( apply @ SY181 @ ( apply @ SV32 @ ( sK2_ElDom @ SY183 @ SY182 @ SY181 @ SV32 @ SV22 @ SV10 ) ) ) ) ) )
| ! [SY184: $i,SY185: $i] :
( ~ ( morphism @ SV10 @ SY182 @ SY183 )
| ~ ( morphism @ SV22 @ SY183 @ SY185 )
| ~ ( morphism @ SV32 @ SY182 @ SY184 )
| ~ ( morphism @ SY181 @ SY184 @ SY185 ) )
| ( commute @ SV10 @ SV22 @ SV32 @ SY181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(159,plain,
! [SV11: $i] :
( ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( morphism @ SV11 @ SY113 @ SY114 )
| ! [SY115: $i] :
( ~ ( element @ SY115 @ SY113 )
| ( element @ ( apply @ SV11 @ SY115 ) @ SY114 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(160,plain,
! [SV11: $i] :
( ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( morphism @ SV11 @ SY116 @ SY117 )
| ( ( apply @ SV11 @ ( zero @ SY116 ) )
= ( zero @ SY117 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(161,plain,
! [SV33: $i,SV23: $i,SV12: $i] :
( ( ~ ( morphism @ SV12 @ SV23 @ SV33 )
| ~ ( surjection @ SV12 )
| ! [SY186: $i] :
( ~ ( element @ SY186 @ SV33 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SY186 @ SV33 @ SV23 @ SV12 ) )
!= SY186 )
| ~ ( element @ ( sK8_ElDom @ SY186 @ SV33 @ SV23 @ SV12 ) @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(162,plain,
! [SV13: $i,SV34: $i,SV24: $i] :
( ( ! [SY187: $i,SY188: $i] :
( ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) )
!= ( zero @ SY188 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) @ SY187 )
| ! [SY189: $i] :
( ( ( apply @ SV13 @ SY189 )
!= ( sK3_ElCodDom @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ SY189 @ SV34 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SY188 ) )
| ~ ( ( ( apply @ SV13 @ ( sK5_SY75 @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) @ SY187 )
| ~ ( ( ( apply @ SV13 @ ( sK4_SY76 @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) ) ) )
| ~ ( morphism @ SV13 @ SV34 @ SY187 )
| ~ ( morphism @ SV24 @ SY187 @ SY188 ) )
| ( exact @ SV13 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(163,plain,
! [SV35: $i,SV25: $i,SV14: $i] :
( ( ! [SY190: $i,SY191: $i] :
( ~ ( exact @ SV14 @ SV25 )
| ~ ( morphism @ SV14 @ SV35 @ SY190 )
| ~ ( morphism @ SV25 @ SY190 @ SY191 )
| ~ ( ~ ! [SY192: $i] :
( ( ( apply @ SV25 @ SY192 )
!= ( zero @ SY191 ) )
| ~ ( element @ SY192 @ SY190 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY192 @ SY191 @ SY190 @ SV35 @ SV25 @ SV14 ) )
!= SY192 )
| ~ ( element @ ( sK6_ElDom @ SY192 @ SY191 @ SY190 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
| ~ ~ ( ~ ! [SY193: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY193 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY193 )
= ( zero @ SY191 ) ) )
| ~ ! [SY195: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY195 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY195 @ SY190 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(164,plain,
! [SV15: $i,SV1: $i] :
( ( ( ~ ( injection @ SV1 ) )
= $true )
| ( ( ! [SY135: $i] :
~ ( morphism @ SV1 @ SV15 @ SY135 ) )
= $true )
| ( ( ! [SY136: $i,SY137: $i] :
( ~ ( element @ SY136 @ SV15 )
| ~ ( element @ SY137 @ SV15 )
| ( ( apply @ SV1 @ SY136 )
!= ( apply @ SV1 @ SY137 ) )
| ( SY136 = SY137 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(165,plain,
! [SV36: $i,SV26: $i,SV16: $i,SV2: $i] :
( ( ! [SY197: $i,SY198: $i] :
( ! [SY199: $i,SY200: $i] :
( ~ ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
| ~ ( morphism @ SV2 @ SY197 @ SY198 )
| ~ ( morphism @ SV16 @ SY198 @ SY200 )
| ~ ( morphism @ SV26 @ SY197 @ SY199 )
| ~ ( morphism @ SV36 @ SY199 @ SY200 ) )
| ! [SY201: $i] :
( ~ ( element @ SY201 @ SY197 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY201 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY201 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(166,plain,
! [SV27: $i,SV3: $i,SV17: $i] :
( ( ( ~ ( element @ SV17 @ SV3 )
| ~ ( element @ SV27 @ SV3 ) )
= $true )
| ( ( element @ ( subtract @ SV3 @ SV17 @ SV27 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(167,plain,
! [SV4: $i,SV18: $i] :
( ( ( element @ SV18 @ SV4 )
= $false )
| ( ( ( subtract @ SV4 @ SV18 @ SV18 )
= ( zero @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(168,plain,
! [SV28: $i,SV5: $i,SV19: $i] :
( ( ( ~ ( element @ SV19 @ SV5 )
| ~ ( element @ SV28 @ SV5 ) )
= $true )
| ( ( ( subtract @ SV5 @ SV19 @ ( subtract @ SV5 @ SV19 @ SV28 ) )
= SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(169,plain,
! [SV29: $i,SV20: $i,SV6: $i] :
( ( ( ~ ( morphism @ SV6 @ SV20 @ SV29 ) )
= $true )
| ( ( ! [SY176: $i,SY177: $i] :
( ~ ( element @ SY176 @ SV20 )
| ~ ( element @ SY177 @ SV20 )
| ( ( apply @ SV6 @ ( subtract @ SV20 @ SY176 @ SY177 ) )
= ( subtract @ SV29 @ ( apply @ SV6 @ SY176 ) @ ( apply @ SV6 @ SY177 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(170,plain,
! [SV21: $i,SV7: $i] :
( ( ( ( ( apply @ delta @ sK1_E )
!= SV7 )
| ~ ( element @ SV7 @ r )
| ~ ( element @ SV21 @ b ) )
= $true )
| ( ( ( ( apply @ h @ ( apply @ beta @ SV21 ) )
!= SV7 ) )
= $true )
| ( ( ( ( apply @ delta @ ( apply @ g @ SV21 ) )
!= SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(171,plain,
! [SV8: $i,SV30: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV30 @ SV8 ) @ SV30 )
| ~ ( element @ ( sK10_SY78 @ SV30 @ SV8 ) @ SV30 ) )
| ( ( apply @ SV8 @ ( sK9_El1 @ SV30 @ SV8 ) )
!= ( apply @ SV8 @ ( sK10_SY78 @ SV30 @ SV8 ) ) ) )
| ~ ( ( ( sK9_El1 @ SV30 @ SV8 )
!= ( sK10_SY78 @ SV30 @ SV8 ) ) ) ) )
= $true )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(172,plain,
! [SV9: $i,SV31: $i,SV37: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) @ SV37 )
| ~ ! [SY202: $i] :
( ( ( apply @ SV9 @ SY202 )
!= ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) )
| ~ ( element @ SY202 @ SV31 ) ) )
| ~ ( morphism @ SV9 @ SV31 @ SV37 ) )
= $true )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(173,plain,
! [SV10: $i,SV22: $i,SV32: $i,SV38: $i] :
( ( ! [SY203: $i,SY204: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY204 @ SY203 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SY203 )
| ~ ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SY204 @ SY203 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
!= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SY204 @ SY203 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) ) ) )
| ! [SY205: $i,SY206: $i] :
( ~ ( morphism @ SV10 @ SY203 @ SY204 )
| ~ ( morphism @ SV22 @ SY204 @ SY206 )
| ~ ( morphism @ SV32 @ SY203 @ SY205 )
| ~ ( morphism @ SV38 @ SY205 @ SY206 ) )
| ( commute @ SV10 @ SV22 @ SV32 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(174,plain,
! [SV11: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ( morphism @ SV11 @ SY113 @ SY114 )
| ! [SY115: $i] :
( ~ ( element @ SY115 @ SY113 )
| ( element @ ( apply @ SV11 @ SY115 ) @ SY114 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(175,plain,
! [SV11: $i] :
( ( ! [SY116: $i,SY117: $i] :
( ~ ( morphism @ SV11 @ SY116 @ SY117 )
| ( ( apply @ SV11 @ ( zero @ SY116 ) )
= ( zero @ SY117 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(176,plain,
! [SV33: $i,SV23: $i,SV12: $i] :
( ( ( ~ ( morphism @ SV12 @ SV23 @ SV33 )
| ~ ( surjection @ SV12 ) )
= $true )
| ( ( ! [SY186: $i] :
( ~ ( element @ SY186 @ SV33 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SY186 @ SV33 @ SV23 @ SV12 ) )
!= SY186 )
| ~ ( element @ ( sK8_ElDom @ SY186 @ SV33 @ SV23 @ SV12 ) @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(177,plain,
! [SV13: $i,SV34: $i,SV24: $i] :
( ( ( ! [SY187: $i,SY188: $i] :
( ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) )
!= ( zero @ SY188 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) @ SY187 )
| ! [SY189: $i] :
( ( ( apply @ SV13 @ SY189 )
!= ( sK3_ElCodDom @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ SY189 @ SV34 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SY188 ) )
| ~ ( ( ( apply @ SV13 @ ( sK5_SY75 @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) @ SY187 )
| ~ ( ( ( apply @ SV13 @ ( sK4_SY76 @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SY188 @ SY187 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) ) ) )
| ~ ( morphism @ SV13 @ SV34 @ SY187 )
| ~ ( morphism @ SV24 @ SY187 @ SY188 ) ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(178,plain,
! [SV39: $i,SV35: $i,SV25: $i,SV14: $i] :
( ( ! [SY207: $i] :
( ~ ( exact @ SV14 @ SV25 )
| ~ ( morphism @ SV14 @ SV35 @ SV39 )
| ~ ( morphism @ SV25 @ SV39 @ SY207 )
| ~ ( ~ ! [SY208: $i] :
( ( ( apply @ SV25 @ SY208 )
!= ( zero @ SY207 ) )
| ~ ( element @ SY208 @ SV39 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY208 @ SY207 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SY208 )
| ~ ( element @ ( sK6_ElDom @ SY208 @ SY207 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
| ~ ~ ( ~ ! [SY193: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY193 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY193 )
= ( zero @ SY207 ) ) )
| ~ ! [SY211: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY211 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY211 @ SV39 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(179,plain,
! [SV15: $i,SV1: $i] :
( ( ( injection @ SV1 )
= $false )
| ( ( ! [SY135: $i] :
~ ( morphism @ SV1 @ SV15 @ SY135 ) )
= $true )
| ( ( ! [SY136: $i,SY137: $i] :
( ~ ( element @ SY136 @ SV15 )
| ~ ( element @ SY137 @ SV15 )
| ( ( apply @ SV1 @ SY136 )
!= ( apply @ SV1 @ SY137 ) )
| ( SY136 = SY137 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(180,plain,
! [SV40: $i,SV36: $i,SV26: $i,SV16: $i,SV2: $i] :
( ( ! [SY213: $i] :
( ! [SY214: $i,SY215: $i] :
( ~ ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
| ~ ( morphism @ SV2 @ SV40 @ SY213 )
| ~ ( morphism @ SV16 @ SY213 @ SY215 )
| ~ ( morphism @ SV26 @ SV40 @ SY214 )
| ~ ( morphism @ SV36 @ SY214 @ SY215 ) )
| ! [SY216: $i] :
( ~ ( element @ SY216 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY216 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY216 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(181,plain,
! [SV27: $i,SV3: $i,SV17: $i] :
( ( ( ~ ( element @ SV17 @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV27 @ SV3 ) )
= $true )
| ( ( element @ ( subtract @ SV3 @ SV17 @ SV27 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(182,plain,
! [SV28: $i,SV5: $i,SV19: $i] :
( ( ( ~ ( element @ SV19 @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV28 @ SV5 ) )
= $true )
| ( ( ( subtract @ SV5 @ SV19 @ ( subtract @ SV5 @ SV19 @ SV28 ) )
= SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(183,plain,
! [SV29: $i,SV20: $i,SV6: $i] :
( ( ( morphism @ SV6 @ SV20 @ SV29 )
= $false )
| ( ( ! [SY176: $i,SY177: $i] :
( ~ ( element @ SY176 @ SV20 )
| ~ ( element @ SY177 @ SV20 )
| ( ( apply @ SV6 @ ( subtract @ SV20 @ SY176 @ SY177 ) )
