%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP397_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:55:31 PM UTC 2026
% Result : Theorem 97.80s 14.81s
% Output : CNFRefutation 97.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 37
% Syntax : Number of formulae : 143 ( 69 unt; 0 typ; 0 def)
% Number of atoms : 253 ( 185 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 190 ( 80 ~; 78 |; 12 &)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 19 ( 18 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 40 ( 40 usr; 8 con; 0-4 aty)
% Number of variables : 266 ( 0 sgn 263 !; 3 ?; 266 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
'C_ell2_c_ell2_cblinfun$': $tType ).
tff(decl_sort2,type,
'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).
tff(decl_sort3,type,
'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).
tff(decl_sort4,type,
'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).
tff(decl_sort5,type,
'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).
tff(decl_sort6,type,
'C_ell2_c_ell2_cblinfun_set$': $tType ).
tff(decl_sort7,type,
'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).
tff(decl_sort8,type,
'A_ell2_a_ell2_cblinfun_set$': $tType ).
tff(decl_sort9,type,
'A_ell2_a_ell2_cblinfun$': $tType ).
tff(decl_sort10,type,
'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).
tff(decl_sort11,type,
'B_ell2_b_ell2_cblinfun$': $tType ).
tff(decl_sort12,type,
'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_b_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_fun$': $tType ).
tff(decl_sort13,type,
'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).
tff(decl_sort14,type,
'B_ell2_b_ell2_cblinfun_set$': $tType ).
tff(decl_sort15,type,
'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).
tff(decl_sort16,type,
'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_b_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun_fun$': $tType ).
tff(decl_sort17,type,
'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_a_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_fun$': $tType ).
tff(decl_sort18,type,
'B_ell2_b_ell2_cblinfun_set_b_ell2_b_ell2_cblinfun_set_fun$': $tType ).
tff(decl_32,type,
'image$': ( 'A_ell2_a_ell2_cblinfun_set$' * 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'C_ell2_c_ell2_cblinfun_set$' ).
tff(decl_34,type,
'inv_into$': ( 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_set$' ) > 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).
tff(decl_41,type,
'fun_app$b': ( 'B_ell2_b_ell2_cblinfun$' * 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'C_ell2_c_ell2_cblinfun$' ).
tff(decl_49,type,
'f$': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).
tff(decl_59,type,
'iso_register$': 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).
tff(decl_60,type,
'inj_on$a': ( 'B_ell2_b_ell2_cblinfun_set$' * 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > $o ).
tff(decl_62,type,
'fun_app$l': ( 'C_ell2_c_ell2_cblinfun$' * 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun$' ).
tff(decl_67,type,
'image$a': ( 'B_ell2_b_ell2_cblinfun_set$' * 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'C_ell2_c_ell2_cblinfun_set$' ).
tff(decl_68,type,
'comp$j': ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).
tff(decl_70,type,
'fun_app$h': ( 'A_ell2_a_ell2_cblinfun$' * 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun$' ).
tff(decl_71,type,
'member$b': ( 'B_ell2_b_ell2_cblinfun_set$' * 'B_ell2_b_ell2_cblinfun$' ) > $o ).
tff(decl_74,type,
'inj_on$e': ( 'B_ell2_b_ell2_cblinfun_set$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > $o ).
tff(decl_78,type,
'id$a': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).
tff(decl_85,type,
'fun_app$f': ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_b_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_fun$' ) > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).
tff(decl_89,type,
'comp$': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_b_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun_fun$' ).
tff(decl_106,type,
'top$a': 'B_ell2_b_ell2_cblinfun_set$' ).
tff(decl_108,type,
'register$b': 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).
tff(decl_112,type,
'fun_app$e': ( 'B_ell2_b_ell2_cblinfun$' * 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun$' ).
tff(decl_117,type,
'i$': 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).
tff(decl_119,type,
'fun_app$i': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_a_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_fun$' ) > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).
tff(decl_123,type,
'comp$a': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_b_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_fun$' ).
tff(decl_125,type,
'fun_app$c': ( 'A_ell2_a_ell2_cblinfun$' * 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'C_ell2_c_ell2_cblinfun$' ).
