TSTP Solution File: ITP397_1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ITP397_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:30:48 EDT 2024
% Result : Theorem 64.84s 9.70s
% Output : CNFRefutation 64.84s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
tff(f2,conjecture,
'fun_app$a'('comp$'('f$'),'i$') = 'g$',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture1) ).
tff(f3,negated_conjecture,
( ~ 'fun_app$a'('comp$'('f$'),'i$') = 'g$' ),
inference(negated_conjecture,[],[f2]) ).
tff(f5,axiom,
'register$a'('f$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3) ).
tff(f6,axiom,
'iso_register$'('i$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4) ).
tff(f7,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'B_ell2_b_ell2_cblinfun$'] : ( 'fun_app$b'('fun_app$a'('comp$'(X0),X1),X2) = 'fun_app$c'(X0,'fun_app$d'(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).
tff(f12,axiom,
'register$b'('i$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10) ).
tff(f15,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun$'] : ( 'fun_app$d'('i$',X0) = 'fun_app$l'('inv_into$'('top$','f$'),'fun_app$b'('g$',X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom13) ).
tff(f23,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ( 'comp$o'(X0,'fun_app$i'('comp$b'(X1),X2)) = 'comp$m'('fun_app$f'('comp$a'(X0),X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom21) ).
tff(f33,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ( 'comp$o'(X0,'fun_app$i'('comp$b'(X1),X2)) = 'comp$m'('fun_app$f'('comp$a'(X0),X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom31) ).
tff(f48,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'B_ell2_b_ell2_cblinfun$'] :
( ( 'fun_app$a'('comp$'(X0),X1) = X2 )
=> ( 'fun_app$c'(X0,'fun_app$d'(X1,X3)) = 'fun_app$b'(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom46) ).
tff(f50,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X3: 'A_ell2_a_ell2_cblinfun$'] :
( ( 'fun_app$i'('comp$b'(X0),X1) = X2 )
=> ( 'fun_app$d'(X0,'fun_app$g'(X1,X3)) = 'fun_app$h'(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom48) ).
tff(f52,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun$'] : 'member$'('fun_app$b'('g$',X0),'image$'('f$','top$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom50) ).
tff(f57,axiom,
'inj_on$'('f$','top$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom55) ).
tff(f71,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun$'] :
( 'member$a'(X0,'top$')
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom69) ).
tff(f86,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( 'register$a'(X1)
& 'register$b'(X0) )
=> 'register$'('fun_app$a'('comp$'(X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom84) ).
tff(f112,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_set$',X1: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ! [X3: 'A_ell2_a_ell2_cblinfun$'] :
( 'member$a'(X3,X0)
=> ( 'fun_app$l'(X1,'fun_app$c'(X2,X3)) = X3 ) )
=> 'inj_on$'(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom110) ).
tff(f130,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun$',X1: 'A_ell2_a_ell2_cblinfun_set$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'member$a'(X0,X1)
=> 'member$'('fun_app$c'(X2,X0),'image$'(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom128) ).
tff(f141,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'C_ell2_c_ell2_cblinfun$'] :
( 'inj_on$a'(X0,'top$a')
=> ( 'member$'(X1,'image$a'(X0,'top$a'))
<=> ? [X2: 'B_ell2_b_ell2_cblinfun$'] :
( ! [X3: 'B_ell2_b_ell2_cblinfun$'] :
( ( 'fun_app$b'(X0,X3) = X1 )
=> ( X2 = X3 ) )
& ( 'fun_app$b'(X0,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom139) ).
tff(f156,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_set$'] :
( 'inj_on$'('comp$k'(X0,X1),X2)
=> 'inj_on$a'(X0,'image$f'(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom154) ).
tff(f163,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_set$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( 'inj_on$'(X2,'fun_app$o'('image$c'(X0),X1))
& 'inj_on$b'(X0,X1) )
=> 'inj_on$'('comp$n'(X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom161) ).
tff(f174,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun$'] : 'member$'('fun_app$b'(X0,X1),'image$a'(X0,'top$a')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom172) ).
tff(f187,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'B_ell2_b_ell2_cblinfun_set$'] :
( 'inj_on$c'('fun_app$f'('comp$a'(X0),X1),X2)
=> 'inj_on$e'(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom185) ).
tff(f188,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_set$'] :
( 'inj_on$b'('fun_app$i'('comp$b'(X0),X1),X2)
=> 'inj_on$f'(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom186) ).
tff(f217,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'B_ell2_b_ell2_cblinfun_set$'] : ( 'image$f'(X0,'image$e'(X1,X2)) = 'fun_app$p'('image$d'('fun_app$f'('comp$a'(X0),X1)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom215) ).
tff(f218,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_set$'] : ( 'image$e'(X0,'image$f'(X1,X2)) = 'fun_app$o'('image$c'('fun_app$i'('comp$b'(X0),X1)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom216) ).
tff(f223,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'B_ell2_b_ell2_cblinfun_set$'] : ( 'image$'(X0,'image$e'(X1,X2)) = 'image$a'('fun_app$a'('comp$'(X0),X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom221) ).
tff(f224,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_set$'] : ( 'image$a'(X0,'image$f'(X1,X2)) = 'image$'('comp$k'(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom222) ).
tff(f278,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'register$'(X0)
=> 'inj_on$a'(X0,'top$a') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom276) ).
tff(f287,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'inj_on$f'(X0,'top$')
=> ( 'comp$k'('fun_app$a'('comp$'(X1),'inv_into$b'('top$',X0)),X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom285) ).
tff(f288,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( 'inj_on$f'(X0,'top$')
=> ( 'comp$m'('fun_app$f'('comp$a'(X1),'inv_into$b'('top$',X0)),X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom286) ).
tff(f291,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'inj_on$e'(X0,'top$a')
=> ( 'fun_app$a'('comp$'('comp$k'(X1,'inv_into$c'('top$a',X0))),X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom289) ).
tff(f323,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_set$'] :
( 'inj_on$'(X0,'top$')
=> ( 'image$h'('inv_into$'('top$',X0),'image$'(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom321) ).
tff(f343,axiom,
! [X0: 'C_ell2_c_ell2_cblinfun$',X1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_set$'] :
( 'member$'(X0,'image$'(X1,X2))
=> ( 'fun_app$c'(X1,'fun_app$l'('inv_into$'(X2,X1),X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom341) ).
tff(f368,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_set$'] :
( ( 'top$a' = 'image$f'(X0,'top$') )
=> ( 'image$f'(X0,'image$e'('inv_into$b'('top$',X0),X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom366) ).
tff(f382,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun$',X2: 'C_ell2_c_ell2_cblinfun$'] :
( ( ( 'fun_app$c'(X0,X1) = X2 )
& 'inj_on$'(X0,'top$') )
=> ( 'fun_app$l'('inv_into$'('top$',X0),X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom380) ).
tff(f387,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_set$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( ! [X4: 'B_ell2_b_ell2_cblinfun$'] :
( 'member$b'(X4,X1)
=> ( 'fun_app$b'('fun_app$a'('comp$'(X2),X0),X4) = 'fun_app$b'('fun_app$a'('comp$'(X3),X0),X4) ) )
& ( 'top$' = 'image$e'(X0,X1) ) )
=> ( X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom385) ).
tff(f390,axiom,
'fun_app$f'('comp$a'('j$'),'i$') = 'id$',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom388) ).
tff(f391,axiom,
'fun_app$i'('comp$b'('i$'),'j$') = 'id$a',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom389) ).
tff(f427,axiom,
'image$d'('id$') = 'id$b',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom425) ).
tff(f428,axiom,
'image$c'('id$a') = 'id$c',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom426) ).
tff(f450,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ! [X1: 'A_ell2_a_ell2_cblinfun$'] : ( 'fun_app$h'(X0,X1) = X1 )
<=> ( 'id$a' = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom448) ).
tff(f456,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_set$'] : 'inj_on$c'('id$',X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom454) ).
tff(f457,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_set$'] : 'inj_on$b'('id$a',X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom455) ).
tff(f475,axiom,
'top$a' = 'fun_app$p'('image$d'('id$'),'top$a'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom473) ).
tff(f519,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'top$' = 'image$e'(X0,'top$a') )
<=> ( 'id$a' = 'fun_app$i'('comp$b'(X0),'inv_into$c'('top$a',X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom517) ).
tff(f530,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( 'inj_on$f'(X0,'top$')
<=> ( 'id$a' = 'fun_app$i'('comp$b'('inv_into$b'('top$',X0)),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom528) ).
tff(f532,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( 'inj_on$e'(X0,'top$a')
<=> ( 'id$' = 'fun_app$f'('comp$a'('inv_into$c'('top$a',X0)),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom530) ).
tff(f533,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'inj_on$a'(X0,'top$a')
<=> ( 'id$' = 'comp$f'('inv_into$a'('top$a',X0),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom531) ).
tff(f545,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( 'iso_register$'(X0)
=> ( 'id$a' = 'fun_app$i'('comp$b'(X0),'inv_into$c'('top$a',X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom543) ).
tff(f621,axiom,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'comp$k'(X0,X1) = X2 )
=> ( 'fun_app$a'('comp$'(X2),X3) = 'comp$j'(X0,'fun_app$f'('comp$a'(X1),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom619) ).
tff(f627,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'fun_app$a'('comp$'(X0),X1) = X2 )
=> ( 'comp$k'(X2,X3) = 'comp$n'(X0,'fun_app$i'('comp$b'(X1),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom625) ).
tff(f642,plain,
'fun_app$a'('comp$'('f$'),'i$') != 'g$',
inference(flattening,[],[f3]) ).
tff(f648,plain,
! [X0: 'A_ell2_a_ell2_cblinfun$'] : 'member$a'(X0,'top$'),
inference(true_and_false_elimination,[],[f71]) ).