= ( subtract @ SV29 @ ( apply @ SV6 @ SY176 ) @ ( apply @ SV6 @ SY177 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(184,plain,
! [SV21: $i,SV7: $i] :
( ( ( ( ( apply @ delta @ sK1_E )
!= SV7 )
| ~ ( element @ SV7 @ r ) )
= $true )
| ( ( ~ ( element @ SV21 @ b ) )
= $true )
| ( ( ( ( apply @ h @ ( apply @ beta @ SV21 ) )
!= SV7 ) )
= $true )
| ( ( ( ( apply @ delta @ ( apply @ g @ SV21 ) )
!= SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(185,plain,
! [SV8: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV30 @ SV8 ) @ SV30 )
| ~ ( element @ ( sK10_SY78 @ SV30 @ SV8 ) @ SV30 ) )
| ( ( apply @ SV8 @ ( sK9_El1 @ SV30 @ SV8 ) )
!= ( apply @ SV8 @ ( sK10_SY78 @ SV30 @ SV8 ) ) ) )
| ~ ( ( ( sK9_El1 @ SV30 @ SV8 )
!= ( sK10_SY78 @ SV30 @ SV8 ) ) ) )
= $false )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(186,plain,
! [SV9: $i,SV31: $i,SV37: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) @ SV37 )
| ~ ! [SY202: $i] :
( ( ( apply @ SV9 @ SY202 )
!= ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) )
| ~ ( element @ SY202 @ SV31 ) ) ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV31 @ SV37 ) )
= $true )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(187,plain,
! [SV10: $i,SV22: $i,SV32: $i,SV38: $i,SV41: $i] :
( ( ! [SY217: $i] :
( ~ ( ~ ( element @ ( sK2_ElDom @ SY217 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
| ~ ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SY217 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
!= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SY217 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) ) ) )
| ! [SY218: $i,SY219: $i] :
( ~ ( morphism @ SV10 @ SV41 @ SY217 )
| ~ ( morphism @ SV22 @ SY217 @ SY219 )
| ~ ( morphism @ SV32 @ SV41 @ SY218 )
| ~ ( morphism @ SV38 @ SY218 @ SY219 ) )
| ( commute @ SV10 @ SV22 @ SV32 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(188,plain,
! [SV42: $i,SV11: $i] :
( ( ! [SY220: $i] :
( ~ ( morphism @ SV11 @ SV42 @ SY220 )
| ! [SY221: $i] :
( ~ ( element @ SY221 @ SV42 )
| ( element @ ( apply @ SV11 @ SY221 ) @ SY220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(189,plain,
! [SV43: $i,SV11: $i] :
( ( ! [SY222: $i] :
( ~ ( morphism @ SV11 @ SV43 @ SY222 )
| ( ( apply @ SV11 @ ( zero @ SV43 ) )
= ( zero @ SY222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(190,plain,
! [SV33: $i,SV23: $i,SV12: $i] :
( ( ( ~ ( morphism @ SV12 @ SV23 @ SV33 ) )
= $true )
| ( ( ~ ( surjection @ SV12 ) )
= $true )
| ( ( ! [SY186: $i] :
( ~ ( element @ SY186 @ SV33 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SY186 @ SV33 @ SV23 @ SV12 ) )
!= SY186 )
| ~ ( element @ ( sK8_ElDom @ SY186 @ SV33 @ SV23 @ SV12 ) @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(191,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV24: $i] :
( ( ( ! [SY223: $i] :
( ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY223 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( zero @ SY223 ) )
| ~ ( element @ ( sK3_ElCodDom @ SY223 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ! [SY224: $i] :
( ( ( apply @ SV13 @ SY224 )
!= ( sK3_ElCodDom @ SY223 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ SY224 @ SV34 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SY223 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SY223 ) )
| ~ ( ( ( apply @ SV13 @ ( sK5_SY75 @ SY223 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SY223 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SY223 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SY223 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ~ ( ( ( apply @ SV13 @ ( sK4_SY76 @ SY223 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SY223 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SY223 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) ) ) )
| ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SY223 ) ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(192,plain,
! [SV45: $i,SV39: $i,SV35: $i,SV25: $i,SV14: $i] :
( ( ~ ( exact @ SV14 @ SV25 )
| ~ ( morphism @ SV14 @ SV35 @ SV39 )
| ~ ( morphism @ SV25 @ SV39 @ SV45 )
| ~ ( ~ ! [SY225: $i] :
( ( ( apply @ SV25 @ SY225 )
!= ( zero @ SV45 ) )
| ~ ( element @ SY225 @ SV39 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SY225 )
| ~ ( element @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
| ~ ~ ( ~ ! [SY226: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY226 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY226 )
= ( zero @ SV45 ) ) )
| ~ ! [SY211: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY211 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY211 @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(193,plain,
! [SV46: $i,SV15: $i,SV1: $i] :
( ( ( ~ ( morphism @ SV1 @ SV15 @ SV46 ) )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( ! [SY136: $i,SY137: $i] :
( ~ ( element @ SY136 @ SV15 )
| ~ ( element @ SY137 @ SV15 )
| ( ( apply @ SV1 @ SY136 )
!= ( apply @ SV1 @ SY137 ) )
| ( SY136 = SY137 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(194,plain,
! [SV47: $i,SV40: $i,SV36: $i,SV26: $i,SV16: $i,SV2: $i] :
( ( ! [SY230: $i,SY231: $i] :
( ~ ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
| ~ ( morphism @ SV2 @ SV40 @ SV47 )
| ~ ( morphism @ SV16 @ SV47 @ SY231 )
| ~ ( morphism @ SV26 @ SV40 @ SY230 )
| ~ ( morphism @ SV36 @ SY230 @ SY231 ) )
| ! [SY216: $i] :
( ~ ( element @ SY216 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY216 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(195,plain,
! [SV27: $i,SV3: $i,SV17: $i] :
( ( ( element @ SV17 @ SV3 )
= $false )
| ( ( ~ ( element @ SV27 @ SV3 ) )
= $true )
| ( ( element @ ( subtract @ SV3 @ SV17 @ SV27 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(196,plain,
! [SV28: $i,SV5: $i,SV19: $i] :
( ( ( element @ SV19 @ SV5 )
= $false )
| ( ( ~ ( element @ SV28 @ SV5 ) )
= $true )
| ( ( ( subtract @ SV5 @ SV19 @ ( subtract @ SV5 @ SV19 @ SV28 ) )
= SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(197,plain,
! [SV29: $i,SV6: $i,SV20: $i,SV48: $i] :
( ( ( ! [SY233: $i] :
( ~ ( element @ SV48 @ SV20 )
| ~ ( element @ SY233 @ SV20 )
| ( ( apply @ SV6 @ ( subtract @ SV20 @ SV48 @ SY233 ) )
= ( subtract @ SV29 @ ( apply @ SV6 @ SV48 ) @ ( apply @ SV6 @ SY233 ) ) ) ) )
= $true )
| ( ( morphism @ SV6 @ SV20 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(198,plain,
! [SV21: $i,SV7: $i] :
( ( ( ( ( apply @ delta @ sK1_E )
!= SV7 ) )
= $true )
| ( ( ~ ( element @ SV7 @ r ) )
= $true )
| ( ( ~ ( element @ SV21 @ b ) )
= $true )
| ( ( ( ( apply @ h @ ( apply @ beta @ SV21 ) )
!= SV7 ) )
= $true )
| ( ( ( ( apply @ delta @ ( apply @ g @ SV21 ) )
!= SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(199,plain,
! [SV8: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV30 @ SV8 ) @ SV30 )
| ~ ( element @ ( sK10_SY78 @ SV30 @ SV8 ) @ SV30 ) )
| ( ( apply @ SV8 @ ( sK9_El1 @ SV30 @ SV8 ) )
!= ( apply @ SV8 @ ( sK10_SY78 @ SV30 @ SV8 ) ) ) ) )
= $false )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(200,plain,
! [SV8: $i,SV30: $i] :
( ( ( ~ ( ( ( sK9_El1 @ SV30 @ SV8 )
!= ( sK10_SY78 @ SV30 @ SV8 ) ) ) )
= $false )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(201,plain,
! [SV9: $i,SV31: $i,SV37: $i] :
( ( ( ~ ( element @ ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) @ SV37 )
| ~ ! [SY202: $i] :
( ( ( apply @ SV9 @ SY202 )
!= ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) )
| ~ ( element @ SY202 @ SV31 ) ) )
= $false )
| ( ( ~ ( morphism @ SV9 @ SV31 @ SV37 ) )
= $true )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(202,plain,
! [SV10: $i,SV22: $i,SV32: $i,SV38: $i,SV41: $i,SV49: $i] :
( ( ~ ( ~ ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
| ~ ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
!= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) ) ) )
| ! [SY234: $i,SY235: $i] :
( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SY235 )
| ~ ( morphism @ SV32 @ SV41 @ SY234 )
| ~ ( morphism @ SV38 @ SY234 @ SY235 ) )
| ( commute @ SV10 @ SV22 @ SV32 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(203,plain,
! [SV50: $i,SV42: $i,SV11: $i] :
( ( ~ ( morphism @ SV11 @ SV42 @ SV50 )
| ! [SY236: $i] :
( ~ ( element @ SY236 @ SV42 )
| ( element @ ( apply @ SV11 @ SY236 ) @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(204,plain,
! [SV51: $i,SV43: $i,SV11: $i] :
( ( ~ ( morphism @ SV11 @ SV43 @ SV51 )
| ( ( apply @ SV11 @ ( zero @ SV43 ) )
= ( zero @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(205,plain,
! [SV33: $i,SV23: $i,SV12: $i] :
( ( ( morphism @ SV12 @ SV23 @ SV33 )
= $false )
| ( ( ~ ( surjection @ SV12 ) )
= $true )
| ( ( ! [SY186: $i] :
( ~ ( element @ SY186 @ SV33 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SY186 @ SV33 @ SV23 @ SV12 ) )
!= SY186 )
| ~ ( element @ ( sK8_ElDom @ SY186 @ SV33 @ SV23 @ SV12 ) @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(206,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV52: $i,SV24: $i] :
( ( ( ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( zero @ SV52 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ! [SY237: $i] :
( ( ( apply @ SV13 @ SY237 )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ SY237 @ SV34 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
| ~ ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ~ ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) ) ) )
| ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(207,plain,
! [SV45: $i,SV39: $i,SV35: $i,SV25: $i,SV14: $i] :
( ( ( ~ ( exact @ SV14 @ SV25 )
| ~ ( morphism @ SV14 @ SV35 @ SV39 )
| ~ ( morphism @ SV25 @ SV39 @ SV45 ) )
= $true )
| ( ( ~ ( ~ ! [SY225: $i] :
( ( ( apply @ SV25 @ SY225 )
!= ( zero @ SV45 ) )
| ~ ( element @ SY225 @ SV39 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SY225 )
| ~ ( element @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
| ~ ~ ( ~ ! [SY226: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY226 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY226 )
= ( zero @ SV45 ) ) )
| ~ ! [SY211: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY211 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY211 @ SV39 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(208,plain,
! [SV46: $i,SV15: $i,SV1: $i] :
( ( ( morphism @ SV1 @ SV15 @ SV46 )
= $false )
| ( ( injection @ SV1 )
= $false )
| ( ( ! [SY136: $i,SY137: $i] :
( ~ ( element @ SY136 @ SV15 )
| ~ ( element @ SY137 @ SV15 )
| ( ( apply @ SV1 @ SY136 )
!= ( apply @ SV1 @ SY137 ) )
| ( SY136 = SY137 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(209,plain,
! [SV47: $i,SV40: $i,SV36: $i,SV26: $i,SV16: $i,SV2: $i] :
( ( ( ! [SY230: $i,SY231: $i] :
( ~ ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
| ~ ( morphism @ SV2 @ SV40 @ SV47 )
| ~ ( morphism @ SV16 @ SV47 @ SY231 )
| ~ ( morphism @ SV26 @ SV40 @ SY230 )