tff(decl_141,type,
'g$': 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).
tff(decl_153,type,
'image$f': ( 'A_ell2_a_ell2_cblinfun_set$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun_set$' ).
tff(decl_155,type,
'fun_app$p': ( 'B_ell2_b_ell2_cblinfun_set$' * 'B_ell2_b_ell2_cblinfun_set_b_ell2_b_ell2_cblinfun_set_fun$' ) > 'B_ell2_b_ell2_cblinfun_set$' ).
tff(decl_168,type,
'inv_into$c': ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_set$' ) > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).
tff(decl_178,type,
'fun_app$d': ( 'B_ell2_b_ell2_cblinfun$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun$' ).
tff(decl_180,type,
'j$': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).
tff(decl_182,type,
'fun_app$g': ( 'A_ell2_a_ell2_cblinfun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun$' ).
tff(decl_191,type,
'member$': ( 'C_ell2_c_ell2_cblinfun_set$' * 'C_ell2_c_ell2_cblinfun$' ) > $o ).
tff(decl_195,type,
'comp$b': 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_a_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_fun$' ).
tff(decl_198,type,
'image$e': ( 'B_ell2_b_ell2_cblinfun_set$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_set$' ).
tff(decl_210,type,
'fun_app$a': ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun_b_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun_fun$' ) > 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).
tff(decl_215,type,
'comp$k': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).
tff(decl_225,type,
'id$': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).
tff(decl_229,type,
'fun_app$n': ( 'C_ell2_c_ell2_cblinfun$' * 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun$' ).
tff(decl_230,type,
'top$': 'A_ell2_a_ell2_cblinfun_set$' ).
tff(decl_238,type,
'inv_into$a': ( 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_set$' ) > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).
tff(decl_239,type,
'image$d': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_set_b_ell2_b_ell2_cblinfun_set_fun$' ).
tff(decl_254,type,
esk14_3: ( 'B_ell2_b_ell2_cblinfun_set$' * ( 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun$' ) ) > 'B_ell2_b_ell2_cblinfun$' ).
tff(decl_265,type,
esk25_4: ( 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * ( 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * ( 'B_ell2_b_ell2_cblinfun_set$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) ) ) > 'B_ell2_b_ell2_cblinfun$' ).
tff(decl_319,type,
esk79_2: ( 'B_ell2_b_ell2_cblinfun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun$' ).
tff(decl_322,type,
esk82_2: ( 'B_ell2_b_ell2_cblinfun$' * 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun$' ).
tff(decl_323,type,
esk83_1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun$' ).
tff(decl_329,type,
esk89_1: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun$' ).
tff(decl_346,type,
esk106_3: ( 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * ( 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_set$' ) ) > 'B_ell2_b_ell2_cblinfun$' ).
tff(axiom550,axiom,
! [X1313: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1314: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1315: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( ( 'fun_app$i'('comp$b'(X1314),X1315) = 'id$a' )
& ( 'fun_app$f'('comp$a'(X1313),X1314) = 'id$' ) )
=> ( X1313 = X1315 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom550) ).
tff(axiom388,axiom,
'fun_app$f'('comp$a'('j$'),'i$') = 'id$',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom388) ).
tff(axiom543,axiom,
! [X1302: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( 'iso_register$'(X1302)
=> ( 'fun_app$i'('comp$b'(X1302),'inv_into$c'('top$a',X1302)) = 'id$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom543) ).
tff(axiom277,axiom,
! [X745: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( 'register$b'(X745)
=> 'inj_on$e'(X745,'top$a') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom277) ).
tff(axiom6,axiom,
! [X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X7: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X5: 'B_ell2_b_ell2_cblinfun$'] : ( 'fun_app$e'('fun_app$f'('comp$a'(X6),X7),X5) = 'fun_app$g'(X6,'fun_app$d'(X7,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6) ).
tff(axiom423,axiom,
! [X1088: 'B_ell2_b_ell2_cblinfun$'] : ( 'fun_app$e'('id$',X1088) = X1088 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom423) ).