tff(f730,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'B_ell2_b_ell2_cblinfun$'] :
( ( 'fun_app$c'(X0,'fun_app$d'(X1,X3)) = 'fun_app$b'(X2,X3) )
| ( 'fun_app$a'('comp$'(X0),X1) != X2 ) ),
inference(ennf_transformation,[],[f48]) ).
tff(f732,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X3: 'A_ell2_a_ell2_cblinfun$'] :
( ( 'fun_app$d'(X0,'fun_app$g'(X1,X3)) = 'fun_app$h'(X2,X3) )
| ( 'fun_app$i'('comp$b'(X0),X1) != X2 ) ),
inference(ennf_transformation,[],[f50]) ).
tff(f770,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'register$'('fun_app$a'('comp$'(X1),X0))
| ~ 'register$a'(X1)
| ~ 'register$b'(X0) ),
inference(ennf_transformation,[],[f86]) ).
tff(f771,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'register$'('fun_app$a'('comp$'(X1),X0))
| ~ 'register$a'(X1)
| ~ 'register$b'(X0) ),
inference(flattening,[],[f770]) ).
tff(f812,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_set$',X1: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'inj_on$'(X2,X0)
| ? [X3: 'A_ell2_a_ell2_cblinfun$'] :
( ( 'fun_app$l'(X1,'fun_app$c'(X2,X3)) != X3 )
& 'member$a'(X3,X0) ) ),
inference(ennf_transformation,[],[f112]) ).
tff(f834,plain,
! [X0: 'A_ell2_a_ell2_cblinfun$',X1: 'A_ell2_a_ell2_cblinfun_set$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'member$'('fun_app$c'(X2,X0),'image$'(X2,X1))
| ~ 'member$a'(X0,X1) ),
inference(ennf_transformation,[],[f130]) ).
tff(f843,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'C_ell2_c_ell2_cblinfun$'] :
( ( 'member$'(X1,'image$a'(X0,'top$a'))
<=> ? [X2: 'B_ell2_b_ell2_cblinfun$'] :
( ! [X3: 'B_ell2_b_ell2_cblinfun$'] :
( ( X2 = X3 )
| ( 'fun_app$b'(X0,X3) != X1 ) )
& ( 'fun_app$b'(X0,X2) = X1 ) ) )
| ~ 'inj_on$a'(X0,'top$a') ),
inference(ennf_transformation,[],[f141]) ).
tff(f858,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_set$'] :
( 'inj_on$a'(X0,'image$f'(X1,X2))
| ~ 'inj_on$'('comp$k'(X0,X1),X2) ),
inference(ennf_transformation,[],[f156]) ).
tff(f868,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_set$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'inj_on$'('comp$n'(X2,X0),X1)
| ~ 'inj_on$'(X2,'fun_app$o'('image$c'(X0),X1))
| ~ 'inj_on$b'(X0,X1) ),
inference(ennf_transformation,[],[f163]) ).
tff(f869,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_set$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'inj_on$'('comp$n'(X2,X0),X1)
| ~ 'inj_on$'(X2,'fun_app$o'('image$c'(X0),X1))
| ~ 'inj_on$b'(X0,X1) ),
inference(flattening,[],[f868]) ).
tff(f892,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'B_ell2_b_ell2_cblinfun_set$'] :
( 'inj_on$e'(X1,X2)
| ~ 'inj_on$c'('fun_app$f'('comp$a'(X0),X1),X2) ),
inference(ennf_transformation,[],[f187]) ).
tff(f893,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_set$'] :
( 'inj_on$f'(X1,X2)
| ~ 'inj_on$b'('fun_app$i'('comp$b'(X0),X1),X2) ),
inference(ennf_transformation,[],[f188]) ).
tff(f986,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'inj_on$a'(X0,'top$a')
| ~ 'register$'(X0) ),
inference(ennf_transformation,[],[f278]) ).
tff(f992,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( 'comp$k'('fun_app$a'('comp$'(X1),'inv_into$b'('top$',X0)),X0) = X1 )
| ~ 'inj_on$f'(X0,'top$') ),
inference(ennf_transformation,[],[f287]) ).
tff(f993,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'comp$m'('fun_app$f'('comp$a'(X1),'inv_into$b'('top$',X0)),X0) = X1 )
| ~ 'inj_on$f'(X0,'top$') ),
inference(ennf_transformation,[],[f288]) ).
tff(f996,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( 'fun_app$a'('comp$'('comp$k'(X1,'inv_into$c'('top$a',X0))),X0) = X1 )
| ~ 'inj_on$e'(X0,'top$a') ),
inference(ennf_transformation,[],[f291]) ).
tff(f1040,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_set$'] :
( ( 'image$h'('inv_into$'('top$',X0),'image$'(X0,X1)) = X1 )
| ~ 'inj_on$'(X0,'top$') ),
inference(ennf_transformation,[],[f323]) ).
tff(f1070,plain,
! [X0: 'C_ell2_c_ell2_cblinfun$',X1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_set$'] :
( ( 'fun_app$c'(X1,'fun_app$l'('inv_into$'(X2,X1),X0)) = X0 )
| ~ 'member$'(X0,'image$'(X1,X2)) ),
inference(ennf_transformation,[],[f343]) ).
tff(f1093,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_set$'] :
( ( 'image$f'(X0,'image$e'('inv_into$b'('top$',X0),X1)) = X1 )
| ( 'top$a' != 'image$f'(X0,'top$') ) ),
inference(ennf_transformation,[],[f368]) ).
tff(f1115,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun$',X2: 'C_ell2_c_ell2_cblinfun$'] :
( ( 'fun_app$l'('inv_into$'('top$',X0),X2) = X1 )
| ( 'fun_app$c'(X0,X1) != X2 )
| ~ 'inj_on$'(X0,'top$') ),
inference(ennf_transformation,[],[f382]) ).
tff(f1116,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun$',X2: 'C_ell2_c_ell2_cblinfun$'] :
( ( 'fun_app$l'('inv_into$'('top$',X0),X2) = X1 )
| ( 'fun_app$c'(X0,X1) != X2 )
| ~ 'inj_on$'(X0,'top$') ),
inference(flattening,[],[f1115]) ).
tff(f1125,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_set$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( X2 = X3 )
| ? [X4: 'B_ell2_b_ell2_cblinfun$'] :
( ( 'fun_app$b'('fun_app$a'('comp$'(X2),X0),X4) != 'fun_app$b'('fun_app$a'('comp$'(X3),X0),X4) )
& 'member$b'(X4,X1) )
| ( 'top$' != 'image$e'(X0,X1) ) ),
inference(ennf_transformation,[],[f387]) ).
tff(f1126,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_set$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( X2 = X3 )
| ? [X4: 'B_ell2_b_ell2_cblinfun$'] :
( ( 'fun_app$b'('fun_app$a'('comp$'(X2),X0),X4) != 'fun_app$b'('fun_app$a'('comp$'(X3),X0),X4) )
& 'member$b'(X4,X1) )
| ( 'top$' != 'image$e'(X0,X1) ) ),
inference(flattening,[],[f1125]) ).
tff(f1254,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'id$a' = 'fun_app$i'('comp$b'(X0),'inv_into$c'('top$a',X0)) )
| ~ 'iso_register$'(X0) ),
inference(ennf_transformation,[],[f545]) ).
tff(f1325,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'fun_app$a'('comp$'(X2),X3) = 'comp$j'(X0,'fun_app$f'('comp$a'(X1),X3)) )
| ( 'comp$k'(X0,X1) != X2 ) ),
inference(ennf_transformation,[],[f621]) ).
tff(f1331,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'comp$k'(X2,X3) = 'comp$n'(X0,'fun_app$i'('comp$b'(X1),X3)) )
| ( 'fun_app$a'('comp$'(X0),X1) != X2 ) ),
inference(ennf_transformation,[],[f627]) ).
tff(f1362,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_set$',X1: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ? [X3: 'A_ell2_a_ell2_cblinfun$'] :
( ( 'fun_app$l'(X1,'fun_app$c'(X2,X3)) != X3 )
& 'member$a'(X3,X0) )
=> ( ( sK10(X0,X1,X2) != 'fun_app$l'(X1,'fun_app$c'(X2,sK10(X0,X1,X2))) )
& 'member$a'(sK10(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f1363,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_set$',X1: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'inj_on$'(X2,X0)
| ( ( sK10(X0,X1,X2) != 'fun_app$l'(X1,'fun_app$c'(X2,sK10(X0,X1,X2))) )
& 'member$a'(sK10(X0,X1,X2),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f812,f1362]) ).
tff(f1421,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'C_ell2_c_ell2_cblinfun$'] :
( ( ( 'member$'(X1,'image$a'(X0,'top$a'))
| ! [X2: 'B_ell2_b_ell2_cblinfun$'] :
( ? [X3: 'B_ell2_b_ell2_cblinfun$'] :
( ( X2 != X3 )
& ( 'fun_app$b'(X0,X3) = X1 ) )
| ( 'fun_app$b'(X0,X2) != X1 ) ) )
& ( ? [X2: 'B_ell2_b_ell2_cblinfun$'] :
( ! [X3: 'B_ell2_b_ell2_cblinfun$'] :
( ( X2 = X3 )
| ( 'fun_app$b'(X0,X3) != X1 ) )
& ( 'fun_app$b'(X0,X2) = X1 ) )
| ~ 'member$'(X1,'image$a'(X0,'top$a')) ) )
| ~ 'inj_on$a'(X0,'top$a') ),
inference(nnf_transformation,[],[f843]) ).