| ~ ( morphism @ SV36 @ SY230 @ SY231 ) ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( element @ SY216 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY216 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY216 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(210,plain,
! [SV17: $i,SV3: $i,SV27: $i] :
( ( ( element @ SV27 @ SV3 )
= $false )
| ( ( element @ SV17 @ SV3 )
= $false )
| ( ( element @ ( subtract @ SV3 @ SV17 @ SV27 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(211,plain,
! [SV19: $i,SV5: $i,SV28: $i] :
( ( ( element @ SV28 @ SV5 )
= $false )
| ( ( element @ SV19 @ SV5 )
= $false )
| ( ( ( subtract @ SV5 @ SV19 @ ( subtract @ SV5 @ SV19 @ SV28 ) )
= SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(212,plain,
! [SV29: $i,SV6: $i,SV53: $i,SV20: $i,SV48: $i] :
( ( ( ~ ( element @ SV48 @ SV20 )
| ~ ( element @ SV53 @ SV20 )
| ( ( apply @ SV6 @ ( subtract @ SV20 @ SV48 @ SV53 ) )
= ( subtract @ SV29 @ ( apply @ SV6 @ SV48 ) @ ( apply @ SV6 @ SV53 ) ) ) )
= $true )
| ( ( morphism @ SV6 @ SV20 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(213,plain,
! [SV21: $i,SV7: $i] :
( ( ( ( apply @ delta @ sK1_E )
= SV7 )
= $false )
| ( ( ~ ( element @ SV7 @ r ) )
= $true )
| ( ( ~ ( element @ SV21 @ b ) )
= $true )
| ( ( ( ( apply @ h @ ( apply @ beta @ SV21 ) )
!= SV7 ) )
= $true )
| ( ( ( ( apply @ delta @ ( apply @ g @ SV21 ) )
!= SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(214,plain,
! [SV8: $i,SV30: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV30 @ SV8 ) @ SV30 )
| ~ ( element @ ( sK10_SY78 @ SV30 @ SV8 ) @ SV30 ) )
| ( ( apply @ SV8 @ ( sK9_El1 @ SV30 @ SV8 ) )
!= ( apply @ SV8 @ ( sK10_SY78 @ SV30 @ SV8 ) ) ) ) )
= $true )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(215,plain,
! [SV8: $i,SV30: $i] :
( ( ( ( ( sK9_El1 @ SV30 @ SV8 )
!= ( sK10_SY78 @ SV30 @ SV8 ) ) )
= $true )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(216,plain,
! [SV9: $i,SV31: $i,SV37: $i] :
( ( ( ~ ( element @ ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) @ SV37 ) )
= $false )
| ( ( ~ ( morphism @ SV9 @ SV31 @ SV37 ) )
= $true )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(217,plain,
! [SV31: $i,SV37: $i,SV9: $i] :
( ( ( ~ ! [SY202: $i] :
( ( ( apply @ SV9 @ SY202 )
!= ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) )
| ~ ( element @ SY202 @ SV31 ) ) )
= $false )
| ( ( ~ ( morphism @ SV9 @ SV31 @ SV37 ) )
= $true )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(218,plain,
! [SV10: $i,SV22: $i,SV32: $i,SV38: $i,SV41: $i,SV49: $i] :
( ( ( ~ ( ~ ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
| ~ ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
!= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) ) ) )
| ! [SY234: $i,SY235: $i] :
( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SY235 )
| ~ ( morphism @ SV32 @ SV41 @ SY234 )
| ~ ( morphism @ SV38 @ SY234 @ SY235 ) ) )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(219,plain,
! [SV50: $i,SV42: $i,SV11: $i] :
( ( ( ~ ( morphism @ SV11 @ SV42 @ SV50 ) )
= $true )
| ( ( ! [SY236: $i] :
( ~ ( element @ SY236 @ SV42 )
| ( element @ ( apply @ SV11 @ SY236 ) @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(220,plain,
! [SV51: $i,SV43: $i,SV11: $i] :
( ( ( ~ ( morphism @ SV11 @ SV43 @ SV51 ) )
= $true )
| ( ( ( apply @ SV11 @ ( zero @ SV43 ) )
= ( zero @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(221,plain,
! [SV33: $i,SV23: $i,SV12: $i] :
( ( ( surjection @ SV12 )
= $false )
| ( ( morphism @ SV12 @ SV23 @ SV33 )
= $false )
| ( ( ! [SY186: $i] :
( ~ ( element @ SY186 @ SV33 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SY186 @ SV33 @ SV23 @ SV12 ) )
!= SY186 )
| ~ ( element @ ( sK8_ElDom @ SY186 @ SV33 @ SV23 @ SV12 ) @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(222,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV52: $i,SV24: $i] :
( ( ( ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( zero @ SV52 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ! [SY237: $i] :
( ( ( apply @ SV13 @ SY237 )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ SY237 @ SV34 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
| ~ ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ~ ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) ) ) ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(223,plain,
! [SV45: $i,SV39: $i,SV35: $i,SV25: $i,SV14: $i] :
( ( ( ~ ( exact @ SV14 @ SV25 )
| ~ ( morphism @ SV14 @ SV35 @ SV39 ) )
= $true )
| ( ( ~ ( morphism @ SV25 @ SV39 @ SV45 ) )
= $true )
| ( ( ~ ( ~ ! [SY225: $i] :
( ( ( apply @ SV25 @ SY225 )
!= ( zero @ SV45 ) )
| ~ ( element @ SY225 @ SV39 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SY225 )
| ~ ( element @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
| ~ ~ ( ~ ! [SY226: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY226 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY226 )
= ( zero @ SV45 ) ) )
| ~ ! [SY211: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY211 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY211 @ SV39 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(224,plain,
! [SV46: $i,SV1: $i,SV15: $i,SV54: $i] :
( ( ( ! [SY238: $i] :
( ~ ( element @ SV54 @ SV15 )
| ~ ( element @ SY238 @ SV15 )
| ( ( apply @ SV1 @ SV54 )
!= ( apply @ SV1 @ SY238 ) )
| ( SV54 = SY238 ) ) )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV15 @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(225,plain,
! [SV55: $i,SV47: $i,SV40: $i,SV36: $i,SV26: $i,SV16: $i,SV2: $i] :
( ( ( ! [SY239: $i] :
( ~ ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
| ~ ( morphism @ SV2 @ SV40 @ SV47 )
| ~ ( morphism @ SV16 @ SV47 @ SY239 )
| ~ ( morphism @ SV26 @ SV40 @ SV55 )
| ~ ( morphism @ SV36 @ SV55 @ SY239 ) ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( element @ SY216 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY216 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY216 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(226,plain,
! [SV29: $i,SV6: $i,SV53: $i,SV20: $i,SV48: $i] :
( ( ( ~ ( element @ SV48 @ SV20 )
| ~ ( element @ SV53 @ SV20 ) )
= $true )
| ( ( ( apply @ SV6 @ ( subtract @ SV20 @ SV48 @ SV53 ) )
= ( subtract @ SV29 @ ( apply @ SV6 @ SV48 ) @ ( apply @ SV6 @ SV53 ) ) )
= $true )
| ( ( morphism @ SV6 @ SV20 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(227,plain,
! [SV21: $i,SV7: $i] :
( ( ( element @ SV7 @ r )
= $false )
| ( ( ( apply @ delta @ sK1_E )
= SV7 )
= $false )
| ( ( ~ ( element @ SV21 @ b ) )
= $true )
| ( ( ( ( apply @ h @ ( apply @ beta @ SV21 ) )
!= SV7 ) )
= $true )
| ( ( ( ( apply @ delta @ ( apply @ g @ SV21 ) )
!= SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(228,plain,
! [SV8: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV30 @ SV8 ) @ SV30 )
| ~ ( element @ ( sK10_SY78 @ SV30 @ SV8 ) @ SV30 ) )
| ( ( apply @ SV8 @ ( sK9_El1 @ SV30 @ SV8 ) )
!= ( apply @ SV8 @ ( sK10_SY78 @ SV30 @ SV8 ) ) ) )
= $false )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(229,plain,
! [SV8: $i,SV30: $i] :
( ( ( ( sK9_El1 @ SV30 @ SV8 )
= ( sK10_SY78 @ SV30 @ SV8 ) )
= $false )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(230,plain,
! [SV9: $i,SV31: $i,SV37: $i] :
( ( ( element @ ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) @ SV37 )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV31 @ SV37 ) )
= $true )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(231,plain,
! [SV31: $i,SV37: $i,SV9: $i] :
( ( ( ! [SY202: $i] :
( ( ( apply @ SV9 @ SY202 )
!= ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) )
| ~ ( element @ SY202 @ SV31 ) ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV31 @ SV37 ) )
= $true )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(232,plain,
! [SV10: $i,SV22: $i,SV32: $i,SV38: $i,SV41: $i,SV49: $i] :
( ( ( ~ ( ~ ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
| ~ ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
!= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY234: $i,SY235: $i] :
( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SY235 )
| ~ ( morphism @ SV32 @ SV41 @ SY234 )
| ~ ( morphism @ SV38 @ SY234 @ SY235 ) ) )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(233,plain,
! [SV50: $i,SV42: $i,SV11: $i] :
( ( ( morphism @ SV11 @ SV42 @ SV50 )
= $false )
| ( ( ! [SY236: $i] :
( ~ ( element @ SY236 @ SV42 )
| ( element @ ( apply @ SV11 @ SY236 ) @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(234,plain,
! [SV51: $i,SV43: $i,SV11: $i] :
( ( ( morphism @ SV11 @ SV43 @ SV51 )
= $false )
| ( ( ( apply @ SV11 @ ( zero @ SV43 ) )
= ( zero @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(235,plain,
! [SV23: $i,SV12: $i,SV33: $i,SV56: $i] :
( ( ( ~ ( element @ SV56 @ SV33 )
| ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SV56 @ SV33 @ SV23 @ SV12 ) )
!= SV56 )
| ~ ( element @ ( sK8_ElDom @ SV56 @ SV33 @ SV23 @ SV12 ) @ SV23 ) ) )
= $true )
| ( ( morphism @ SV12 @ SV23 @ SV33 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(236,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV52: $i,SV24: $i] :
( ( ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( zero @ SV52 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ! [SY237: $i] :
( ( ( apply @ SV13 @ SY237 )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ SY237 @ SV34 ) ) )
| ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
| ~ ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ~ ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(237,plain,
! [SV45: $i,SV39: $i,SV35: $i,SV25: $i,SV14: $i] :
( ( ( ~ ( exact @ SV14 @ SV25 ) )
= $true )
| ( ( ~ ( morphism @ SV14 @ SV35 @ SV39 ) )
= $true )
| ( ( ~ ( morphism @ SV25 @ SV39 @ SV45 ) )
= $true )
| ( ( ~ ( ~ ! [SY225: $i] :
( ( ( apply @ SV25 @ SY225 )
!= ( zero @ SV45 ) )
| ~ ( element @ SY225 @ SV39 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SY225 )
| ~ ( element @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
| ~ ~ ( ~ ! [SY226: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY226 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY226 )
= ( zero @ SV45 ) ) )
| ~ ! [SY211: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY211 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY211 @ SV39 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(238,plain,
! [SV46: $i,SV1: $i,SV57: $i,SV15: $i,SV54: $i] :
( ( ( ~ ( element @ SV54 @ SV15 )
| ~ ( element @ SV57 @ SV15 )
| ( ( apply @ SV1 @ SV54 )
!= ( apply @ SV1 @ SV57 ) )
| ( SV54 = SV57 ) )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV15 @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(239,plain,
! [SV55: $i,SV58: $i,SV47: $i,SV40: $i,SV36: $i,SV26: $i,SV16: $i,SV2: $i] :
( ( ( ~ ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
| ~ ( morphism @ SV2 @ SV40 @ SV47 )
| ~ ( morphism @ SV16 @ SV47 @ SV58 )
| ~ ( morphism @ SV26 @ SV40 @ SV55 )