tff(axiom7,axiom,
! [X8: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X9: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X10: 'A_ell2_a_ell2_cblinfun$'] : ( 'fun_app$h'('fun_app$i'('comp$b'(X8),X9),X10) = 'fun_app$d'(X8,'fun_app$g'(X9,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom7) ).
tff(axiom424,axiom,
! [X1089: 'A_ell2_a_ell2_cblinfun$'] : ( 'fun_app$h'('id$a',X1089) = X1089 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom424) ).
tff(axiom317,axiom,
! [X826: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( 'inj_on$e'(X826,'top$a')
=> ( 'image$f'('inv_into$c'('top$a',X826),'top$') = 'top$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom317) ).
tff(axiom4,axiom,
'iso_register$'('i$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4) ).
tff(axiom10,axiom,
'register$b'('i$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).
tff(axiom559,axiom,
! [X1340: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1341: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1342: 'A_ell2_a_ell2_cblinfun$'] :
( ( 'fun_app$i'('comp$b'(X1340),X1341) = 'id$a' )
=> ( 'fun_app$d'(X1340,'fun_app$g'(X1341,X1342)) = X1342 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom559) ).
tff(axiom389,axiom,
'fun_app$i'('comp$b'('i$'),'j$') = 'id$a',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom389) ).
tff(axiom211,axiom,
! [X545: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X546: 'B_ell2_b_ell2_cblinfun$'] :
( ( 'image$f'(X545,'top$') = 'top$a' )
=> ? [X547: 'A_ell2_a_ell2_cblinfun$'] : ( X546 = 'fun_app$g'(X545,X547) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom211) ).
tff(axiom447,axiom,
! [X1108: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ! [X1109: 'B_ell2_b_ell2_cblinfun$'] : ( 'fun_app$e'(X1108,X1109) = X1109 )
<=> ( X1108 = 'id$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom447) ).
tff(axiom18,axiom,
! [X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X29: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X30: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ( 'comp$j'(X28,'fun_app$f'('comp$a'(X29),X30)) = 'fun_app$a'('comp$'('comp$k'(X28,X29)),X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom18) ).
tff(axiom289,axiom,
! [X763: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X764: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( 'inj_on$e'(X763,'top$a')
=> ( 'fun_app$a'('comp$'('comp$k'(X764,'inv_into$c'('top$a',X763))),X763) = X764 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom289) ).
tff(axiom379,axiom,
! [X958: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X959: 'B_ell2_b_ell2_cblinfun$'] :
( 'inj_on$a'(X958,'top$a')
=> ( 'fun_app$n'('inv_into$a'('top$a',X958),'fun_app$b'(X958,X959)) = X959 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom379) ).
tff(axiom5,axiom,
! [X3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X5: 'B_ell2_b_ell2_cblinfun$'] : ( 'fun_app$b'('fun_app$a'('comp$'(X3),X4),X5) = 'fun_app$c'(X3,'fun_app$d'(X4,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5) ).
tff(axiom50,axiom,
! [X136: 'B_ell2_b_ell2_cblinfun$'] : 'member$'('fun_app$b'('g$',X136),'image$'('f$','top$')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom50) ).
tff(axiom126,axiom,
! [X328: 'C_ell2_c_ell2_cblinfun$',X329: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X330: 'B_ell2_b_ell2_cblinfun_set$'] :
( 'member$'(X328,'image$a'(X329,X330))
<=> ? [X331: 'B_ell2_b_ell2_cblinfun$'] :
( ( X328 = 'fun_app$b'(X329,X331) )
& 'member$b'(X331,X330) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom126) ).
tff(axiom171,axiom,
! [X452: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X453: 'A_ell2_a_ell2_cblinfun$'] : 'member$'('fun_app$c'(X452,X453),'image$'(X452,'top$')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom171) ).
tff(axiom222,axiom,
! [X574: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X575: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X576: 'A_ell2_a_ell2_cblinfun_set$'] : ( 'image$a'(X574,'image$f'(X575,X576)) = 'image$'('comp$k'(X574,X575),X576) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom222) ).