tff(f1422,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'C_ell2_c_ell2_cblinfun$'] :
( ( ( 'member$'(X1,'image$a'(X0,'top$a'))
| ! [X2: 'B_ell2_b_ell2_cblinfun$'] :
( ? [X3: 'B_ell2_b_ell2_cblinfun$'] :
( ( X2 != X3 )
& ( 'fun_app$b'(X0,X3) = X1 ) )
| ( 'fun_app$b'(X0,X2) != X1 ) ) )
& ( ? [X4: 'B_ell2_b_ell2_cblinfun$'] :
( ! [X5: 'B_ell2_b_ell2_cblinfun$'] :
( ( X4 = X5 )
| ( 'fun_app$b'(X0,X5) != X1 ) )
& ( 'fun_app$b'(X0,X4) = X1 ) )
| ~ 'member$'(X1,'image$a'(X0,'top$a')) ) )
| ~ 'inj_on$a'(X0,'top$a') ),
inference(rectify,[],[f1421]) ).
tff(f1423,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'C_ell2_c_ell2_cblinfun$',X2: 'B_ell2_b_ell2_cblinfun$'] :
( ? [X3: 'B_ell2_b_ell2_cblinfun$'] :
( ( X2 != X3 )
& ( 'fun_app$b'(X0,X3) = X1 ) )
=> ( ( sK29(X0,X1,X2) != X2 )
& ( 'fun_app$b'(X0,sK29(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1424,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'C_ell2_c_ell2_cblinfun$'] :
( ? [X4: 'B_ell2_b_ell2_cblinfun$'] :
( ! [X5: 'B_ell2_b_ell2_cblinfun$'] :
( ( X4 = X5 )
| ( 'fun_app$b'(X0,X5) != X1 ) )
& ( 'fun_app$b'(X0,X4) = X1 ) )
=> ( ! [X5: 'B_ell2_b_ell2_cblinfun$'] :
( ( sK30(X0,X1) = X5 )
| ( 'fun_app$b'(X0,X5) != X1 ) )
& ( 'fun_app$b'(X0,sK30(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1425,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'C_ell2_c_ell2_cblinfun$'] :
( ( ( 'member$'(X1,'image$a'(X0,'top$a'))
| ! [X2: 'B_ell2_b_ell2_cblinfun$'] :
( ( ( sK29(X0,X1,X2) != X2 )
& ( 'fun_app$b'(X0,sK29(X0,X1,X2)) = X1 ) )
| ( 'fun_app$b'(X0,X2) != X1 ) ) )
& ( ( ! [X5: 'B_ell2_b_ell2_cblinfun$'] :
( ( sK30(X0,X1) = X5 )
| ( 'fun_app$b'(X0,X5) != X1 ) )
& ( 'fun_app$b'(X0,sK30(X0,X1)) = X1 ) )
| ~ 'member$'(X1,'image$a'(X0,'top$a')) ) )
| ~ 'inj_on$a'(X0,'top$a') ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30])],[f1422,f1424,f1423]) ).
tff(f1603,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_set$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ? [X4: 'B_ell2_b_ell2_cblinfun$'] :
( ( 'fun_app$b'('fun_app$a'('comp$'(X2),X0),X4) != 'fun_app$b'('fun_app$a'('comp$'(X3),X0),X4) )
& 'member$b'(X4,X1) )
=> ( ( 'fun_app$b'('fun_app$a'('comp$'(X2),X0),sK112(X0,X1,X2,X3)) != 'fun_app$b'('fun_app$a'('comp$'(X3),X0),sK112(X0,X1,X2,X3)) )
& 'member$b'(sK112(X0,X1,X2,X3),X1) ) ),
introduced(choice_axiom,[]) ).
tff(f1604,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_set$',X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( X2 = X3 )
| ( ( 'fun_app$b'('fun_app$a'('comp$'(X2),X0),sK112(X0,X1,X2,X3)) != 'fun_app$b'('fun_app$a'('comp$'(X3),X0),sK112(X0,X1,X2,X3)) )
& 'member$b'(sK112(X0,X1,X2,X3),X1) )
| ( 'top$' != 'image$e'(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK112])],[f1126,f1603]) ).
tff(f1616,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( ! [X1: 'A_ell2_a_ell2_cblinfun$'] : ( 'fun_app$h'(X0,X1) = X1 )
| ( 'id$a' != X0 ) )
& ( ( 'id$a' = X0 )
| ? [X1: 'A_ell2_a_ell2_cblinfun$'] : ( 'fun_app$h'(X0,X1) != X1 ) ) ),
inference(nnf_transformation,[],[f450]) ).
tff(f1617,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( ! [X1: 'A_ell2_a_ell2_cblinfun$'] : ( 'fun_app$h'(X0,X1) = X1 )
| ( 'id$a' != X0 ) )
& ( ( 'id$a' = X0 )
| ? [X2: 'A_ell2_a_ell2_cblinfun$'] : ( 'fun_app$h'(X0,X2) != X2 ) ) ),
inference(rectify,[],[f1616]) ).
tff(f1618,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ? [X2: 'A_ell2_a_ell2_cblinfun$'] : ( 'fun_app$h'(X0,X2) != X2 )
=> ( sK116(X0) != 'fun_app$h'(X0,sK116(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1619,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( ! [X1: 'A_ell2_a_ell2_cblinfun$'] : ( 'fun_app$h'(X0,X1) = X1 )
| ( 'id$a' != X0 ) )
& ( ( 'id$a' = X0 )
| ( sK116(X0) != 'fun_app$h'(X0,sK116(X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK116])],[f1617,f1618]) ).
tff(f1667,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( ( 'top$' = 'image$e'(X0,'top$a') )
| ( 'id$a' != 'fun_app$i'('comp$b'(X0),'inv_into$c'('top$a',X0)) ) )
& ( ( 'id$a' = 'fun_app$i'('comp$b'(X0),'inv_into$c'('top$a',X0)) )
| ( 'top$' != 'image$e'(X0,'top$a') ) ) ),
inference(nnf_transformation,[],[f519]) ).
tff(f1686,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'inj_on$f'(X0,'top$')
| ( 'id$a' != 'fun_app$i'('comp$b'('inv_into$b'('top$',X0)),X0) ) )
& ( ( 'id$a' = 'fun_app$i'('comp$b'('inv_into$b'('top$',X0)),X0) )
| ~ 'inj_on$f'(X0,'top$') ) ),
inference(nnf_transformation,[],[f530]) ).
tff(f1688,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'inj_on$e'(X0,'top$a')
| ( 'id$' != 'fun_app$f'('comp$a'('inv_into$c'('top$a',X0)),X0) ) )
& ( ( 'id$' = 'fun_app$f'('comp$a'('inv_into$c'('top$a',X0)),X0) )
| ~ 'inj_on$e'(X0,'top$a') ) ),
inference(nnf_transformation,[],[f532]) ).
tff(f1689,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( 'inj_on$a'(X0,'top$a')
| ( 'id$' != 'comp$f'('inv_into$a'('top$a',X0),X0) ) )
& ( ( 'id$' = 'comp$f'('inv_into$a'('top$a',X0),X0) )
| ~ 'inj_on$a'(X0,'top$a') ) ),
inference(nnf_transformation,[],[f533]) ).
tff(f1746,plain,
'fun_app$a'('comp$'('f$'),'i$') != 'g$',
inference(cnf_transformation,[],[f642]) ).
tff(f1748,plain,
'register$a'('f$'),
inference(cnf_transformation,[],[f5]) ).
tff(f1749,plain,
'iso_register$'('i$'),
inference(cnf_transformation,[],[f6]) ).
tff(f1750,plain,
! [X2: 'B_ell2_b_ell2_cblinfun$',X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ( 'fun_app$b'('fun_app$a'('comp$'(X0),X1),X2) = 'fun_app$c'(X0,'fun_app$d'(X1,X2)) ),
inference(cnf_transformation,[],[f7]) ).
tff(f1755,plain,
'register$b'('i$'),
inference(cnf_transformation,[],[f12]) ).
tff(f1758,plain,
! [X0: 'B_ell2_b_ell2_cblinfun$'] : ( 'fun_app$d'('i$',X0) = 'fun_app$l'('inv_into$'('top$','f$'),'fun_app$b'('g$',X0)) ),
inference(cnf_transformation,[],[f15]) ).
tff(f1766,plain,
! [X2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ( 'comp$o'(X0,'fun_app$i'('comp$b'(X1),X2)) = 'comp$m'('fun_app$f'('comp$a'(X0),X1),X2) ),
inference(cnf_transformation,[],[f23]) ).
tff(f1776,plain,
! [X2: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ( 'comp$o'(X0,'fun_app$i'('comp$b'(X1),X2)) = 'comp$m'('fun_app$f'('comp$a'(X0),X1),X2) ),
inference(cnf_transformation,[],[f33]) ).
tff(f1791,plain,
! [X2: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'B_ell2_b_ell2_cblinfun$',X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'fun_app$c'(X0,'fun_app$d'(X1,X3)) = 'fun_app$b'(X2,X3) )
| ( 'fun_app$a'('comp$'(X0),X1) != X2 ) ),
inference(cnf_transformation,[],[f730]) ).
tff(f1793,plain,
! [X2: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X3: 'A_ell2_a_ell2_cblinfun$',X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'fun_app$d'(X0,'fun_app$g'(X1,X3)) = 'fun_app$h'(X2,X3) )
| ( 'fun_app$i'('comp$b'(X0),X1) != X2 ) ),
inference(cnf_transformation,[],[f732]) ).
tff(f1795,plain,
! [X0: 'B_ell2_b_ell2_cblinfun$'] : 'member$'('fun_app$b'('g$',X0),'image$'('f$','top$')),
inference(cnf_transformation,[],[f52]) ).
tff(f1800,plain,
'inj_on$'('f$','top$'),
inference(cnf_transformation,[],[f57]) ).
tff(f1814,plain,
! [X0: 'A_ell2_a_ell2_cblinfun$'] : 'member$a'(X0,'top$'),
inference(cnf_transformation,[],[f648]) ).