| ~ ( morphism @ SV36 @ SV55 @ SV58 ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( element @ SY216 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY216 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY216 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(240,plain,
! [SV29: $i,SV6: $i,SV53: $i,SV20: $i,SV48: $i] :
( ( ( ~ ( element @ SV48 @ SV20 ) )
= $true )
| ( ( ~ ( element @ SV53 @ SV20 ) )
= $true )
| ( ( ( apply @ SV6 @ ( subtract @ SV20 @ SV48 @ SV53 ) )
= ( subtract @ SV29 @ ( apply @ SV6 @ SV48 ) @ ( apply @ SV6 @ SV53 ) ) )
= $true )
| ( ( morphism @ SV6 @ SV20 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(241,plain,
! [SV7: $i,SV21: $i] :
( ( ( element @ SV21 @ b )
= $false )
| ( ( ( apply @ delta @ sK1_E )
= SV7 )
= $false )
| ( ( element @ SV7 @ r )
= $false )
| ( ( ( ( apply @ h @ ( apply @ beta @ SV21 ) )
!= SV7 ) )
= $true )
| ( ( ( ( apply @ delta @ ( apply @ g @ SV21 ) )
!= SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(242,plain,
! [SV8: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_El1 @ SV30 @ SV8 ) @ SV30 )
| ~ ( element @ ( sK10_SY78 @ SV30 @ SV8 ) @ SV30 ) ) )
= $false )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(243,plain,
! [SV30: $i,SV8: $i] :
( ( ( ( ( apply @ SV8 @ ( sK9_El1 @ SV30 @ SV8 ) )
!= ( apply @ SV8 @ ( sK10_SY78 @ SV30 @ SV8 ) ) ) )
= $false )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(244,plain,
! [SV59: $i,SV30: $i,SV8: $i] :
( ( ( ~ ( morphism @ SV8 @ SV30 @ SV59 ) )
= $true )
| ( ( ( sK9_El1 @ SV30 @ SV8 )
= ( sK10_SY78 @ SV30 @ SV8 ) )
= $false )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(245,plain,
! [SV37: $i,SV31: $i,SV9: $i] :
( ( ( morphism @ SV9 @ SV31 @ SV37 )
= $false )
| ( ( element @ ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) @ SV37 )
= $true )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(246,plain,
! [SV31: $i,SV37: $i,SV60: $i,SV9: $i] :
( ( ( ( ( apply @ SV9 @ SV60 )
!= ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) )
| ~ ( element @ SV60 @ SV31 ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV31 @ SV37 ) )
= $true )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(247,plain,
! [SV10: $i,SV22: $i,SV32: $i,SV38: $i,SV41: $i,SV49: $i] :
( ( ( ~ ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
| ~ ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
!= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) ) ) )
= $false )
| ( ( ! [SY234: $i,SY235: $i] :
( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SY235 )
| ~ ( morphism @ SV32 @ SV41 @ SY234 )
| ~ ( morphism @ SV38 @ SY234 @ SY235 ) ) )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(248,plain,
! [SV50: $i,SV11: $i,SV42: $i,SV61: $i] :
( ( ( ~ ( element @ SV61 @ SV42 )
| ( element @ ( apply @ SV11 @ SV61 ) @ SV50 ) )
= $true )
| ( ( morphism @ SV11 @ SV42 @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(249,plain,
! [SV23: $i,SV12: $i,SV33: $i,SV56: $i] :
( ( ( ~ ( element @ SV56 @ SV33 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SV56 @ SV33 @ SV23 @ SV12 ) )
!= SV56 )
| ~ ( element @ ( sK8_ElDom @ SV56 @ SV33 @ SV23 @ SV12 ) @ SV23 ) ) )
= $true )
| ( ( morphism @ SV12 @ SV23 @ SV33 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(250,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV52: $i,SV24: $i] :
( ( ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( zero @ SV52 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ! [SY237: $i] :
( ( ( apply @ SV13 @ SY237 )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ SY237 @ SV34 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(251,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV52: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
| ~ ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ~ ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(252,plain,
! [SV45: $i,SV39: $i,SV35: $i,SV25: $i,SV14: $i] :
( ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( ~ ( morphism @ SV14 @ SV35 @ SV39 ) )
= $true )
| ( ( ~ ( morphism @ SV25 @ SV39 @ SV45 ) )
= $true )
| ( ( ~ ( ~ ! [SY225: $i] :
( ( ( apply @ SV25 @ SY225 )
!= ( zero @ SV45 ) )
| ~ ( element @ SY225 @ SV39 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SY225 )
| ~ ( element @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
| ~ ~ ( ~ ! [SY226: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY226 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY226 )
= ( zero @ SV45 ) ) )
| ~ ! [SY211: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY211 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY211 @ SV39 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(253,plain,
! [SV46: $i,SV1: $i,SV57: $i,SV15: $i,SV54: $i] :
( ( ( ~ ( element @ SV54 @ SV15 )
| ~ ( element @ SV57 @ SV15 )
| ( ( apply @ SV1 @ SV54 )
!= ( apply @ SV1 @ SV57 ) ) )
= $true )
| ( ( SV54 = SV57 )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV15 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(254,plain,
! [SV55: $i,SV58: $i,SV47: $i,SV40: $i,SV36: $i,SV26: $i,SV16: $i,SV2: $i] :
( ( ( ~ ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
| ~ ( morphism @ SV2 @ SV40 @ SV47 )
| ~ ( morphism @ SV16 @ SV47 @ SV58 )
| ~ ( morphism @ SV26 @ SV40 @ SV55 ) )
= $true )
| ( ( ~ ( morphism @ SV36 @ SV55 @ SV58 ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( element @ SY216 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY216 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY216 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(255,plain,
! [SV29: $i,SV6: $i,SV53: $i,SV20: $i,SV48: $i] :
( ( ( element @ SV48 @ SV20 )
= $false )
| ( ( ~ ( element @ SV53 @ SV20 ) )
= $true )
| ( ( ( apply @ SV6 @ ( subtract @ SV20 @ SV48 @ SV53 ) )
= ( subtract @ SV29 @ ( apply @ SV6 @ SV48 ) @ ( apply @ SV6 @ SV53 ) ) )
= $true )
| ( ( morphism @ SV6 @ SV20 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(256,plain,
! [SV7: $i,SV21: $i] :
( ( ( ( apply @ h @ ( apply @ beta @ SV21 ) )
= SV7 )
= $false )
| ( ( element @ SV7 @ r )
= $false )
| ( ( ( apply @ delta @ sK1_E )
= SV7 )
= $false )
| ( ( element @ SV21 @ b )
= $false )
| ( ( ( ( apply @ delta @ ( apply @ g @ SV21 ) )
!= SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(257,plain,
! [SV8: $i,SV30: $i] :
( ( ( ~ ( ~ ( element @ ( sK9_El1 @ SV30 @ SV8 ) @ SV30 )
| ~ ( element @ ( sK10_SY78 @ SV30 @ SV8 ) @ SV30 ) ) )
= $true )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(258,plain,
! [SV30: $i,SV8: $i] :
( ( ( ( apply @ SV8 @ ( sK9_El1 @ SV30 @ SV8 ) )
= ( apply @ SV8 @ ( sK10_SY78 @ SV30 @ SV8 ) ) )
= $true )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(259,plain,
! [SV59: $i,SV30: $i,SV8: $i] :
( ( ( morphism @ SV8 @ SV30 @ SV59 )
= $false )
| ( ( ( sK9_El1 @ SV30 @ SV8 )
= ( sK10_SY78 @ SV30 @ SV8 ) )
= $false )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(260,plain,
! [SV31: $i,SV37: $i,SV60: $i,SV9: $i] :
( ( ( ( ( apply @ SV9 @ SV60 )
!= ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) ) )
= $true )
| ( ( ~ ( element @ SV60 @ SV31 ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV31 @ SV37 ) )
= $true )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(261,plain,
! [SV10: $i,SV22: $i,SV32: $i,SV38: $i,SV41: $i,SV49: $i] :
( ( ( ~ ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 ) )
= $false )
| ( ( ! [SY234: $i,SY235: $i] :
( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SY235 )
| ~ ( morphism @ SV32 @ SV41 @ SY234 )
| ~ ( morphism @ SV38 @ SY234 @ SY235 ) ) )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(262,plain,
! [SV32: $i,SV38: $i,SV41: $i,SV49: $i,SV10: $i,SV22: $i] :
( ( ( ~ ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
!= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) ) ) )
= $false )
| ( ( ! [SY234: $i,SY235: $i] :
( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SY235 )
| ~ ( morphism @ SV32 @ SV41 @ SY234 )
| ~ ( morphism @ SV38 @ SY234 @ SY235 ) ) )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(263,plain,
! [SV50: $i,SV11: $i,SV42: $i,SV61: $i] :
( ( ( ~ ( element @ SV61 @ SV42 ) )
= $true )
| ( ( element @ ( apply @ SV11 @ SV61 ) @ SV50 )
= $true )
| ( ( morphism @ SV11 @ SV42 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(264,plain,
! [SV23: $i,SV12: $i,SV33: $i,SV56: $i] :
( ( ( element @ SV56 @ SV33 )
= $false )
| ( ( ~ ( ( ( apply @ SV12 @ ( sK8_ElDom @ SV56 @ SV33 @ SV23 @ SV12 ) )
!= SV56 )
| ~ ( element @ ( sK8_ElDom @ SV56 @ SV33 @ SV23 @ SV12 ) @ SV23 ) ) )
= $true )
| ( ( morphism @ SV12 @ SV23 @ SV33 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(265,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV52: $i,SV24: $i] :
( ( ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( zero @ SV52 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ! [SY237: $i] :
( ( ( apply @ SV13 @ SY237 )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ SY237 @ SV34 ) ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(266,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV52: $i,SV24: $i] :
( ( ( ~ ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
| ~ ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ~ ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) ) ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(267,plain,
! [SV45: $i,SV25: $i,SV39: $i,SV35: $i,SV14: $i] :
( ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( ~ ( morphism @ SV25 @ SV39 @ SV45 ) )
= $true )
| ( ( ~ ( ~ ! [SY225: $i] :
( ( ( apply @ SV25 @ SY225 )
!= ( zero @ SV45 ) )
| ~ ( element @ SY225 @ SV39 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SY225 )
| ~ ( element @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
| ~ ~ ( ~ ! [SY226: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY226 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY226 )
= ( zero @ SV45 ) ) )
| ~ ! [SY211: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY211 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY211 @ SV39 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(268,plain,
! [SV46: $i,SV1: $i,SV57: $i,SV15: $i,SV54: $i] :
( ( ( ~ ( element @ SV54 @ SV15 )
| ~ ( element @ SV57 @ SV15 ) )
= $true )
| ( ( ( ( apply @ SV1 @ SV54 )
!= ( apply @ SV1 @ SV57 ) ) )
= $true )
| ( ( SV54 = SV57 )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV15 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(269,plain,
! [SV55: $i,SV58: $i,SV47: $i,SV40: $i,SV36: $i,SV26: $i,SV16: $i,SV2: $i] :
( ( ( ~ ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
| ~ ( morphism @ SV2 @ SV40 @ SV47 )
| ~ ( morphism @ SV16 @ SV47 @ SV58 ) )
= $true )
| ( ( ~ ( morphism @ SV26 @ SV40 @ SV55 ) )
= $true )
| ( ( ~ ( morphism @ SV36 @ SV55 @ SV58 ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( element @ SY216 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY216 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY216 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(270,plain,