tff(axiom111,axiom,
! [X260: 'B_ell2_b_ell2_cblinfun_set$',X261: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X262: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ! [X263: 'B_ell2_b_ell2_cblinfun$'] :
( 'member$b'(X263,X260)
=> ( 'fun_app$n'(X261,'fun_app$b'(X262,X263)) = X263 ) )
=> 'inj_on$a'(X262,X260) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom111) ).
tff(axiom517,axiom,
! [X1262: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'image$e'(X1262,'top$a') = 'top$' )
<=> ( 'fun_app$i'('comp$b'(X1262),'inv_into$c'('top$a',X1262)) = 'id$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom517) ).
tff(axiom385,axiom,
! [X977: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X978: 'B_ell2_b_ell2_cblinfun_set$',X979: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X980: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( ! [X90: 'B_ell2_b_ell2_cblinfun$'] :
( 'member$b'(X90,X978)
=> ( 'fun_app$b'('fun_app$a'('comp$'(X979),X977),X90) = 'fun_app$b'('fun_app$a'('comp$'(X980),X977),X90) ) )
& ( 'image$e'(X977,X978) = 'top$' ) )
=> ( X979 = X980 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom385) ).
tff(axiom341,axiom,
! [X872: 'C_ell2_c_ell2_cblinfun$',X873: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X874: 'A_ell2_a_ell2_cblinfun_set$'] :
( 'member$'(X872,'image$'(X873,X874))
=> ( 'fun_app$c'(X873,'fun_app$l'('inv_into$'(X874,X873),X872)) = X872 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom341) ).
tff(axiom9,axiom,
! [X14: 'B_ell2_b_ell2_cblinfun$'] : ( 'fun_app$d'('i$',X14) = 'fun_app$l'('inv_into$'('top$','f$'),'fun_app$b'('g$',X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).
tff(axiom347,axiom,
! [X891: 'B_ell2_b_ell2_cblinfun_set$',X892: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X893: 'C_ell2_c_ell2_cblinfun$',X894: 'C_ell2_c_ell2_cblinfun$'] :
( ( 'member$'(X894,'image$a'(X892,X891))
& 'member$'(X893,'image$a'(X892,X891))
& ( 'fun_app$n'('inv_into$a'(X891,X892),X893) = 'fun_app$n'('inv_into$a'(X891,X892),X894) ) )
=> ( X893 = X894 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom347) ).
tff(axiom96,axiom,
! [X212: 'A_ell2_a_ell2_cblinfun$'] : ( 'fun_app$g'('j$',X212) = 'fun_app$n'('inv_into$a'('top$a','g$'),'fun_app$c'('f$',X212)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom96) ).
tff(axiom196,axiom,
! [X509: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'fun_app$p'('image$d'(X509),'top$a') = 'top$a' )
<=> ! [X510: 'B_ell2_b_ell2_cblinfun$'] :
? [X5: 'B_ell2_b_ell2_cblinfun$'] : ( X510 = 'fun_app$e'(X509,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom196) ).
tff(axiom215,axiom,
! [X553: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X554: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X555: 'B_ell2_b_ell2_cblinfun_set$'] : ( 'image$f'(X553,'image$e'(X554,X555)) = 'fun_app$p'('image$d'('fun_app$f'('comp$a'(X553),X554)),X555) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom215) ).
tff(axiom97,axiom,
'image$'('f$','top$') = 'image$a'('g$','top$a'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom97) ).
tff(axiom336,axiom,
'inj_on$a'('g$','top$a'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom336) ).
tff(axiom368,axiom,
! [X934: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X935: 'A_ell2_a_ell2_cblinfun_set$'] :
( ( 'image$e'(X934,'top$a') = 'top$' )
=> ( 'image$e'(X934,'image$f'('inv_into$c'('top$a',X934),X935)) = X935 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom368) ).
tff(axiom558,axiom,
! [X1338: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1339: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X5: 'B_ell2_b_ell2_cblinfun$'] :
( ( 'fun_app$f'('comp$a'(X1338),X1339) = 'id$' )
=> ( 'fun_app$g'(X1338,'fun_app$d'(X1339,X5)) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom558) ).
tff(conjecture1,conjecture,
'fun_app$a'('comp$'('f$'),'i$') = 'g$',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture1) ).