tff(f1827,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'register$'('fun_app$a'('comp$'(X1),X0))
| ~ 'register$a'(X1)
| ~ 'register$b'(X0) ),
inference(cnf_transformation,[],[f771]) ).
tff(f1874,plain,
! [X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X0: 'A_ell2_a_ell2_cblinfun_set$',X1: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( 'inj_on$'(X2,X0)
| ( sK10(X0,X1,X2) != 'fun_app$l'(X1,'fun_app$c'(X2,sK10(X0,X1,X2))) ) ),
inference(cnf_transformation,[],[f1363]) ).
tff(f1921,plain,
! [X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X0: 'A_ell2_a_ell2_cblinfun$',X1: 'A_ell2_a_ell2_cblinfun_set$'] :
( 'member$'('fun_app$c'(X2,X0),'image$'(X2,X1))
| ~ 'member$a'(X0,X1) ),
inference(cnf_transformation,[],[f834]) ).
tff(f1941,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'C_ell2_c_ell2_cblinfun$'] :
( ( 'fun_app$b'(X0,sK30(X0,X1)) = X1 )
| ~ 'member$'(X1,'image$a'(X0,'top$a'))
| ~ 'inj_on$a'(X0,'top$a') ),
inference(cnf_transformation,[],[f1425]) ).
tff(f1942,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'C_ell2_c_ell2_cblinfun$',X5: 'B_ell2_b_ell2_cblinfun$'] :
( ( sK30(X0,X1) = X5 )
| ( 'fun_app$b'(X0,X5) != X1 )
| ~ 'member$'(X1,'image$a'(X0,'top$a'))
| ~ 'inj_on$a'(X0,'top$a') ),
inference(cnf_transformation,[],[f1425]) ).
tff(f1968,plain,
! [X2: 'A_ell2_a_ell2_cblinfun_set$',X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( 'inj_on$a'(X0,'image$f'(X1,X2))
| ~ 'inj_on$'('comp$k'(X0,X1),X2) ),
inference(cnf_transformation,[],[f858]) ).
tff(f1975,plain,
! [X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X0: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_set$'] :
( 'inj_on$'('comp$n'(X2,X0),X1)
| ~ 'inj_on$'(X2,'fun_app$o'('image$c'(X0),X1))
| ~ 'inj_on$b'(X0,X1) ),
inference(cnf_transformation,[],[f869]) ).
tff(f1986,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun$'] : 'member$'('fun_app$b'(X0,X1),'image$a'(X0,'top$a')),
inference(cnf_transformation,[],[f174]) ).
tff(f2003,plain,
! [X2: 'B_ell2_b_ell2_cblinfun_set$',X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( 'inj_on$e'(X1,X2)
| ~ 'inj_on$c'('fun_app$f'('comp$a'(X0),X1),X2) ),
inference(cnf_transformation,[],[f892]) ).
tff(f2004,plain,
! [X2: 'A_ell2_a_ell2_cblinfun_set$',X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( 'inj_on$f'(X1,X2)
| ~ 'inj_on$b'('fun_app$i'('comp$b'(X0),X1),X2) ),
inference(cnf_transformation,[],[f893]) ).
tff(f2039,plain,
! [X2: 'B_ell2_b_ell2_cblinfun_set$',X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ( 'image$f'(X0,'image$e'(X1,X2)) = 'fun_app$p'('image$d'('fun_app$f'('comp$a'(X0),X1)),X2) ),
inference(cnf_transformation,[],[f217]) ).
tff(f2040,plain,
! [X2: 'A_ell2_a_ell2_cblinfun_set$',X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ( 'image$e'(X0,'image$f'(X1,X2)) = 'fun_app$o'('image$c'('fun_app$i'('comp$b'(X0),X1)),X2) ),
inference(cnf_transformation,[],[f218]) ).
tff(f2045,plain,
! [X2: 'B_ell2_b_ell2_cblinfun_set$',X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ( 'image$'(X0,'image$e'(X1,X2)) = 'image$a'('fun_app$a'('comp$'(X0),X1),X2) ),
inference(cnf_transformation,[],[f223]) ).
tff(f2046,plain,
! [X2: 'A_ell2_a_ell2_cblinfun_set$',X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ( 'image$a'(X0,'image$f'(X1,X2)) = 'image$'('comp$k'(X0,X1),X2) ),
inference(cnf_transformation,[],[f224]) ).
tff(f2120,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'inj_on$a'(X0,'top$a')
| ~ 'register$'(X0) ),
inference(cnf_transformation,[],[f986]) ).
tff(f2129,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( 'comp$k'('fun_app$a'('comp$'(X1),'inv_into$b'('top$',X0)),X0) = X1 )
| ~ 'inj_on$f'(X0,'top$') ),
inference(cnf_transformation,[],[f992]) ).
tff(f2130,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'comp$m'('fun_app$f'('comp$a'(X1),'inv_into$b'('top$',X0)),X0) = X1 )
| ~ 'inj_on$f'(X0,'top$') ),
inference(cnf_transformation,[],[f993]) ).
tff(f2133,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( 'fun_app$a'('comp$'('comp$k'(X1,'inv_into$c'('top$a',X0))),X0) = X1 )
| ~ 'inj_on$e'(X0,'top$a') ),
inference(cnf_transformation,[],[f996]) ).
tff(f2165,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_set$'] :
( ( 'image$h'('inv_into$'('top$',X0),'image$'(X0,X1)) = X1 )
| ~ 'inj_on$'(X0,'top$') ),
inference(cnf_transformation,[],[f1040]) ).
tff(f2187,plain,
! [X2: 'A_ell2_a_ell2_cblinfun_set$',X0: 'C_ell2_c_ell2_cblinfun$',X1: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( 'fun_app$c'(X1,'fun_app$l'('inv_into$'(X2,X1),X0)) = X0 )
| ~ 'member$'(X0,'image$'(X1,X2)) ),
inference(cnf_transformation,[],[f1070]) ).
tff(f2218,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_set$'] :
( ( 'image$f'(X0,'image$e'('inv_into$b'('top$',X0),X1)) = X1 )
| ( 'top$a' != 'image$f'(X0,'top$') ) ),
inference(cnf_transformation,[],[f1093]) ).
tff(f2232,plain,
! [X2: 'C_ell2_c_ell2_cblinfun$',X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun$'] :
( ( 'fun_app$l'('inv_into$'('top$',X0),X2) = X1 )
| ( 'fun_app$c'(X0,X1) != X2 )
| ~ 'inj_on$'(X0,'top$') ),
inference(cnf_transformation,[],[f1116]) ).
tff(f2239,plain,
! [X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_set$'] :
( ( X2 = X3 )
| ( 'fun_app$b'('fun_app$a'('comp$'(X2),X0),sK112(X0,X1,X2,X3)) != 'fun_app$b'('fun_app$a'('comp$'(X3),X0),sK112(X0,X1,X2,X3)) )
| ( 'top$' != 'image$e'(X0,X1) ) ),
inference(cnf_transformation,[],[f1604]) ).
tff(f2244,plain,
'fun_app$f'('comp$a'('j$'),'i$') = 'id$',
inference(cnf_transformation,[],[f390]) ).
tff(f2245,plain,
'fun_app$i'('comp$b'('i$'),'j$') = 'id$a',
inference(cnf_transformation,[],[f391]) ).
tff(f2284,plain,
'image$d'('id$') = 'id$b',
inference(cnf_transformation,[],[f427]) ).
tff(f2285,plain,
'image$c'('id$a') = 'id$c',
inference(cnf_transformation,[],[f428]) ).
tff(f2309,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun$'] :
( ( 'fun_app$h'(X0,X1) = X1 )
| ( 'id$a' != X0 ) ),
inference(cnf_transformation,[],[f1619]) ).
tff(f2315,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_set$'] : 'inj_on$c'('id$',X0),
inference(cnf_transformation,[],[f456]) ).
tff(f2316,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_set$'] : 'inj_on$b'('id$a',X0),
inference(cnf_transformation,[],[f457]) ).
tff(f2324,plain,
'top$a' = 'fun_app$p'('image$d'('id$'),'top$a'),
inference(cnf_transformation,[],[f475]) ).
tff(f2407,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'top$' = 'image$e'(X0,'top$a') )
| ( 'id$a' != 'fun_app$i'('comp$b'(X0),'inv_into$c'('top$a',X0)) ) ),
inference(cnf_transformation,[],[f1667]) ).
tff(f2428,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'id$a' = 'fun_app$i'('comp$b'('inv_into$b'('top$',X0)),X0) )
| ~ 'inj_on$f'(X0,'top$') ),
inference(cnf_transformation,[],[f1686]) ).
tff(f2432,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'id$' = 'fun_app$f'('comp$a'('inv_into$c'('top$a',X0)),X0) )
| ~ 'inj_on$e'(X0,'top$a') ),
inference(cnf_transformation,[],[f1688]) ).
tff(f2434,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( 'id$' = 'comp$f'('inv_into$a'('top$a',X0),X0) )
| ~ 'inj_on$a'(X0,'top$a') ),
inference(cnf_transformation,[],[f1689]) ).
tff(f2435,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'inj_on$a'(X0,'top$a')
| ( 'id$' != 'comp$f'('inv_into$a'('top$a',X0),X0) ) ),
inference(cnf_transformation,[],[f1689]) ).
tff(f2453,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'id$a' = 'fun_app$i'('comp$b'(X0),'inv_into$c'('top$a',X0)) )
| ~ 'iso_register$'(X0) ),
inference(cnf_transformation,[],[f1254]) ).
tff(f2531,plain,
! [X2: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'fun_app$a'('comp$'(X2),X3) = 'comp$j'(X0,'fun_app$f'('comp$a'(X1),X3)) )
| ( 'comp$k'(X0,X1) != X2 ) ),
inference(cnf_transformation,[],[f1325]) ).