! [SV29: $i,SV6: $i,SV48: $i,SV20: $i,SV53: $i] :
( ( ( element @ SV53 @ SV20 )
= $false )
| ( ( element @ SV48 @ SV20 )
= $false )
| ( ( ( apply @ SV6 @ ( subtract @ SV20 @ SV48 @ SV53 ) )
= ( subtract @ SV29 @ ( apply @ SV6 @ SV48 ) @ ( apply @ SV6 @ SV53 ) ) )
= $true )
| ( ( morphism @ SV6 @ SV20 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(271,plain,
! [SV7: $i,SV21: $i] :
( ( ( ( apply @ delta @ ( apply @ g @ SV21 ) )
= SV7 )
= $false )
| ( ( element @ SV21 @ b )
= $false )
| ( ( ( apply @ delta @ sK1_E )
= SV7 )
= $false )
| ( ( element @ SV7 @ r )
= $false )
| ( ( ( apply @ h @ ( apply @ beta @ SV21 ) )
= SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(272,plain,
! [SV8: $i,SV30: $i] :
( ( ( ~ ( element @ ( sK9_El1 @ SV30 @ SV8 ) @ SV30 )
| ~ ( element @ ( sK10_SY78 @ SV30 @ SV8 ) @ SV30 ) )
= $false )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(273,plain,
! [SV62: $i,SV30: $i,SV8: $i] :
( ( ( ~ ( morphism @ SV8 @ SV30 @ SV62 ) )
= $true )
| ( ( ( apply @ SV8 @ ( sK9_El1 @ SV30 @ SV8 ) )
= ( apply @ SV8 @ ( sK10_SY78 @ SV30 @ SV8 ) ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(274,plain,
! [SV31: $i,SV37: $i,SV60: $i,SV9: $i] :
( ( ( ( apply @ SV9 @ SV60 )
= ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) )
= $false )
| ( ( ~ ( element @ SV60 @ SV31 ) )
= $true )
| ( ( ~ ( morphism @ SV9 @ SV31 @ SV37 ) )
= $true )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(275,plain,
! [SV10: $i,SV22: $i,SV32: $i,SV38: $i,SV41: $i,SV49: $i] :
( ( ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
= $true )
| ( ( ! [SY234: $i,SY235: $i] :
( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SY235 )
| ~ ( morphism @ SV32 @ SV41 @ SY234 )
| ~ ( morphism @ SV38 @ SY234 @ SY235 ) ) )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(276,plain,
! [SV32: $i,SV38: $i,SV41: $i,SV49: $i,SV10: $i,SV22: $i] :
( ( ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
!= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) ) )
= $true )
| ( ( ! [SY234: $i,SY235: $i] :
( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SY235 )
| ~ ( morphism @ SV32 @ SV41 @ SY234 )
| ~ ( morphism @ SV38 @ SY234 @ SY235 ) ) )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(277,plain,
! [SV50: $i,SV11: $i,SV42: $i,SV61: $i] :
( ( ( element @ SV61 @ SV42 )
= $false )
| ( ( element @ ( apply @ SV11 @ SV61 ) @ SV50 )
= $true )
| ( ( morphism @ SV11 @ SV42 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(278,plain,
! [SV23: $i,SV33: $i,SV56: $i,SV12: $i] :
( ( ( ( ( apply @ SV12 @ ( sK8_ElDom @ SV56 @ SV33 @ SV23 @ SV12 ) )
!= SV56 )
| ~ ( element @ ( sK8_ElDom @ SV56 @ SV33 @ SV23 @ SV12 ) @ SV23 ) )
= $false )
| ( ( element @ SV56 @ SV33 )
= $false )
| ( ( morphism @ SV12 @ SV23 @ SV33 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(279,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV52: $i,SV24: $i] :
( ( ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( zero @ SV52 ) )
| ~ ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 ) )
= $true )
| ( ( ! [SY237: $i] :
( ( ( apply @ SV13 @ SY237 )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ SY237 @ SV34 ) ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(280,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV52: $i,SV24: $i] :
( ( ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
| ~ ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) )
| ~ ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ~ ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(281,plain,
! [SV35: $i,SV14: $i,SV45: $i,SV39: $i,SV25: $i] :
( ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( ~ ( ~ ! [SY225: $i] :
( ( ( apply @ SV25 @ SY225 )
!= ( zero @ SV45 ) )
| ~ ( element @ SY225 @ SV39 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SY225 )
| ~ ( element @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
| ~ ~ ( ~ ! [SY226: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY226 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY226 )
= ( zero @ SV45 ) ) )
| ~ ! [SY211: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY211 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY211 @ SV39 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(282,plain,
! [SV46: $i,SV1: $i,SV57: $i,SV15: $i,SV54: $i] :
( ( ( ~ ( element @ SV54 @ SV15 ) )
= $true )
| ( ( ~ ( element @ SV57 @ SV15 ) )
= $true )
| ( ( ( ( apply @ SV1 @ SV54 )
!= ( apply @ SV1 @ SV57 ) ) )
= $true )
| ( ( SV54 = SV57 )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV15 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(283,plain,
! [SV55: $i,SV58: $i,SV47: $i,SV40: $i,SV36: $i,SV26: $i,SV16: $i,SV2: $i] :
( ( ( ~ ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
| ~ ( morphism @ SV2 @ SV40 @ SV47 ) )
= $true )
| ( ( ~ ( morphism @ SV16 @ SV47 @ SV58 ) )
= $true )
| ( ( ~ ( morphism @ SV26 @ SV40 @ SV55 ) )
= $true )
| ( ( ~ ( morphism @ SV36 @ SV55 @ SV58 ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( element @ SY216 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY216 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY216 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(284,plain,
! [SV8: $i,SV30: $i] :
( ( ( ~ ( element @ ( sK9_El1 @ SV30 @ SV8 ) @ SV30 ) )
= $false )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(285,plain,
! [SV8: $i,SV30: $i] :
( ( ( ~ ( element @ ( sK10_SY78 @ SV30 @ SV8 ) @ SV30 ) )
= $false )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(286,plain,
! [SV62: $i,SV30: $i,SV8: $i] :
( ( ( morphism @ SV8 @ SV30 @ SV62 )
= $false )
| ( ( ( apply @ SV8 @ ( sK9_El1 @ SV30 @ SV8 ) )
= ( apply @ SV8 @ ( sK10_SY78 @ SV30 @ SV8 ) ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(287,plain,
! [SV37: $i,SV9: $i,SV31: $i,SV60: $i] :
( ( ( element @ SV60 @ SV31 )
= $false )
| ( ( ( apply @ SV9 @ SV60 )
= ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) )
= $false )
| ( ( ~ ( morphism @ SV9 @ SV31 @ SV37 ) )
= $true )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(288,plain,
! [SV38: $i,SV63: $i,SV32: $i,SV22: $i,SV49: $i,SV41: $i,SV10: $i] :
( ( ( ! [SY240: $i] :
( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SY240 )
| ~ ( morphism @ SV32 @ SV41 @ SV63 )
| ~ ( morphism @ SV38 @ SV63 @ SY240 ) ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(289,plain,
! [SV32: $i,SV38: $i,SV41: $i,SV49: $i,SV10: $i,SV22: $i] :
( ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) )
= $false )
| ( ( ! [SY234: $i,SY235: $i] :
( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SY235 )
| ~ ( morphism @ SV32 @ SV41 @ SY234 )
| ~ ( morphism @ SV38 @ SY234 @ SY235 ) ) )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(290,plain,
! [SV23: $i,SV33: $i,SV56: $i,SV12: $i] :
( ( ( ( ( apply @ SV12 @ ( sK8_ElDom @ SV56 @ SV33 @ SV23 @ SV12 ) )
!= SV56 ) )
= $false )
| ( ( element @ SV56 @ SV33 )
= $false )
| ( ( morphism @ SV12 @ SV23 @ SV33 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(291,plain,
! [SV12: $i,SV23: $i,SV33: $i,SV56: $i] :
( ( ( ~ ( element @ ( sK8_ElDom @ SV56 @ SV33 @ SV23 @ SV12 ) @ SV23 ) )
= $false )
| ( ( element @ SV56 @ SV33 )
= $false )
| ( ( morphism @ SV12 @ SV23 @ SV33 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(292,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV52: $i,SV24: $i] :
( ( ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( zero @ SV52 ) ) )
= $true )
| ( ( ~ ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 ) )
= $true )
| ( ( ! [SY237: $i] :
( ( ( apply @ SV13 @ SY237 )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ SY237 @ SV34 ) ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(293,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV52: $i,SV24: $i] :
( ( ( ~ ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
| ~ ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(294,plain,
! [SV13: $i,SV24: $i,SV34: $i,SV44: $i,SV52: $i] :
( ( ( ~ ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ~ ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) ) )
= $false )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(295,plain,
! [SV35: $i,SV14: $i,SV39: $i,SV45: $i,SV25: $i] :
( ( ( ~ ! [SY225: $i] :
( ( ( apply @ SV25 @ SY225 )
!= ( zero @ SV45 ) )
| ~ ( element @ SY225 @ SV39 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SY225 )
| ~ ( element @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
| ~ ~ ( ~ ! [SY226: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY226 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY226 )
= ( zero @ SV45 ) ) )
| ~ ! [SY211: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY211 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY211 @ SV39 ) ) ) )
= $false )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(296,plain,
! [SV46: $i,SV1: $i,SV57: $i,SV15: $i,SV54: $i] :
( ( ( element @ SV54 @ SV15 )
= $false )
| ( ( ~ ( element @ SV57 @ SV15 ) )
= $true )
| ( ( ( ( apply @ SV1 @ SV54 )
!= ( apply @ SV1 @ SV57 ) ) )
= $true )
| ( ( SV54 = SV57 )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV15 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(297,plain,
! [SV55: $i,SV58: $i,SV47: $i,SV40: $i,SV36: $i,SV26: $i,SV16: $i,SV2: $i] :
( ( ( ~ ( commute @ SV2 @ SV16 @ SV26 @ SV36 ) )
= $true )
| ( ( ~ ( morphism @ SV2 @ SV40 @ SV47 ) )
= $true )
| ( ( ~ ( morphism @ SV16 @ SV47 @ SV58 ) )
= $true )
| ( ( ~ ( morphism @ SV26 @ SV40 @ SV55 ) )
= $true )
| ( ( ~ ( morphism @ SV36 @ SV55 @ SV58 ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( element @ SY216 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY216 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY216 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(298,plain,
! [SV8: $i,SV30: $i] :
( ( ( element @ ( sK9_El1 @ SV30 @ SV8 ) @ SV30 )
= $true )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(299,plain,
! [SV8: $i,SV30: $i] :
( ( ( element @ ( sK10_SY78 @ SV30 @ SV8 ) @ SV30 )
= $true )
| ( ( ! [SY178: $i] :
~ ( morphism @ SV8 @ SV30 @ SY178 ) )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(300,plain,
! [SV60: $i,SV37: $i,SV31: $i,SV9: $i] :
( ( ( morphism @ SV9 @ SV31 @ SV37 )
= $false )
| ( ( ( apply @ SV9 @ SV60 )
= ( sK7_ElCod @ SV37 @ SV31 @ SV9 ) )
= $false )
| ( ( element @ SV60 @ SV31 )
= $false )
| ( ( surjection @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(301,plain,
! [SV38: $i,SV63: $i,SV32: $i,SV64: $i,SV22: $i,SV49: $i,SV41: $i,SV10: $i] :
( ( ( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SV64 )
| ~ ( morphism @ SV32 @ SV41 @ SV63 )
| ~ ( morphism @ SV38 @ SV63 @ SV64 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(302,plain,
! [SV38: $i,SV65: $i,SV32: $i,SV22: $i,SV49: $i,SV41: $i,SV10: $i] :
( ( ( ! [SY241: $i] :
( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SY241 )
| ~ ( morphism @ SV32 @ SV41 @ SV65 )
| ~ ( morphism @ SV38 @ SV65 @ SY241 ) ) )
= $true )
| ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) )
= $false )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(303,plain,
! [SV23: $i,SV33: $i,SV56: $i,SV12: $i] :
( ( ( ( apply @ SV12 @ ( sK8_ElDom @ SV56 @ SV33 @ SV23 @ SV12 ) )
= SV56 )
= $true )
| ( ( element @ SV56 @ SV33 )
= $false )
| ( ( morphism @ SV12 @ SV23 @ SV33 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(304,plain,
! [SV12: $i,SV23: $i,SV33: $i,SV56: $i] :
( ( ( element @ ( sK8_ElDom @ SV56 @ SV33 @ SV23 @ SV12 ) @ SV23 )
= $true )
| ( ( element @ SV56 @ SV33 )
= $false )
| ( ( morphism @ SV12 @ SV23 @ SV33 )
= $false )
| ( ( surjection @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(305,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV52: $i,SV24: $i] :
( ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $false )
| ( ( ~ ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 ) )
= $true )
| ( ( ! [SY237: $i] :
( ( ( apply @ SV13 @ SY237 )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ SY237 @ SV34 ) ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(306,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV52: $i,SV24: $i] :
( ( ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
| ~ ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(307,plain,
! [SV13: $i,SV24: $i,SV34: $i,SV44: $i,SV52: $i] :
( ( ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
| ~ ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(308,plain,
! [SV35: $i,SV14: $i,SV39: $i,SV45: $i,SV25: $i] :
( ( ( ~ ! [SY225: $i] :
( ( ( apply @ SV25 @ SY225 )
!= ( zero @ SV45 ) )
| ~ ( element @ SY225 @ SV39 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SY225 )
| ~ ( element @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) ) )
= $false )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(309,plain,
! [SV39: $i,SV45: $i,SV25: $i,SV35: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ! [SY226: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY226 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY226 )
= ( zero @ SV45 ) ) )
| ~ ! [SY211: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY211 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY211 @ SV39 ) ) ) )
= $false )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(310,plain,
! [SV46: $i,SV1: $i,SV54: $i,SV15: $i,SV57: $i] :
( ( ( element @ SV57 @ SV15 )
= $false )
| ( ( element @ SV54 @ SV15 )
= $false )
| ( ( ( ( apply @ SV1 @ SV54 )
!= ( apply @ SV1 @ SV57 ) ) )
= $true )
| ( ( SV54 = SV57 )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV15 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(311,plain,
! [SV55: $i,SV58: $i,SV47: $i,SV40: $i,SV36: $i,SV26: $i,SV16: $i,SV2: $i] :
( ( ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
= $false )
| ( ( ~ ( morphism @ SV2 @ SV40 @ SV47 ) )
= $true )
| ( ( ~ ( morphism @ SV16 @ SV47 @ SV58 ) )
= $true )
| ( ( ~ ( morphism @ SV26 @ SV40 @ SV55 ) )
= $true )
| ( ( ~ ( morphism @ SV36 @ SV55 @ SV58 ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( element @ SY216 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY216 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY216 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(312,plain,
! [SV66: $i,SV30: $i,SV8: $i] :
( ( ( ~ ( morphism @ SV8 @ SV30 @ SV66 ) )
= $true )
| ( ( element @ ( sK9_El1 @ SV30 @ SV8 ) @ SV30 )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(313,plain,
! [SV67: $i,SV30: $i,SV8: $i] :
( ( ( ~ ( morphism @ SV8 @ SV30 @ SV67 ) )
= $true )
| ( ( element @ ( sK10_SY78 @ SV30 @ SV8 ) @ SV30 )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(314,plain,
! [SV38: $i,SV63: $i,SV32: $i,SV64: $i,SV22: $i,SV49: $i,SV41: $i,SV10: $i] :
( ( ( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SV64 )
| ~ ( morphism @ SV32 @ SV41 @ SV63 ) )
= $true )
| ( ( ~ ( morphism @ SV38 @ SV63 @ SV64 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(315,plain,
! [SV38: $i,SV65: $i,SV32: $i,SV68: $i,SV22: $i,SV49: $i,SV41: $i,SV10: $i] :
( ( ( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SV68 )
| ~ ( morphism @ SV32 @ SV41 @ SV65 )
| ~ ( morphism @ SV38 @ SV65 @ SV68 ) )
= $true )
| ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) )
= $false )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(316,plain,
! [SV13: $i,SV24: $i,SV34: $i,SV44: $i,SV52: $i] :
( ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $false )
| ( ( ! [SY237: $i] :
( ( ( apply @ SV13 @ SY237 )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ SY237 @ SV34 ) ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(317,plain,
! [SV13: $i,SV34: $i,SV44: $i,SV52: $i,SV24: $i] :
( ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(318,plain,
! [SV13: $i,SV24: $i,SV34: $i,SV44: $i,SV52: $i] :
( ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $true )
| ( ( ~ ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(319,plain,
! [SV35: $i,SV14: $i,SV39: $i,SV45: $i,SV25: $i] :
( ( ( ! [SY225: $i] :
( ( ( apply @ SV25 @ SY225 )
!= ( zero @ SV45 ) )
| ~ ( element @ SY225 @ SV39 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SY225 )
| ~ ( element @ ( sK6_ElDom @ SY225 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(320,plain,
! [SV39: $i,SV45: $i,SV25: $i,SV35: $i,SV14: $i] :
( ( ( ~ ( ~ ! [SY226: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY226 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY226 )
= ( zero @ SV45 ) ) )
| ~ ! [SY211: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY211 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY211 @ SV39 ) ) ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(321,plain,
! [SV46: $i,SV15: $i,SV57: $i,SV54: $i,SV1: $i] :
( ( ( ( apply @ SV1 @ SV54 )
= ( apply @ SV1 @ SV57 ) )
= $false )
| ( ( element @ SV54 @ SV15 )
= $false )
| ( ( element @ SV57 @ SV15 )
= $false )
| ( ( SV54 = SV57 )
= $true )
| ( ( injection @ SV1 )
= $false )
| ( ( morphism @ SV1 @ SV15 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(322,plain,
! [SV55: $i,SV58: $i,SV36: $i,SV26: $i,SV16: $i,SV47: $i,SV40: $i,SV2: $i] :
( ( ( morphism @ SV2 @ SV40 @ SV47 )
= $false )
| ( ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
= $false )
| ( ( ~ ( morphism @ SV16 @ SV47 @ SV58 ) )
= $true )
| ( ( ~ ( morphism @ SV26 @ SV40 @ SV55 ) )
= $true )
| ( ( ~ ( morphism @ SV36 @ SV55 @ SV58 ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( element @ SY216 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY216 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY216 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(323,plain,
! [SV66: $i,SV30: $i,SV8: $i] :
( ( ( morphism @ SV8 @ SV30 @ SV66 )
= $false )
| ( ( element @ ( sK9_El1 @ SV30 @ SV8 ) @ SV30 )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(324,plain,
! [SV67: $i,SV30: $i,SV8: $i] :
( ( ( morphism @ SV8 @ SV30 @ SV67 )
= $false )
| ( ( element @ ( sK10_SY78 @ SV30 @ SV8 ) @ SV30 )
= $true )
| ( ( injection @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(325,plain,
! [SV38: $i,SV63: $i,SV32: $i,SV64: $i,SV22: $i,SV49: $i,SV41: $i,SV10: $i] :
( ( ( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SV64 ) )
= $true )
| ( ( ~ ( morphism @ SV32 @ SV41 @ SV63 ) )
= $true )
| ( ( ~ ( morphism @ SV38 @ SV63 @ SV64 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(326,plain,
! [SV38: $i,SV65: $i,SV32: $i,SV68: $i,SV22: $i,SV49: $i,SV41: $i,SV10: $i] :
( ( ( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SV68 )
| ~ ( morphism @ SV32 @ SV41 @ SV65 ) )
= $true )
| ( ( ~ ( morphism @ SV38 @ SV65 @ SV68 ) )
= $true )
| ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) )
= $false )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(327,plain,
! [SV24: $i,SV34: $i,SV44: $i,SV52: $i,SV69: $i,SV13: $i] :
( ( ( ( ( apply @ SV13 @ SV69 )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ SV69 @ SV34 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $false )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(328,plain,
! [SV24: $i,SV34: $i,SV44: $i,SV52: $i,SV13: $i] :
( ( ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(329,plain,
! [SV24: $i,SV34: $i,SV44: $i,SV52: $i,SV13: $i] :
( ( ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
| ~ ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(330,plain,
! [SV35: $i,SV14: $i,SV39: $i,SV45: $i,SV70: $i,SV25: $i] :
( ( ( ( ( apply @ SV25 @ SV70 )
!= ( zero @ SV45 ) )
| ~ ( element @ SV70 @ SV39 )
| ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SV70 )
| ~ ( element @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(331,plain,
! [SV39: $i,SV45: $i,SV25: $i,SV35: $i,SV14: $i] :
( ( ( ~ ! [SY226: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY226 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY226 )
= ( zero @ SV45 ) ) )
| ~ ! [SY211: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY211 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY211 @ SV39 ) ) )
= $false )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(332,plain,
! [SV55: $i,SV40: $i,SV36: $i,SV26: $i,SV2: $i,SV58: $i,SV47: $i,SV16: $i] :
( ( ( morphism @ SV16 @ SV47 @ SV58 )
= $false )
| ( ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
= $false )
| ( ( morphism @ SV2 @ SV40 @ SV47 )
= $false )
| ( ( ~ ( morphism @ SV26 @ SV40 @ SV55 ) )
= $true )
| ( ( ~ ( morphism @ SV36 @ SV55 @ SV58 ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( element @ SY216 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY216 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY216 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(333,plain,
! [SV38: $i,SV63: $i,SV32: $i,SV64: $i,SV22: $i,SV49: $i,SV41: $i,SV10: $i] :
( ( ( ~ ( morphism @ SV10 @ SV41 @ SV49 ) )
= $true )
| ( ( ~ ( morphism @ SV22 @ SV49 @ SV64 ) )
= $true )
| ( ( ~ ( morphism @ SV32 @ SV41 @ SV63 ) )
= $true )
| ( ( ~ ( morphism @ SV38 @ SV63 @ SV64 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(334,plain,
! [SV38: $i,SV65: $i,SV32: $i,SV68: $i,SV22: $i,SV49: $i,SV41: $i,SV10: $i] :
( ( ( ~ ( morphism @ SV10 @ SV41 @ SV49 )
| ~ ( morphism @ SV22 @ SV49 @ SV68 ) )
= $true )
| ( ( ~ ( morphism @ SV32 @ SV41 @ SV65 ) )
= $true )
| ( ( ~ ( morphism @ SV38 @ SV65 @ SV68 ) )
= $true )
| ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) )
= $false )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(335,plain,
! [SV24: $i,SV34: $i,SV44: $i,SV52: $i,SV69: $i,SV13: $i] :
( ( ( ( ( apply @ SV13 @ SV69 )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) ) )
= $true )
| ( ( ~ ( element @ SV69 @ SV34 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $false )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(336,plain,