tff(c_0_37,plain,
! [X2066: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2067: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2068: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( X2066 = X2068 )
| ( 'fun_app$i'('comp$b'(X2067),X2068) != 'id$a' )
| ( 'fun_app$f'('comp$a'(X2066),X2067) != 'id$' ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom550])])]) ).
tcf(c_0_38,plain,
! [X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X9: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'fun_app$i'('comp$b'(X4),X9) != 'id$a' )
| ( 'fun_app$f'('comp$a'(X6),X4) != 'id$' )
| ( X6 = X9 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
tcf(c_0_39,plain,
'fun_app$f'('comp$a'('j$'),'i$') = 'id$',
inference(split_conjunct,[status(thm)],[axiom388]) ).
tff(c_0_40,plain,
! [X2063: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'fun_app$i'('comp$b'(X2063),'inv_into$c'('top$a',X2063)) = 'id$a' )
| ~ 'iso_register$'(X2063) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom543])])]) ).
tff(c_0_41,plain,
! [X2065: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( 'inj_on$e'(X2065,'top$a')
| ~ 'register$b'(X2065) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom277])])]) ).
tff(c_0_42,plain,
! [X1794: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1795: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1796: 'B_ell2_b_ell2_cblinfun$'] : ( 'fun_app$e'('fun_app$f'('comp$a'(X1794),X1795),X1796) = 'fun_app$g'(X1794,'fun_app$d'(X1795,X1796)) ),
inference(variable_rename,[status(thm)],[axiom6]) ).
tff(c_0_43,plain,
! [X2153: 'B_ell2_b_ell2_cblinfun$'] : ( 'fun_app$e'('id$',X2153) = X2153 ),
inference(variable_rename,[status(thm)],[axiom423]) ).
tff(c_0_44,plain,
! [X1797: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1798: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1799: 'A_ell2_a_ell2_cblinfun$'] : ( 'fun_app$h'('fun_app$i'('comp$b'(X1797),X1798),X1799) = 'fun_app$d'(X1797,'fun_app$g'(X1798,X1799)) ),
inference(variable_rename,[status(thm)],[axiom7]) ).
tff(c_0_45,plain,
! [X2219: 'A_ell2_a_ell2_cblinfun$'] : ( 'fun_app$h'('id$a',X2219) = X2219 ),
inference(variable_rename,[status(thm)],[axiom424]) ).
tff(c_0_46,plain,
! [X2358: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'image$f'('inv_into$c'('top$a',X2358),'top$') = 'top$a' )
| ~ 'inj_on$e'(X2358,'top$a') ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom317])])]) ).
tcf(c_0_47,plain,
! [X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'fun_app$i'('comp$b'('i$'),X6) != 'id$a' )
| ( 'j$' = X6 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
tcf(c_0_48,plain,
! [X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ~ 'iso_register$'(X4)
| ( 'fun_app$i'('comp$b'(X4),'inv_into$c'('top$a',X4)) = 'id$a' ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
tcf(c_0_49,plain,
'iso_register$'('i$'),
inference(split_conjunct,[status(thm)],[axiom4]) ).
tcf(c_0_50,plain,
! [X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ~ 'register$b'(X4)
| 'inj_on$e'(X4,'top$a') ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
tcf(c_0_51,plain,
'register$b'('i$'),
inference(split_conjunct,[status(thm)],[axiom10]) ).
tcf(c_0_52,plain,
! [X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X5: 'B_ell2_b_ell2_cblinfun$'] : 'fun_app$e'('fun_app$f'('comp$a'(X6),X4),X5) = 'fun_app$g'(X6,'fun_app$d'(X4,X5)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
tcf(c_0_53,plain,
! [X5: 'B_ell2_b_ell2_cblinfun$'] : 'fun_app$e'('id$',X5) = X5,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
tff(c_0_54,plain,
! [X1896: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1897: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1898: 'A_ell2_a_ell2_cblinfun$'] :
( ( 'fun_app$d'(X1896,'fun_app$g'(X1897,X1898)) = X1898 )
| ( 'fun_app$i'('comp$b'(X1896),X1897) != 'id$a' ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom559])])]) ).