tff(f2537,plain,
! [X2: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X3: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'comp$k'(X2,X3) = 'comp$n'(X0,'fun_app$i'('comp$b'(X1),X3)) )
| ( 'fun_app$a'('comp$'(X0),X1) != X2 ) ),
inference(cnf_transformation,[],[f1331]) ).
tff(f2548,plain,
! [X3: 'B_ell2_b_ell2_cblinfun$',X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ( 'fun_app$c'(X0,'fun_app$d'(X1,X3)) = 'fun_app$b'('fun_app$a'('comp$'(X0),X1),X3) ),
inference(equality_resolution,[],[f1791]) ).
tff(f2550,plain,
! [X3: 'A_ell2_a_ell2_cblinfun$',X0: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ( 'fun_app$d'(X0,'fun_app$g'(X1,X3)) = 'fun_app$h'('fun_app$i'('comp$b'(X0),X1),X3) ),
inference(equality_resolution,[],[f1793]) ).
tff(f2574,plain,
! [X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X5: 'B_ell2_b_ell2_cblinfun$'] :
( ( sK30(X0,'fun_app$b'(X0,X5)) = X5 )
| ~ 'member$'('fun_app$b'(X0,X5),'image$a'(X0,'top$a'))
| ~ 'inj_on$a'(X0,'top$a') ),
inference(equality_resolution,[],[f1942]) ).
tff(f2591,plain,
! [X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun$'] :
( ( 'fun_app$l'('inv_into$'('top$',X0),'fun_app$c'(X0,X1)) = X1 )
| ~ 'inj_on$'(X0,'top$') ),
inference(equality_resolution,[],[f2232]) ).
tff(f2594,plain,
! [X1: 'A_ell2_a_ell2_cblinfun$'] : ( 'fun_app$h'('id$a',X1) = X1 ),
inference(equality_resolution,[],[f2309]) ).
tff(f2651,plain,
! [X3: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X0: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ( 'comp$j'(X0,'fun_app$f'('comp$a'(X1),X3)) = 'fun_app$a'('comp$'('comp$k'(X0,X1)),X3) ),
inference(equality_resolution,[],[f2531]) ).
tff(f2657,plain,
! [X3: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X0: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ( 'comp$n'(X0,'fun_app$i'('comp$b'(X1),X3)) = 'comp$k'('fun_app$a'('comp$'(X0),X1),X3) ),
inference(equality_resolution,[],[f2537]) ).
cnf(c_51,negated_conjecture,
'fun_app$a'('comp$'('f$'),'i$') != 'g$',
inference(cnf_transformation,[],[f1746]) ).
cnf(c_53,plain,
'register$a'('f$'),
inference(cnf_transformation,[],[f1748]) ).
cnf(c_54,plain,
'iso_register$'('i$'),
inference(cnf_transformation,[],[f1749]) ).
cnf(c_55,plain,
'fun_app$b'('fun_app$a'('comp$'(X0_13),X0_64),X0_18) = 'fun_app$c'(X0_13,'fun_app$d'(X0_64,X0_18)),
inference(cnf_transformation,[],[f1750]) ).
cnf(c_60,plain,
'register$b'('i$'),
inference(cnf_transformation,[],[f1755]) ).
cnf(c_63,plain,
'fun_app$l'('inv_into$'('top$','f$'),'fun_app$b'('g$',X0_18)) = 'fun_app$d'('i$',X0_18),
inference(cnf_transformation,[],[f1758]) ).
cnf(c_71,plain,
'comp$o'(X0_48,'fun_app$i'('comp$b'(X0_64),X1_48)) = 'comp$m'('fun_app$f'('comp$a'(X0_48),X0_64),X1_48),
inference(cnf_transformation,[],[f1766]) ).
cnf(c_81,plain,
'comp$o'(X0_48,'fun_app$i'('comp$b'(X0_64),X1_48)) = 'comp$m'('fun_app$f'('comp$a'(X0_48),X0_64),X1_48),
inference(cnf_transformation,[],[f1776]) ).
cnf(c_96,plain,
'fun_app$b'('fun_app$a'('comp$'(X0_13),X0_64),X0_18) = 'fun_app$c'(X0_13,'fun_app$d'(X0_64,X0_18)),
inference(cnf_transformation,[],[f2548]) ).
cnf(c_98,plain,
'fun_app$h'('fun_app$i'('comp$b'(X0_64),X0_48),X0_14) = 'fun_app$d'(X0_64,'fun_app$g'(X0_48,X0_14)),
inference(cnf_transformation,[],[f2550]) ).
cnf(c_100,plain,
'member$'('fun_app$b'('g$',X0_18),'image$'('f$','top$')),
inference(cnf_transformation,[],[f1795]) ).
cnf(c_105,plain,
'inj_on$'('f$','top$'),
inference(cnf_transformation,[],[f1800]) ).
cnf(c_119,plain,
'member$a'(X0_14,'top$'),
inference(cnf_transformation,[],[f1814]) ).
cnf(c_132,plain,
( ~ 'register$b'(X0_64)
| ~ 'register$a'(X0_13)
| 'register$'('fun_app$a'('comp$'(X0_13),X0_64)) ),
inference(cnf_transformation,[],[f1827]) ).
cnf(c_178,plain,
( 'fun_app$l'(X0_82,'fun_app$c'(X0_13,sK10(X0_54,X0_82,X0_13))) != sK10(X0_54,X0_82,X0_13)
| 'inj_on$'(X0_13,X0_54) ),
inference(cnf_transformation,[],[f1874]) ).
cnf(c_226,plain,
( ~ 'member$a'(X0_14,X0_54)
| 'member$'('fun_app$c'(X0_13,X0_14),'image$'(X0_13,X0_54)) ),
inference(cnf_transformation,[],[f1921]) ).
cnf(c_246,plain,
( ~ 'member$'('fun_app$b'(X0_51,X0_18),'image$a'(X0_51,'top$a'))
| ~ 'inj_on$a'(X0_51,'top$a')
| sK30(X0_51,'fun_app$b'(X0_51,X0_18)) = X0_18 ),
inference(cnf_transformation,[],[f2574]) ).
cnf(c_247,plain,
( ~ 'member$'(X0_30,'image$a'(X0_51,'top$a'))
| ~ 'inj_on$a'(X0_51,'top$a')
| 'fun_app$b'(X0_51,sK30(X0_51,X0_30)) = X0_30 ),
inference(cnf_transformation,[],[f1941]) ).
cnf(c_271,plain,
( ~ 'inj_on$'('comp$k'(X0_51,X0_48),X0_54)
| 'inj_on$a'(X0_51,'image$f'(X0_48,X0_54)) ),
inference(cnf_transformation,[],[f1968]) ).
cnf(c_278,plain,
( ~ 'inj_on$'(X0_13,'fun_app$o'('image$c'(X0_71),X0_54))
| ~ 'inj_on$b'(X0_71,X0_54)
| 'inj_on$'('comp$n'(X0_13,X0_71),X0_54) ),
inference(cnf_transformation,[],[f1975]) ).
cnf(c_289,plain,
'member$'('fun_app$b'(X0_51,X0_18),'image$a'(X0_51,'top$a')),
inference(cnf_transformation,[],[f1986]) ).
cnf(c_304,plain,
( ~ 'inj_on$c'('fun_app$f'('comp$a'(X0_48),X0_64),X0_52)
| 'inj_on$e'(X0_64,X0_52) ),
inference(cnf_transformation,[],[f2003]) ).
cnf(c_305,plain,
( ~ 'inj_on$b'('fun_app$i'('comp$b'(X0_64),X0_48),X0_54)
| 'inj_on$f'(X0_48,X0_54) ),
inference(cnf_transformation,[],[f2004]) ).
cnf(c_340,plain,
'fun_app$p'('image$d'('fun_app$f'('comp$a'(X0_48),X0_64)),X0_52) = 'image$f'(X0_48,'image$e'(X0_64,X0_52)),
inference(cnf_transformation,[],[f2039]) ).
cnf(c_341,plain,
'fun_app$o'('image$c'('fun_app$i'('comp$b'(X0_64),X0_48)),X0_54) = 'image$e'(X0_64,'image$f'(X0_48,X0_54)),
inference(cnf_transformation,[],[f2040]) ).
cnf(c_346,plain,
'image$a'('fun_app$a'('comp$'(X0_13),X0_64),X0_52) = 'image$'(X0_13,'image$e'(X0_64,X0_52)),
inference(cnf_transformation,[],[f2045]) ).
cnf(c_347,plain,
'image$'('comp$k'(X0_51,X0_48),X0_54) = 'image$a'(X0_51,'image$f'(X0_48,X0_54)),
inference(cnf_transformation,[],[f2046]) ).
cnf(c_421,plain,
( ~ 'register$'(X0_51)
| 'inj_on$a'(X0_51,'top$a') ),
inference(cnf_transformation,[],[f2120]) ).
cnf(c_430,plain,
( ~ 'inj_on$f'(X0_48,'top$')
| 'comp$k'('fun_app$a'('comp$'(X0_13),'inv_into$b'('top$',X0_48)),X0_48) = X0_13 ),
inference(cnf_transformation,[],[f2129]) ).
cnf(c_431,plain,
( ~ 'inj_on$f'(X0_48,'top$')
| 'comp$m'('fun_app$f'('comp$a'(X1_48),'inv_into$b'('top$',X0_48)),X0_48) = X1_48 ),
inference(cnf_transformation,[],[f2130]) ).
cnf(c_434,plain,
( ~ 'inj_on$e'(X0_64,'top$a')
| 'fun_app$a'('comp$'('comp$k'(X0_51,'inv_into$c'('top$a',X0_64))),X0_64) = X0_51 ),
inference(cnf_transformation,[],[f2133]) ).