! [SV24: $i,SV34: $i,SV44: $i,SV52: $i,SV13: $i] :
( ( ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) ) )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(337,plain,
! [SV13: $i,SV24: $i,SV34: $i,SV44: $i,SV52: $i] :
( ( ( ~ ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(338,plain,
! [SV24: $i,SV34: $i,SV44: $i,SV52: $i,SV13: $i] :
( ( ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
!= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(339,plain,
! [SV13: $i,SV24: $i,SV34: $i,SV44: $i,SV52: $i] :
( ( ( ~ ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(340,plain,
! [SV35: $i,SV14: $i,SV39: $i,SV45: $i,SV70: $i,SV25: $i] :
( ( ( ( ( apply @ SV25 @ SV70 )
!= ( zero @ SV45 ) )
| ~ ( element @ SV70 @ SV39 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SV70 )
| ~ ( element @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(341,plain,
! [SV39: $i,SV45: $i,SV25: $i,SV35: $i,SV14: $i] :
( ( ( ~ ! [SY226: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY226 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY226 )
= ( zero @ SV45 ) ) ) )
= $false )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(342,plain,
! [SV45: $i,SV25: $i,SV39: $i,SV35: $i,SV14: $i] :
( ( ( ~ ! [SY211: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY211 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY211 @ SV39 ) ) )
= $false )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(343,plain,
! [SV58: $i,SV36: $i,SV16: $i,SV47: $i,SV2: $i,SV55: $i,SV40: $i,SV26: $i] :
( ( ( morphism @ SV26 @ SV40 @ SV55 )
= $false )
| ( ( morphism @ SV2 @ SV40 @ SV47 )
= $false )
| ( ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
= $false )
| ( ( morphism @ SV16 @ SV47 @ SV58 )
= $false )
| ( ( ~ ( morphism @ SV36 @ SV55 @ SV58 ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( element @ SY216 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY216 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY216 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(344,plain,
! [SV38: $i,SV63: $i,SV32: $i,SV64: $i,SV22: $i,SV49: $i,SV41: $i,SV10: $i] :
( ( ( morphism @ SV10 @ SV41 @ SV49 )
= $false )
| ( ( ~ ( morphism @ SV22 @ SV49 @ SV64 ) )
= $true )
| ( ( ~ ( morphism @ SV32 @ SV41 @ SV63 ) )
= $true )
| ( ( ~ ( morphism @ SV38 @ SV63 @ SV64 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(345,plain,
! [SV38: $i,SV65: $i,SV32: $i,SV68: $i,SV22: $i,SV49: $i,SV41: $i,SV10: $i] :
( ( ( ~ ( morphism @ SV10 @ SV41 @ SV49 ) )
= $true )
| ( ( ~ ( morphism @ SV22 @ SV49 @ SV68 ) )
= $true )
| ( ( ~ ( morphism @ SV32 @ SV41 @ SV65 ) )
= $true )
| ( ( ~ ( morphism @ SV38 @ SV65 @ SV68 ) )
= $true )
| ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) )
= $false )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(346,plain,
! [SV24: $i,SV34: $i,SV44: $i,SV52: $i,SV69: $i,SV13: $i] :
( ( ( ( apply @ SV13 @ SV69 )
= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= $false )
| ( ( ~ ( element @ SV69 @ SV34 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $false )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(347,plain,
! [SV24: $i,SV34: $i,SV44: $i,SV52: $i,SV13: $i] :
( ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(348,plain,
! [SV13: $i,SV24: $i,SV34: $i,SV44: $i,SV52: $i] :
( ( ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(349,plain,
! [SV24: $i,SV34: $i,SV44: $i,SV52: $i,SV13: $i] :
( ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(350,plain,
! [SV13: $i,SV24: $i,SV34: $i,SV44: $i,SV52: $i] :
( ( ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $true )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(351,plain,
! [SV35: $i,SV14: $i,SV39: $i,SV45: $i,SV70: $i,SV25: $i] :
( ( ( ( ( apply @ SV25 @ SV70 )
!= ( zero @ SV45 ) ) )
= $true )
| ( ( ~ ( element @ SV70 @ SV39 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SV70 )
| ~ ( element @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(352,plain,
! [SV39: $i,SV45: $i,SV25: $i,SV35: $i,SV14: $i] :
( ( ( ! [SY226: $i] :
( ! [SY194: $i] :
( ( ( apply @ SV14 @ SY194 )
!= SY226 )
| ~ ( element @ SY194 @ SV35 ) )
| ( ( apply @ SV25 @ SY226 )
= ( zero @ SV45 ) ) ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(353,plain,
! [SV45: $i,SV25: $i,SV39: $i,SV35: $i,SV14: $i] :
( ( ( ! [SY211: $i] :
( ! [SY196: $i] :
( ( ( apply @ SV14 @ SY196 )
!= SY211 )
| ~ ( element @ SY196 @ SV35 ) )
| ( element @ SY211 @ SV39 ) ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(354,plain,
! [SV40: $i,SV26: $i,SV2: $i,SV47: $i,SV16: $i,SV58: $i,SV55: $i,SV36: $i] :
( ( ( morphism @ SV36 @ SV55 @ SV58 )
= $false )
| ( ( morphism @ SV16 @ SV47 @ SV58 )
= $false )
| ( ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
= $false )
| ( ( morphism @ SV2 @ SV40 @ SV47 )
= $false )
| ( ( morphism @ SV26 @ SV40 @ SV55 )
= $false )
| ( ( ! [SY216: $i] :
( ~ ( element @ SY216 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SY216 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SY216 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(355,plain,
! [SV38: $i,SV63: $i,SV32: $i,SV41: $i,SV10: $i,SV64: $i,SV49: $i,SV22: $i] :
( ( ( morphism @ SV22 @ SV49 @ SV64 )
= $false )
| ( ( morphism @ SV10 @ SV41 @ SV49 )
= $false )
| ( ( ~ ( morphism @ SV32 @ SV41 @ SV63 ) )
= $true )
| ( ( ~ ( morphism @ SV38 @ SV63 @ SV64 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(356,plain,
! [SV38: $i,SV65: $i,SV32: $i,SV68: $i,SV22: $i,SV49: $i,SV41: $i,SV10: $i] :
( ( ( morphism @ SV10 @ SV41 @ SV49 )
= $false )
| ( ( ~ ( morphism @ SV22 @ SV49 @ SV68 ) )
= $true )
| ( ( ~ ( morphism @ SV32 @ SV41 @ SV65 ) )
= $true )
| ( ( ~ ( morphism @ SV38 @ SV65 @ SV68 ) )
= $true )
| ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) )
= $false )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(357,plain,
! [SV24: $i,SV44: $i,SV52: $i,SV13: $i,SV34: $i,SV69: $i] :
( ( ( element @ SV69 @ SV34 )
= $false )
| ( ( ( apply @ SV13 @ SV69 )
= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $false )
| ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 )
| ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(358,plain,
! [SV52: $i,SV24: $i,SV44: $i,SV34: $i,SV13: $i] :
( ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 ) )
= $true )
| ( ( ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $true )
| ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(359,plain,
! [SV52: $i,SV24: $i,SV44: $i,SV34: $i,SV13: $i] :
( ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 ) )
= $true )
| ( ( ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $true )
| ( ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(360,plain,
! [SV52: $i,SV24: $i,SV44: $i,SV34: $i,SV13: $i] :
( ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 ) )
= $true )
| ( ( ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $true )
| ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(361,plain,
! [SV52: $i,SV24: $i,SV44: $i,SV34: $i,SV13: $i] :
( ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 ) )
= $true )
| ( ( ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $true )
| ( ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(362,plain,
! [SV35: $i,SV14: $i,SV39: $i,SV45: $i,SV70: $i,SV25: $i] :
( ( ( ( apply @ SV25 @ SV70 )
= ( zero @ SV45 ) )
= $false )
| ( ( ~ ( element @ SV70 @ SV39 ) )
= $true )
| ( ( ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SV70 )
| ~ ( element @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(363,plain,
! [SV39: $i,SV45: $i,SV25: $i,SV35: $i,SV71: $i,SV14: $i] :
( ( ( ! [SY242: $i] :
( ( ( apply @ SV14 @ SY242 )
!= SV71 )
| ~ ( element @ SY242 @ SV35 ) )
| ( ( apply @ SV25 @ SV71 )
= ( zero @ SV45 ) ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(364,plain,
! [SV45: $i,SV25: $i,SV39: $i,SV35: $i,SV72: $i,SV14: $i] :
( ( ( ! [SY243: $i] :
( ( ( apply @ SV14 @ SY243 )
!= SV72 )
| ~ ( element @ SY243 @ SV35 ) )
| ( element @ SV72 @ SV39 ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(365,plain,
! [SV58: $i,SV47: $i,SV55: $i,SV26: $i,SV36: $i,SV2: $i,SV16: $i,SV40: $i,SV73: $i] :
( ( ( ~ ( element @ SV73 @ SV40 )
| ( ( apply @ SV16 @ ( apply @ SV2 @ SV73 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SV73 ) ) ) )
= $true )
| ( ( morphism @ SV26 @ SV40 @ SV55 )
= $false )
| ( ( morphism @ SV2 @ SV40 @ SV47 )
= $false )
| ( ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
= $false )
| ( ( morphism @ SV16 @ SV47 @ SV58 )
= $false )
| ( ( morphism @ SV36 @ SV55 @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(366,plain,
! [SV38: $i,SV64: $i,SV22: $i,SV49: $i,SV10: $i,SV63: $i,SV41: $i,SV32: $i] :
( ( ( morphism @ SV32 @ SV41 @ SV63 )
= $false )
| ( ( morphism @ SV10 @ SV41 @ SV49 )
= $false )
| ( ( morphism @ SV22 @ SV49 @ SV64 )
= $false )
| ( ( ~ ( morphism @ SV38 @ SV63 @ SV64 ) )
= $true )
| ( ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(367,plain,
! [SV38: $i,SV65: $i,SV32: $i,SV41: $i,SV10: $i,SV68: $i,SV49: $i,SV22: $i] :
( ( ( morphism @ SV22 @ SV49 @ SV68 )
= $false )
| ( ( morphism @ SV10 @ SV41 @ SV49 )
= $false )
| ( ( ~ ( morphism @ SV32 @ SV41 @ SV65 ) )
= $true )
| ( ( ~ ( morphism @ SV38 @ SV65 @ SV68 ) )
= $true )
| ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) )
= $false )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(368,plain,
! [SV69: $i,SV52: $i,SV24: $i,SV44: $i,SV34: $i,SV13: $i] :
( ( ( ~ ( morphism @ SV13 @ SV34 @ SV44 ) )
= $true )
| ( ( ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $false )
| ( ( ( apply @ SV13 @ SV69 )
= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= $false )
| ( ( element @ SV69 @ SV34 )
= $false )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(369,plain,
! [SV52: $i,SV24: $i,SV44: $i,SV34: $i,SV13: $i] :
( ( ( morphism @ SV13 @ SV34 @ SV44 )
= $false )
| ( ( ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $true )
| ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(370,plain,
! [SV52: $i,SV24: $i,SV44: $i,SV34: $i,SV13: $i] :
( ( ( morphism @ SV13 @ SV34 @ SV44 )
= $false )
| ( ( ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $true )
| ( ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(371,plain,
! [SV52: $i,SV24: $i,SV44: $i,SV34: $i,SV13: $i] :
( ( ( morphism @ SV13 @ SV34 @ SV44 )
= $false )
| ( ( ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $true )
| ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(372,plain,
! [SV52: $i,SV24: $i,SV44: $i,SV34: $i,SV13: $i] :
( ( ( morphism @ SV13 @ SV34 @ SV44 )
= $false )
| ( ( ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $true )
| ( ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(373,plain,
! [SV35: $i,SV14: $i,SV45: $i,SV25: $i,SV39: $i,SV70: $i] :
( ( ( element @ SV70 @ SV39 )
= $false )
| ( ( ( apply @ SV25 @ SV70 )
= ( zero @ SV45 ) )
= $false )
| ( ( ~ ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SV70 )