tcf(c_0_55,plain,
! [X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X10: 'A_ell2_a_ell2_cblinfun$'] : 'fun_app$h'('fun_app$i'('comp$b'(X4),X6),X10) = 'fun_app$d'(X4,'fun_app$g'(X6,X10)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
tcf(c_0_56,plain,
'fun_app$i'('comp$b'('i$'),'j$') = 'id$a',
inference(split_conjunct,[status(thm)],[axiom389]) ).
tcf(c_0_57,plain,
! [X10: 'A_ell2_a_ell2_cblinfun$'] : 'fun_app$h'('id$a',X10) = X10,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
tff(c_0_58,plain,
! [X2117: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2118: 'B_ell2_b_ell2_cblinfun$'] :
( ( X2118 = 'fun_app$g'(X2117,esk79_2(X2117,X2118)) )
| ( 'image$f'(X2117,'top$') != 'top$a' ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom211])])])])])]) ).
tcf(c_0_59,plain,
! [X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ~ 'inj_on$e'(X4,'top$a')
| ( 'image$f'('inv_into$c'('top$a',X4),'top$') = 'top$a' ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
tcf(c_0_60,plain,
'inv_into$c'('top$a','i$') = 'j$',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
tcf(c_0_61,plain,
'inj_on$e'('i$','top$a'),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
tff(c_0_62,plain,
! [X2155: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2157: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2158: 'B_ell2_b_ell2_cblinfun$'] :
( ( ( 'fun_app$e'(X2157,X2158) = X2158 )
| ( X2157 != 'id$' ) )
& ( ( X2155 = 'id$' )
| ( 'fun_app$e'(X2155,esk89_1(X2155)) != esk89_1(X2155) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom447])])])])])]) ).
tcf(c_0_63,plain,
! [X5: 'B_ell2_b_ell2_cblinfun$'] : 'fun_app$g'('j$','fun_app$d'('i$',X5)) = X5,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_39]),c_0_53]) ).
tcf(c_0_64,plain,
! [X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X10: 'A_ell2_a_ell2_cblinfun$',X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'fun_app$i'('comp$b'(X4),X6) != 'id$a' )
| ( 'fun_app$d'(X4,'fun_app$g'(X6,X10)) = X10 ) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
tcf(c_0_65,plain,
! [X10: 'A_ell2_a_ell2_cblinfun$'] : 'fun_app$d'('i$','fun_app$g'('j$',X10)) = X10,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
tcf(c_0_66,plain,
! [X5: 'B_ell2_b_ell2_cblinfun$',X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'image$f'(X6,'top$') != 'top$a' )
| ( X5 = 'fun_app$g'(X6,esk79_2(X6,X5)) ) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
tcf(c_0_67,plain,
'image$f'('j$','top$') = 'top$a',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
tff(c_0_68,plain,
! [X2251: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X2252: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2253: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : ( 'comp$j'(X2251,'fun_app$f'('comp$a'(X2252),X2253)) = 'fun_app$a'('comp$'('comp$k'(X2251,X2252)),X2253) ),
inference(variable_rename,[status(thm)],[axiom18]) ).
tcf(c_0_69,plain,
! [X31: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'fun_app$e'(X31,esk89_1(X31)) != esk89_1(X31) )
| ( X31 = 'id$' ) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
tcf(c_0_70,plain,
! [X10: 'A_ell2_a_ell2_cblinfun$',X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'fun_app$i'('comp$b'('i$'),X6) != 'id$a' )
| ( 'fun_app$g'('j$',X10) = 'fun_app$g'(X6,X10) ) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
tcf(c_0_71,plain,
! [X5: 'B_ell2_b_ell2_cblinfun$'] : esk79_2('j$',X5) = 'fun_app$d'('i$',X5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67])]) ).
tff(c_0_72,plain,
! [X2283: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2284: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( 'fun_app$a'('comp$'('comp$k'(X2284,'inv_into$c'('top$a',X2283))),X2283) = X2284 )
| ~ 'inj_on$e'(X2283,'top$a') ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom289])])]) ).