cnf(c_466,plain,
( ~ 'inj_on$'(X0_13,'top$')
| 'image$h'('inv_into$'('top$',X0_13),'image$'(X0_13,X0_54)) = X0_54 ),
inference(cnf_transformation,[],[f2165]) ).
cnf(c_488,plain,
( ~ 'member$'(X0_30,'image$'(X0_13,X0_54))
| 'fun_app$c'(X0_13,'fun_app$l'('inv_into$'(X0_54,X0_13),X0_30)) = X0_30 ),
inference(cnf_transformation,[],[f2187]) ).
cnf(c_519,plain,
( 'image$f'(X0_48,'top$') != 'top$a'
| 'image$f'(X0_48,'image$e'('inv_into$b'('top$',X0_48),X0_52)) = X0_52 ),
inference(cnf_transformation,[],[f2218]) ).
cnf(c_533,plain,
( ~ 'inj_on$'(X0_13,'top$')
| 'fun_app$l'('inv_into$'('top$',X0_13),'fun_app$c'(X0_13,X0_14)) = X0_14 ),
inference(cnf_transformation,[],[f2591]) ).
cnf(c_539,plain,
( 'fun_app$b'('fun_app$a'('comp$'(X0_13),X0_64),sK112(X0_64,X0_52,X0_13,X1_13)) != 'fun_app$b'('fun_app$a'('comp$'(X1_13),X0_64),sK112(X0_64,X0_52,X0_13,X1_13))
| 'image$e'(X0_64,X0_52) != 'top$'
| X0_13 = X1_13 ),
inference(cnf_transformation,[],[f2239]) ).
cnf(c_545,plain,
'fun_app$f'('comp$a'('j$'),'i$') = 'id$',
inference(cnf_transformation,[],[f2244]) ).
cnf(c_546,plain,
'fun_app$i'('comp$b'('i$'),'j$') = 'id$a',
inference(cnf_transformation,[],[f2245]) ).
cnf(c_585,plain,
'image$d'('id$') = 'id$b',
inference(cnf_transformation,[],[f2284]) ).
cnf(c_586,plain,
'image$c'('id$a') = 'id$c',
inference(cnf_transformation,[],[f2285]) ).
cnf(c_609,plain,
'fun_app$h'('id$a',X0_14) = X0_14,
inference(cnf_transformation,[],[f2594]) ).
cnf(c_616,plain,
'inj_on$c'('id$',X0_52),
inference(cnf_transformation,[],[f2315]) ).
cnf(c_617,plain,
'inj_on$b'('id$a',X0_54),
inference(cnf_transformation,[],[f2316]) ).
cnf(c_625,plain,
'fun_app$p'('image$d'('id$'),'top$a') = 'top$a',
inference(cnf_transformation,[],[f2324]) ).
cnf(c_707,plain,
( 'fun_app$i'('comp$b'(X0_64),'inv_into$c'('top$a',X0_64)) != 'id$a'
| 'image$e'(X0_64,'top$a') = 'top$' ),
inference(cnf_transformation,[],[f2407]) ).
cnf(c_730,plain,
( ~ 'inj_on$f'(X0_48,'top$')
| 'fun_app$i'('comp$b'('inv_into$b'('top$',X0_48)),X0_48) = 'id$a' ),
inference(cnf_transformation,[],[f2428]) ).
cnf(c_734,plain,
( ~ 'inj_on$e'(X0_64,'top$a')
| 'fun_app$f'('comp$a'('inv_into$c'('top$a',X0_64)),X0_64) = 'id$' ),
inference(cnf_transformation,[],[f2432]) ).
cnf(c_735,plain,
( 'comp$f'('inv_into$a'('top$a',X0_51),X0_51) != 'id$'
| 'inj_on$a'(X0_51,'top$a') ),
inference(cnf_transformation,[],[f2435]) ).
cnf(c_736,plain,
( ~ 'inj_on$a'(X0_51,'top$a')
| 'comp$f'('inv_into$a'('top$a',X0_51),X0_51) = 'id$' ),
inference(cnf_transformation,[],[f2434]) ).
cnf(c_754,plain,
( ~ 'iso_register$'(X0_64)
| 'fun_app$i'('comp$b'(X0_64),'inv_into$c'('top$a',X0_64)) = 'id$a' ),
inference(cnf_transformation,[],[f2453]) ).
cnf(c_829,plain,
'comp$j'(X0_51,'fun_app$f'('comp$a'(X0_48),X0_64)) = 'fun_app$a'('comp$'('comp$k'(X0_51,X0_48)),X0_64),
inference(cnf_transformation,[],[f2651]) ).
cnf(c_835,plain,
'comp$n'(X0_13,'fun_app$i'('comp$b'(X0_64),X0_48)) = 'comp$k'('fun_app$a'('comp$'(X0_13),X0_64),X0_48),
inference(cnf_transformation,[],[f2657]) ).
cnf(c_949,plain,
( ~ 'iso_register$'('i$')
| 'fun_app$i'('comp$b'('i$'),'inv_into$c'('top$a','i$')) = 'id$a' ),
inference(instantiation,[status(thm)],[c_754]) ).
cnf(c_1092,plain,
( 'fun_app$i'('comp$b'('i$'),'inv_into$c'('top$a','i$')) != 'id$a'
| 'image$e'('i$','top$a') = 'top$' ),
inference(instantiation,[status(thm)],[c_707]) ).
cnf(c_1536,plain,
( ~ 'iso_register$'(X0_64)
| 'image$e'(X0_64,'top$a') = 'top$' ),
inference(prop_impl_just,[status(thm)],[c_754,c_707]) ).
cnf(c_1982,plain,
( ~ 'inj_on$f'(X0_48,'top$')
| 'comp$m'('fun_app$f'('comp$a'(X1_48),'inv_into$b'('top$',X0_48)),X0_48) = X1_48 ),
inference(prop_impl_just,[status(thm)],[c_431]) ).
cnf(c_6412,plain,
'fun_app$p'('id$b','top$a') = 'top$a',
inference(light_normalisation,[status(thm)],[c_625,c_585]) ).
cnf(c_7272,plain,
( ~ 'inj_on$f'(X0_48,'top$')
| 'comp$o'(X1_48,'fun_app$i'('comp$b'('inv_into$b'('top$',X0_48)),X0_48)) = X1_48 ),
inference(demodulation,[status(thm)],[c_1982,c_71]) ).
cnf(c_8916,plain,
( 'fun_app$c'(X0_13,'fun_app$d'(X0_64,sK112(X0_64,X0_52,X0_13,X1_13))) != 'fun_app$c'(X1_13,'fun_app$d'(X0_64,sK112(X0_64,X0_52,X0_13,X1_13)))
| 'image$e'(X0_64,X0_52) != 'top$'
| X0_13 = X1_13 ),
inference(demodulation,[status(thm)],[c_539,c_55]) ).
cnf(c_32748,plain,
( ~ 'iso_register$'(X0_64)
| 'image$e'(X0_64,'top$a') = 'top$' ),
inference(prop_impl_just,[status(thm)],[c_1536]) ).
cnf(c_32934,plain,
( ~ 'inj_on$a'(X0_51,'top$a')
| sK30(X0_51,'fun_app$b'(X0_51,X0_18)) = X0_18 ),
inference(prop_impl_just,[status(thm)],[c_289,c_246]) ).
cnf(c_33210,plain,
( ~ 'inj_on$f'(X0_48,'top$')
| 'comp$o'(X1_48,'fun_app$i'('comp$b'('inv_into$b'('top$',X0_48)),X0_48)) = X1_48 ),
inference(prop_impl_just,[status(thm)],[c_7272]) ).
cnf(c_47844,plain,
'comp$'('f$') = sP0_iProver_def,
definition ).
cnf(c_47845,plain,
'fun_app$a'(sP0_iProver_def,'i$') = sP1_iProver_def,
definition ).
cnf(c_47846,negated_conjecture,
sP1_iProver_def != 'g$',
inference(demodulation,[status(thm)],[c_51,c_47844,c_47845]) ).
cnf(c_55210,plain,
'image$e'('i$','top$a') = 'top$',
inference(superposition,[status(thm)],[c_54,c_32748]) ).
cnf(c_55368,plain,
( ~ 'inj_on$c'('id$',X0_52)
| 'inj_on$e'('i$',X0_52) ),
inference(superposition,[status(thm)],[c_545,c_304]) ).
cnf(c_55369,plain,
'inj_on$e'('i$',X0_52),
inference(forward_subsumption_resolution,[status(thm)],[c_55368,c_616]) ).
cnf(c_55375,plain,
( ~ 'inj_on$b'('id$a',X0_54)
| 'inj_on$f'('j$',X0_54) ),
inference(superposition,[status(thm)],[c_546,c_305]) ).
cnf(c_55376,plain,
'inj_on$f'('j$',X0_54),
inference(forward_subsumption_resolution,[status(thm)],[c_55375,c_617]) ).
cnf(c_55803,plain,
( ~ 'register$b'(X0_64)
| ~ 'register$a'('f$')
| 'register$'('fun_app$a'(sP0_iProver_def,X0_64)) ),
inference(superposition,[status(thm)],[c_47844,c_132]) ).
cnf(c_55809,plain,
( ~ 'register$b'(X0_64)
| 'register$'('fun_app$a'(sP0_iProver_def,X0_64)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_55803,c_53]) ).
cnf(c_55835,plain,
( ~ 'register$b'('i$')
| 'register$'(sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_47845,c_55809]) ).
cnf(c_55838,plain,
'register$'(sP1_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_55835,c_60]) ).
cnf(c_57002,plain,
( ~ 'register$'(X0_51)
| 'comp$f'('inv_into$a'('top$a',X0_51),X0_51) = 'id$' ),
inference(superposition,[status(thm)],[c_421,c_736]) ).