| ~ ( element @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(374,plain,
! [SV39: $i,SV45: $i,SV25: $i,SV35: $i,SV71: $i,SV14: $i] :
( ( ( ! [SY242: $i] :
( ( ( apply @ SV14 @ SY242 )
!= SV71 )
| ~ ( element @ SY242 @ SV35 ) ) )
= $true )
| ( ( ( apply @ SV25 @ SV71 )
= ( zero @ SV45 ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(375,plain,
! [SV45: $i,SV25: $i,SV39: $i,SV35: $i,SV72: $i,SV14: $i] :
( ( ( ! [SY243: $i] :
( ( ( apply @ SV14 @ SY243 )
!= SV72 )
| ~ ( element @ SY243 @ SV35 ) ) )
= $true )
| ( ( element @ SV72 @ SV39 )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(376,plain,
! [SV58: $i,SV47: $i,SV55: $i,SV26: $i,SV36: $i,SV2: $i,SV16: $i,SV40: $i,SV73: $i] :
( ( ( ~ ( element @ SV73 @ SV40 ) )
= $true )
| ( ( ( apply @ SV16 @ ( apply @ SV2 @ SV73 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SV73 ) ) )
= $true )
| ( ( morphism @ SV26 @ SV40 @ SV55 )
= $false )
| ( ( morphism @ SV2 @ SV40 @ SV47 )
= $false )
| ( ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
= $false )
| ( ( morphism @ SV16 @ SV47 @ SV58 )
= $false )
| ( ( morphism @ SV36 @ SV55 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(377,plain,
! [SV32: $i,SV41: $i,SV10: $i,SV49: $i,SV22: $i,SV64: $i,SV63: $i,SV38: $i] :
( ( ( morphism @ SV38 @ SV63 @ SV64 )
= $false )
| ( ( morphism @ SV22 @ SV49 @ SV64 )
= $false )
| ( ( morphism @ SV10 @ SV41 @ SV49 )
= $false )
| ( ( morphism @ SV32 @ SV41 @ SV63 )
= $false )
| ( ( element @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) @ SV41 )
= $true )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(378,plain,
! [SV38: $i,SV68: $i,SV22: $i,SV49: $i,SV10: $i,SV65: $i,SV41: $i,SV32: $i] :
( ( ( morphism @ SV32 @ SV41 @ SV65 )
= $false )
| ( ( morphism @ SV10 @ SV41 @ SV49 )
= $false )
| ( ( morphism @ SV22 @ SV49 @ SV68 )
= $false )
| ( ( ~ ( morphism @ SV38 @ SV65 @ SV68 ) )
= $true )
| ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) )
= $false )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(379,plain,
! [SV69: $i,SV52: $i,SV24: $i,SV44: $i,SV34: $i,SV13: $i] :
( ( ( morphism @ SV13 @ SV34 @ SV44 )
= $false )
| ( ( ~ ( morphism @ SV24 @ SV44 @ SV52 ) )
= $true )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $false )
| ( ( ( apply @ SV13 @ SV69 )
= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= $false )
| ( ( element @ SV69 @ SV34 )
= $false )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(380,plain,
! [SV34: $i,SV13: $i,SV52: $i,SV44: $i,SV24: $i] :
( ( ( morphism @ SV24 @ SV44 @ SV52 )
= $false )
| ( ( morphism @ SV13 @ SV34 @ SV44 )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $true )
| ( ( ( apply @ SV13 @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(381,plain,
! [SV34: $i,SV13: $i,SV52: $i,SV44: $i,SV24: $i] :
( ( ( morphism @ SV24 @ SV44 @ SV52 )
= $false )
| ( ( morphism @ SV13 @ SV34 @ SV44 )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $true )
| ( ( element @ ( sK5_SY75 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(382,plain,
! [SV34: $i,SV13: $i,SV52: $i,SV44: $i,SV24: $i] :
( ( ( morphism @ SV24 @ SV44 @ SV52 )
= $false )
| ( ( morphism @ SV13 @ SV34 @ SV44 )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $true )
| ( ( ( apply @ SV13 @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(383,plain,
! [SV34: $i,SV13: $i,SV52: $i,SV44: $i,SV24: $i] :
( ( ( morphism @ SV24 @ SV44 @ SV52 )
= $false )
| ( ( morphism @ SV13 @ SV34 @ SV44 )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $true )
| ( ( element @ ( sK4_SY76 @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV34 )
= $true )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(384,plain,
! [SV25: $i,SV35: $i,SV39: $i,SV45: $i,SV70: $i,SV14: $i] :
( ( ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SV70 )
| ~ ( element @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) )
= $false )
| ( ( ( apply @ SV25 @ SV70 )
= ( zero @ SV45 ) )
= $false )
| ( ( element @ SV70 @ SV39 )
= $false )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(385,plain,
! [SV39: $i,SV45: $i,SV25: $i,SV35: $i,SV71: $i,SV74: $i,SV14: $i] :
( ( ( ( ( apply @ SV14 @ SV74 )
!= SV71 )
| ~ ( element @ SV74 @ SV35 ) )
= $true )
| ( ( ( apply @ SV25 @ SV71 )
= ( zero @ SV45 ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(386,plain,
! [SV45: $i,SV25: $i,SV39: $i,SV35: $i,SV72: $i,SV75: $i,SV14: $i] :
( ( ( ( ( apply @ SV14 @ SV75 )
!= SV72 )
| ~ ( element @ SV75 @ SV35 ) )
= $true )
| ( ( element @ SV72 @ SV39 )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(387,plain,
! [SV58: $i,SV47: $i,SV55: $i,SV26: $i,SV36: $i,SV2: $i,SV16: $i,SV40: $i,SV73: $i] :
( ( ( element @ SV73 @ SV40 )
= $false )
| ( ( ( apply @ SV16 @ ( apply @ SV2 @ SV73 ) )
= ( apply @ SV36 @ ( apply @ SV26 @ SV73 ) ) )
= $true )
| ( ( morphism @ SV26 @ SV40 @ SV55 )
= $false )
| ( ( morphism @ SV2 @ SV40 @ SV47 )
= $false )
| ( ( commute @ SV2 @ SV16 @ SV26 @ SV36 )
= $false )
| ( ( morphism @ SV16 @ SV47 @ SV58 )
= $false )
| ( ( morphism @ SV36 @ SV55 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(388,plain,
! [SV32: $i,SV41: $i,SV10: $i,SV49: $i,SV22: $i,SV68: $i,SV65: $i,SV38: $i] :
( ( ( morphism @ SV38 @ SV65 @ SV68 )
= $false )
| ( ( morphism @ SV22 @ SV49 @ SV68 )
= $false )
| ( ( morphism @ SV10 @ SV41 @ SV49 )
= $false )
| ( ( morphism @ SV32 @ SV41 @ SV65 )
= $false )
| ( ( ( apply @ SV22 @ ( apply @ SV10 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) )
= ( apply @ SV38 @ ( apply @ SV32 @ ( sK2_ElDom @ SV49 @ SV41 @ SV38 @ SV32 @ SV22 @ SV10 ) ) ) )
= $false )
| ( ( commute @ SV10 @ SV22 @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(389,plain,
! [SV69: $i,SV34: $i,SV13: $i,SV52: $i,SV44: $i,SV24: $i] :
( ( ( morphism @ SV24 @ SV44 @ SV52 )
= $false )
| ( ( morphism @ SV13 @ SV34 @ SV44 )
= $false )
| ( ( element @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) @ SV44 )
= $false )
| ( ( ( apply @ SV24 @ ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= ( zero @ SV52 ) )
= $false )
| ( ( ( apply @ SV13 @ SV69 )
= ( sK3_ElCodDom @ SV52 @ SV44 @ SV34 @ SV24 @ SV13 ) )
= $false )
| ( ( element @ SV69 @ SV34 )
= $false )
| ( ( exact @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(390,plain,
! [SV25: $i,SV35: $i,SV39: $i,SV45: $i,SV70: $i,SV14: $i] :
( ( ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
!= SV70 ) )
= $false )
| ( ( ( apply @ SV25 @ SV70 )
= ( zero @ SV45 ) )
= $false )
| ( ( element @ SV70 @ SV39 )
= $false )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(391,plain,
! [SV14: $i,SV25: $i,SV35: $i,SV39: $i,SV45: $i,SV70: $i] :
( ( ( ~ ( element @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 ) )
= $false )
| ( ( ( apply @ SV25 @ SV70 )
= ( zero @ SV45 ) )
= $false )
| ( ( element @ SV70 @ SV39 )
= $false )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(392,plain,
! [SV39: $i,SV45: $i,SV25: $i,SV35: $i,SV71: $i,SV74: $i,SV14: $i] :
( ( ( ( ( apply @ SV14 @ SV74 )
!= SV71 ) )
= $true )
| ( ( ~ ( element @ SV74 @ SV35 ) )
= $true )
| ( ( ( apply @ SV25 @ SV71 )
= ( zero @ SV45 ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(393,plain,
! [SV45: $i,SV25: $i,SV39: $i,SV35: $i,SV72: $i,SV75: $i,SV14: $i] :
( ( ( ( ( apply @ SV14 @ SV75 )
!= SV72 ) )
= $true )
| ( ( ~ ( element @ SV75 @ SV35 ) )
= $true )
| ( ( element @ SV72 @ SV39 )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(394,plain,
! [SV25: $i,SV35: $i,SV39: $i,SV45: $i,SV70: $i,SV14: $i] :
( ( ( ( apply @ SV14 @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) )
= SV70 )
= $true )
| ( ( ( apply @ SV25 @ SV70 )
= ( zero @ SV45 ) )
= $false )
| ( ( element @ SV70 @ SV39 )
= $false )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(395,plain,
! [SV14: $i,SV25: $i,SV35: $i,SV39: $i,SV45: $i,SV70: $i] :
( ( ( element @ ( sK6_ElDom @ SV70 @ SV45 @ SV39 @ SV35 @ SV25 @ SV14 ) @ SV35 )
= $true )
| ( ( ( apply @ SV25 @ SV70 )
= ( zero @ SV45 ) )
= $false )
| ( ( element @ SV70 @ SV39 )
= $false )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(396,plain,
! [SV39: $i,SV45: $i,SV25: $i,SV35: $i,SV71: $i,SV74: $i,SV14: $i] :
( ( ( ( apply @ SV14 @ SV74 )
= SV71 )
= $false )
| ( ( ~ ( element @ SV74 @ SV35 ) )
= $true )
| ( ( ( apply @ SV25 @ SV71 )
= ( zero @ SV45 ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(397,plain,
! [SV45: $i,SV25: $i,SV39: $i,SV35: $i,SV72: $i,SV75: $i,SV14: $i] :
( ( ( ( apply @ SV14 @ SV75 )
= SV72 )
= $false )
| ( ( ~ ( element @ SV75 @ SV35 ) )
= $true )
| ( ( element @ SV72 @ SV39 )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(398,plain,
! [SV39: $i,SV45: $i,SV25: $i,SV71: $i,SV14: $i,SV35: $i,SV74: $i] :
( ( ( element @ SV74 @ SV35 )
= $false )
| ( ( ( apply @ SV14 @ SV74 )
= SV71 )
= $false )
| ( ( ( apply @ SV25 @ SV71 )
= ( zero @ SV45 ) )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(399,plain,
! [SV45: $i,SV25: $i,SV39: $i,SV72: $i,SV14: $i,SV35: $i,SV75: $i] :
( ( ( element @ SV75 @ SV35 )
= $false )
| ( ( ( apply @ SV14 @ SV75 )
= SV72 )
= $false )
| ( ( element @ SV72 @ SV39 )
= $true )
| ( ( morphism @ SV14 @ SV35 @ SV39 )
= $false )
| ( ( exact @ SV14 @ SV25 )
= $false )
| ( ( morphism @ SV25 @ SV39 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(400,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[82,399,398,395,394,389,388,387,383,382,381,380,377,324,323,321,304,303,300,286,277,271,270,259,245,234,211,210,167,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,83]) ).
thf(401,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[400]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HAL004+1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 21:30:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.40
% 0.19/0.40 No.of.Axioms: 30
% 0.19/0.40
% 0.19/0.40 Length.of.Defs: 0
% 0.19/0.40
% 0.19/0.40 Contains.Choice.Funs: false
% 0.19/0.43 .
% 0.19/0.46 (rf:0,axioms:30,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:32,loop_count:0,foatp_calls:0,translation:fof_full)..................................
% 70.11/70.32
% 70.11/70.32 ********************************
% 70.11/70.32 * All subproblems solved! *
% 70.11/70.32 ********************************
% 70.11/70.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:31,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:400,loop_count:0,foatp_calls:1,translation:fof_full)
% 70.18/70.44
% 70.18/70.44 %**** Beginning of derivation protocol ****
% 70.18/70.44 % SZS output start CNFRefutation
% See solution above
% 70.18/70.44
% 70.18/70.44 %**** End of derivation protocol ****
% 70.18/70.44 %**** no. of clauses in derivation: 401 ****
% 70.18/70.44 %**** clause counter: 400 ****
% 70.18/70.44
% 70.18/70.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:31,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:400,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------