cnf(c_57103,plain,
'comp$f'('inv_into$a'('top$a',sP1_iProver_def),sP1_iProver_def) = 'id$',
inference(superposition,[status(thm)],[c_55838,c_57002]) ).
cnf(c_57121,plain,
'inj_on$a'(sP1_iProver_def,'top$a'),
inference(superposition,[status(thm)],[c_57103,c_735]) ).
cnf(c_57134,plain,
sK30(sP1_iProver_def,'fun_app$b'(sP1_iProver_def,X0_18)) = X0_18,
inference(superposition,[status(thm)],[c_57121,c_32934]) ).
cnf(c_57145,plain,
'fun_app$b'('fun_app$a'(sP0_iProver_def,X0_64),X0_18) = 'fun_app$c'('f$','fun_app$d'(X0_64,X0_18)),
inference(superposition,[status(thm)],[c_47844,c_96]) ).
cnf(c_57160,plain,
'fun_app$d'('i$','fun_app$g'('j$',X0_14)) = 'fun_app$h'('id$a',X0_14),
inference(superposition,[status(thm)],[c_546,c_98]) ).
cnf(c_57162,plain,
'fun_app$d'('i$','fun_app$g'('j$',X0_14)) = X0_14,
inference(light_normalisation,[status(thm)],[c_57160,c_609]) ).
cnf(c_57595,plain,
'fun_app$c'('f$','fun_app$d'('i$',X0_18)) = 'fun_app$b'(sP1_iProver_def,X0_18),
inference(superposition,[status(thm)],[c_47845,c_57145]) ).
cnf(c_57603,plain,
'fun_app$b'(sP1_iProver_def,'fun_app$g'('j$',X0_14)) = 'fun_app$c'('f$',X0_14),
inference(superposition,[status(thm)],[c_57162,c_57595]) ).
cnf(c_57609,plain,
( 'fun_app$c'(X0_13,'fun_app$d'('i$',sK112('i$',X0_52,'f$',X0_13))) != 'fun_app$b'(sP1_iProver_def,sK112('i$',X0_52,'f$',X0_13))
| 'image$e'('i$',X0_52) != 'top$'
| X0_13 = 'f$' ),
inference(superposition,[status(thm)],[c_57595,c_8916]) ).
cnf(c_57661,plain,
'image$'('f$','image$e'(X0_64,X0_52)) = 'image$a'('fun_app$a'(sP0_iProver_def,X0_64),X0_52),
inference(superposition,[status(thm)],[c_47844,c_346]) ).
cnf(c_57668,plain,
'image$'('comp$k'('fun_app$a'('comp$'(X0_13),X0_64),X0_48),X0_54) = 'image$'(X0_13,'image$e'(X0_64,'image$f'(X0_48,X0_54))),
inference(superposition,[status(thm)],[c_346,c_347]) ).
cnf(c_57703,plain,
sK30(sP1_iProver_def,'fun_app$c'('f$',X0_14)) = 'fun_app$g'('j$',X0_14),
inference(superposition,[status(thm)],[c_57603,c_57134]) ).
cnf(c_57955,plain,
'image$'('f$','image$e'('i$',X0_52)) = 'image$a'(sP1_iProver_def,X0_52),
inference(superposition,[status(thm)],[c_47845,c_57661]) ).
cnf(c_57981,plain,
( ~ 'member$a'(X0_14,'image$e'('i$',X0_52))
| 'member$'('fun_app$c'('f$',X0_14),'image$a'(sP1_iProver_def,X0_52)) ),
inference(superposition,[status(thm)],[c_57955,c_226]) ).
cnf(c_58479,plain,
'fun_app$i'('comp$b'('inv_into$b'('top$','j$')),'j$') = 'id$a',
inference(superposition,[status(thm)],[c_55376,c_730]) ).
cnf(c_58496,plain,
'fun_app$f'('comp$a'('inv_into$c'('top$a','i$')),'i$') = 'id$',
inference(superposition,[status(thm)],[c_55369,c_734]) ).
cnf(c_58546,plain,
'comp$o'('j$','fun_app$i'('comp$b'('i$'),X0_48)) = 'comp$m'('id$',X0_48),
inference(superposition,[status(thm)],[c_545,c_81]) ).
cnf(c_58548,plain,
'comp$o'('inv_into$c'('top$a','i$'),'fun_app$i'('comp$b'('i$'),X0_48)) = 'comp$m'('id$',X0_48),
inference(superposition,[status(thm)],[c_58496,c_81]) ).
cnf(c_58648,plain,
'comp$o'('j$','id$a') = 'comp$m'('id$','j$'),
inference(superposition,[status(thm)],[c_546,c_58546]) ).
cnf(c_58720,plain,
'image$f'('j$','image$e'('i$',X0_52)) = 'fun_app$p'('image$d'('id$'),X0_52),
inference(superposition,[status(thm)],[c_545,c_340]) ).
cnf(c_58726,plain,
'image$f'('j$','image$e'('i$',X0_52)) = 'fun_app$p'('id$b',X0_52),
inference(light_normalisation,[status(thm)],[c_58720,c_585]) ).
cnf(c_58788,plain,
'image$f'('j$','top$') = 'fun_app$p'('id$b','top$a'),
inference(superposition,[status(thm)],[c_55210,c_58726]) ).
cnf(c_58794,plain,
'image$f'('j$','top$') = 'top$a',
inference(light_normalisation,[status(thm)],[c_58788,c_6412]) ).
cnf(c_58830,plain,
'image$e'('i$','image$f'('j$',X0_54)) = 'fun_app$o'('image$c'('id$a'),X0_54),
inference(superposition,[status(thm)],[c_546,c_341]) ).
cnf(c_58832,plain,
'image$e'('inv_into$b'('top$','j$'),'image$f'('j$',X0_54)) = 'fun_app$o'('image$c'('id$a'),X0_54),
inference(superposition,[status(thm)],[c_58479,c_341]) ).
cnf(c_58837,plain,
'image$e'('i$','image$f'('j$',X0_54)) = 'fun_app$o'('id$c',X0_54),
inference(light_normalisation,[status(thm)],[c_58830,c_586]) ).
cnf(c_58839,plain,
'image$e'('inv_into$b'('top$','j$'),'image$f'('j$',X0_54)) = 'fun_app$o'('id$c',X0_54),
inference(light_normalisation,[status(thm)],[c_58832,c_586]) ).
cnf(c_59093,plain,
'image$h'('inv_into$'('top$','f$'),'image$'('f$',X0_54)) = X0_54,
inference(superposition,[status(thm)],[c_105,c_466]) ).
cnf(c_59337,plain,
'fun_app$l'('inv_into$'('top$','f$'),'fun_app$c'('f$',X0_14)) = X0_14,
inference(superposition,[status(thm)],[c_105,c_533]) ).
cnf(c_60211,plain,
'fun_app$a'('comp$'('comp$k'(X0_51,'j$')),'i$') = 'comp$j'(X0_51,'id$'),
inference(superposition,[status(thm)],[c_545,c_829]) ).
cnf(c_60745,plain,
'comp$k'('fun_app$a'('comp$'(X0_13),'i$'),'j$') = 'comp$n'(X0_13,'id$a'),
inference(superposition,[status(thm)],[c_546,c_835]) ).
cnf(c_63998,plain,
'comp$k'('fun_app$a'('comp$'(X0_13),'inv_into$b'('top$','j$')),'j$') = X0_13,
inference(superposition,[status(thm)],[c_55376,c_430]) ).
cnf(c_64164,plain,
'fun_app$a'('comp$'('comp$k'(X0_51,'inv_into$c'('top$a','i$'))),'i$') = X0_51,
inference(superposition,[status(thm)],[c_55369,c_434]) ).
cnf(c_64265,plain,
'comp$k'('fun_app$a'(sP0_iProver_def,'i$'),'j$') = 'comp$n'('f$','id$a'),
inference(superposition,[status(thm)],[c_47844,c_60745]) ).
cnf(c_64285,plain,
'comp$n'('f$','id$a') = 'comp$k'(sP1_iProver_def,'j$'),
inference(light_normalisation,[status(thm)],[c_64265,c_47845]) ).
cnf(c_65067,plain,
'comp$o'(X0_48,'fun_app$i'('comp$b'('inv_into$b'('top$','j$')),'j$')) = X0_48,
inference(superposition,[status(thm)],[c_55376,c_33210]) ).
cnf(c_65079,plain,
'comp$o'(X0_48,'id$a') = X0_48,
inference(light_normalisation,[status(thm)],[c_65067,c_58479]) ).
cnf(c_65101,plain,
'comp$m'('id$','j$') = 'j$',
inference(demodulation,[status(thm)],[c_58648,c_65079]) ).
cnf(c_67595,plain,
'fun_app$c'('f$','fun_app$l'('inv_into$'('top$','f$'),'fun_app$b'('g$',X0_18))) = 'fun_app$b'('g$',X0_18),
inference(superposition,[status(thm)],[c_100,c_488]) ).
cnf(c_67629,plain,
'fun_app$b'('g$',X0_18) = 'fun_app$b'(sP1_iProver_def,X0_18),
inference(light_normalisation,[status(thm)],[c_67595,c_63,c_57595]) ).
cnf(c_72225,plain,
'image$'(X0_13,'image$e'('inv_into$b'('top$','j$'),'image$f'('j$',X0_54))) = 'image$'(X0_13,X0_54),
inference(superposition,[status(thm)],[c_63998,c_57668]) ).
cnf(c_72268,plain,
'image$'(X0_13,'fun_app$o'('id$c',X0_54)) = 'image$'(X0_13,X0_54),
inference(light_normalisation,[status(thm)],[c_72225,c_58839]) ).
cnf(c_72577,plain,
'image$h'('inv_into$'('top$','f$'),'image$'('f$',X0_54)) = 'fun_app$o'('id$c',X0_54),
inference(superposition,[status(thm)],[c_72268,c_59093]) ).
cnf(c_72580,plain,
'fun_app$o'('id$c',X0_54) = X0_54,
inference(light_normalisation,[status(thm)],[c_72577,c_59093]) ).
cnf(c_72610,plain,
'image$e'('i$','image$f'('j$',X0_54)) = X0_54,
inference(demodulation,[status(thm)],[c_58837,c_72580]) ).
cnf(c_72854,plain,
'image$f'('j$','image$e'('inv_into$b'('top$','j$'),X0_52)) = X0_52,
inference(superposition,[status(thm)],[c_58794,c_519]) ).
cnf(c_73299,plain,
'image$e'('inv_into$b'('top$','j$'),X0_52) = 'image$e'('i$',X0_52),
inference(superposition,[status(thm)],[c_72854,c_72610]) ).
cnf(c_73306,plain,
'image$f'('j$','image$e'('i$',X0_52)) = X0_52,
inference(demodulation,[status(thm)],[c_72854,c_73299]) ).
cnf(c_73307,plain,
'fun_app$p'('id$b',X0_52) = X0_52,
inference(light_normalisation,[status(thm)],[c_73306,c_58726]) ).
cnf(c_73310,plain,
'image$f'('j$','image$e'('i$',X0_52)) = X0_52,
inference(demodulation,[status(thm)],[c_58726,c_73307]) ).
cnf(c_74045,plain,
'inj_on$'('f$',X0_54),
inference(superposition,[status(thm)],[c_59337,c_178]) ).
cnf(c_74062,plain,
( ~ 'inj_on$b'(X0_71,X0_54)
| 'inj_on$'('comp$n'('f$',X0_71),X0_54) ),
inference(superposition,[status(thm)],[c_74045,c_278]) ).
cnf(c_74078,plain,
( ~ 'inj_on$b'('id$a',X0_54)
| 'inj_on$'('comp$k'(sP1_iProver_def,'j$'),X0_54) ),
inference(superposition,[status(thm)],[c_64285,c_74062]) ).
cnf(c_74088,plain,
'inj_on$'('comp$k'(sP1_iProver_def,'j$'),X0_54),
inference(forward_subsumption_resolution,[status(thm)],[c_74078,c_617]) ).
cnf(c_74128,plain,
'inj_on$a'(sP1_iProver_def,'image$f'('j$',X0_54)),
inference(superposition,[status(thm)],[c_74088,c_271]) ).
cnf(c_74142,plain,
'inj_on$a'(sP1_iProver_def,X0_52),
inference(superposition,[status(thm)],[c_73310,c_74128]) ).
cnf(c_79092,plain,
'comp$o'('inv_into$c'('top$a','i$'),'id$a') = 'comp$m'('id$','j$'),
inference(superposition,[status(thm)],[c_546,c_58548]) ).
cnf(c_79098,plain,
'comp$o'('inv_into$c'('top$a','i$'),'id$a') = 'j$',
inference(light_normalisation,[status(thm)],[c_79092,c_65101]) ).
cnf(c_79202,plain,
'inv_into$c'('top$a','i$') = 'j$',
inference(demodulation,[status(thm)],[c_79098,c_65079]) ).
cnf(c_81873,plain,
'comp$j'(X0_51,'id$') = X0_51,
inference(light_normalisation,[status(thm)],[c_64164,c_60211,c_79202]) ).
cnf(c_81894,plain,
'fun_app$a'('comp$'('comp$k'(X0_51,'j$')),'i$') = X0_51,
inference(demodulation,[status(thm)],[c_60211,c_81873]) ).
cnf(c_82287,plain,
'fun_app$c'('comp$k'(X0_51,'j$'),'fun_app$d'('i$',X0_18)) = 'fun_app$b'(X0_51,X0_18),
inference(superposition,[status(thm)],[c_81894,c_96]) ).
cnf(c_101551,plain,
'fun_app$b'(X0_51,'fun_app$g'('j$',X0_14)) = 'fun_app$c'('comp$k'(X0_51,'j$'),X0_14),
inference(superposition,[status(thm)],[c_57162,c_82287]) ).
cnf(c_107038,plain,
'fun_app$b'(sP1_iProver_def,'fun_app$g'('j$',X0_14)) = 'fun_app$c'('comp$k'('g$','j$'),X0_14),
inference(superposition,[status(thm)],[c_101551,c_67629]) ).
cnf(c_107575,plain,
( ~ 'member$a'(X0_14,'image$e'('i$','top$a'))
| ~ 'inj_on$a'(sP1_iProver_def,'top$a')
| 'fun_app$b'(sP1_iProver_def,sK30(sP1_iProver_def,'fun_app$c'('f$',X0_14))) = 'fun_app$c'('f$',X0_14) ),
inference(superposition,[status(thm)],[c_57981,c_247]) ).
cnf(c_107604,plain,
( ~ 'member$a'(X0_14,'top$')
| ~ 'inj_on$a'(sP1_iProver_def,'top$a')
| 'fun_app$c'('comp$k'('g$','j$'),X0_14) = 'fun_app$c'('f$',X0_14) ),
inference(light_normalisation,[status(thm)],[c_107575,c_55210,c_57703,c_107038]) ).
cnf(c_107605,plain,
'fun_app$c'('comp$k'('g$','j$'),X0_14) = 'fun_app$c'('f$',X0_14),
inference(forward_subsumption_resolution,[status(thm)],[c_107604,c_74142,c_119]) ).
cnf(c_107758,plain,
( 'fun_app$c'('f$','fun_app$d'('i$',sK112('i$',X0_52,'f$','comp$k'('g$','j$')))) != 'fun_app$b'(sP1_iProver_def,sK112('i$',X0_52,'f$','comp$k'('g$','j$')))
| 'image$e'('i$',X0_52) != 'top$'
| 'comp$k'('g$','j$') = 'f$' ),
inference(superposition,[status(thm)],[c_107605,c_57609]) ).
cnf(c_107830,plain,
( 'image$e'('i$',X0_52) != 'top$'
| 'comp$k'('g$','j$') = 'f$' ),
inference(forward_subsumption_resolution,[status(thm)],[c_107758,c_57595]) ).
cnf(c_107853,plain,
( 'image$e'('i$','top$a') != 'top$'
| 'comp$k'('g$','j$') = 'f$' ),
inference(instantiation,[status(thm)],[c_107830]) ).
cnf(c_166642,plain,
'comp$k'('g$','j$') = 'f$',
inference(global_subsumption_just,[status(thm)],[c_107830,c_54,c_949,c_1092,c_107853]) ).
cnf(c_166686,plain,
'fun_app$a'('comp$'('f$'),'i$') = 'g$',
inference(superposition,[status(thm)],[c_166642,c_81894]) ).
cnf(c_166707,plain,
'g$' = sP1_iProver_def,
inference(light_normalisation,[status(thm)],[c_166686,c_47844,c_47845]) ).
cnf(c_166804,plain,
sP1_iProver_def != sP1_iProver_def,
inference(demodulation,[status(thm)],[c_47846,c_166707]) ).
cnf(c_166805,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_166804]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ITP397_1 : TPTP v8.1.2. Released v8.0.0.
% 0.11/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 2 22:15:03 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.45 Running first-order theorem proving
% 0.18/0.45 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 64.84/9.70 % SZS status Started for theBenchmark.p
% 64.84/9.70 % SZS status Theorem for theBenchmark.p
% 64.84/9.70
% 64.84/9.70 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 64.84/9.70
% 64.84/9.70 ------ iProver source info
% 64.84/9.70
% 64.84/9.70 git: date: 2024-05-02 19:28:25 +0000
% 64.84/9.70 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 64.84/9.70 git: non_committed_changes: false
% 64.84/9.70
% 64.84/9.70 ------ Parsing...
% 64.84/9.70 ------ Clausification by vclausify_rel & Parsing by iProver...------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 64.84/9.70
% 64.84/9.70
% 64.84/9.70 ------ Preprocessing... sup_sim: 56 pe_s pe:1:0s pe:2:0s pe_e sup_sim: 1 pe_s pe_e sup_sim: 0 pe_s pe_e
% 64.84/9.70
% 64.84/9.70 ------ Preprocessing...------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 64.84/9.70 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 64.84/9.70
% 64.84/9.70
% 64.84/9.70 ------ Preprocessing...
% 64.84/9.70 ------ Proving...
% 64.84/9.70 ------ Problem Properties
% 64.84/9.70
% 64.84/9.70
% 64.84/9.70 clauses 611
% 64.84/9.70 conjectures 1
% 64.84/9.70 EPR 44
% 64.84/9.70 Horn 542
% 64.84/9.70 unary 87
% 64.84/9.70 binary 289
% 64.84/9.70 lits 1446
% 64.84/9.70 lits eq 731
% 64.84/9.70 fd_pure 0
% 64.84/9.70 fd_pseudo 0
% 64.84/9.70 fd_cond 5
% 64.84/9.70 fd_pseudo_cond 54
% 64.84/9.70 AC symbols 0
% 64.84/9.70
% 64.84/9.70 ------ Schedule dynamic 5 is on
% 64.84/9.70
% 64.84/9.70 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 64.84/9.70
% 64.84/9.70
% 64.84/9.70 ------
% 64.84/9.70 Current options:
% 64.84/9.70 ------
% 64.84/9.70
% 64.84/9.70
% 64.84/9.70
% 64.84/9.70
% 64.84/9.70 ------ Proving...
% 64.84/9.70
% 64.84/9.70
% 64.84/9.70 % SZS status Theorem for theBenchmark.p
% 64.84/9.70
% 64.84/9.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 64.84/9.71
% 64.84/9.71
%------------------------------------------------------------------------------