tcf(c_0_73,plain,
! [X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] : 'comp$j'(X28,'fun_app$f'('comp$a'(X6),X4)) = 'fun_app$a'('comp$'('comp$k'(X28,X6)),X4),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
tff(c_0_74,plain,
! [X2420: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X2421: 'B_ell2_b_ell2_cblinfun$'] :
( ( 'fun_app$n'('inv_into$a'('top$a',X2420),'fun_app$b'(X2420,X2421)) = X2421 )
| ~ 'inj_on$a'(X2420,'top$a') ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom379])])]) ).
tff(c_0_75,plain,
! [X1685: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1686: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1687: 'B_ell2_b_ell2_cblinfun$'] : ( 'fun_app$b'('fun_app$a'('comp$'(X1685),X1686),X1687) = 'fun_app$c'(X1685,'fun_app$d'(X1686,X1687)) ),
inference(variable_rename,[status(thm)],[axiom5]) ).
tcf(c_0_76,plain,
! [X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'fun_app$g'(X6,'fun_app$d'(X4,esk89_1('fun_app$f'('comp$a'(X6),X4)))) != esk89_1('fun_app$f'('comp$a'(X6),X4)) )
| ( 'fun_app$f'('comp$a'(X6),X4) = 'id$' ) ),
inference(spm,[status(thm)],[c_0_69,c_0_52]) ).
tcf(c_0_77,plain,
! [X5: 'B_ell2_b_ell2_cblinfun$',X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'fun_app$i'('comp$b'('i$'),X6) != 'id$a' )
| ( 'fun_app$g'(X6,'fun_app$d'('i$',X5)) = X5 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_70]),c_0_71]),c_0_67])]) ).
tcf(c_0_78,plain,
! [X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ~ 'inj_on$e'(X4,'top$a')
| ( 'fun_app$a'('comp$'('comp$k'(X28,'inv_into$c'('top$a',X4))),X4) = X28 ) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
tcf(c_0_79,plain,
! [X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : 'fun_app$a'('comp$'('comp$k'(X28,'j$')),'i$') = 'comp$j'(X28,'id$'),
inference(spm,[status(thm)],[c_0_73,c_0_39]) ).
tff(c_0_80,plain,
! [X1619: 'B_ell2_b_ell2_cblinfun$'] : 'member$'('fun_app$b'('g$',X1619),'image$'('f$','top$')),
inference(variable_rename,[status(thm)],[axiom50]) ).
tff(c_0_81,plain,
! [X1736: 'C_ell2_c_ell2_cblinfun$',X1737: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1738: 'B_ell2_b_ell2_cblinfun_set$',X1740: 'C_ell2_c_ell2_cblinfun$',X1741: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1742: 'B_ell2_b_ell2_cblinfun_set$',X1743: 'B_ell2_b_ell2_cblinfun$'] :
( ( 'member$'(X1740,'image$a'(X1741,X1742))
| ( X1740 != 'fun_app$b'(X1741,X1743) )
| ~ 'member$b'(X1743,X1742) )
& ( ~ 'member$'(X1736,'image$a'(X1737,X1738))
| ( X1736 = 'fun_app$b'(X1737,esk14_3(X1736,X1737,X1738)) ) )
& ( ~ 'member$'(X1736,'image$a'(X1737,X1738))
| 'member$b'(esk14_3(X1736,X1737,X1738),X1738) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom126])])])])])])]) ).
tff(c_0_82,plain,
! [X1938: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1939: 'A_ell2_a_ell2_cblinfun$'] : 'member$'('fun_app$c'(X1938,X1939),'image$'(X1938,'top$')),
inference(variable_rename,[status(thm)],[axiom171]) ).
tff(c_0_83,plain,
! [X2272: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X2273: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2274: 'A_ell2_a_ell2_cblinfun_set$'] : ( 'image$a'(X2272,'image$f'(X2273,X2274)) = 'image$'('comp$k'(X2272,X2273),X2274) ),
inference(variable_rename,[status(thm)],[axiom222]) ).
tff(c_0_84,plain,
! [X2380: 'B_ell2_b_ell2_cblinfun_set$',X2381: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2382: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( 'inj_on$a'(X2382,X2380)
| ( 'fun_app$n'(X2381,'fun_app$b'(X2382,esk106_3(X2380,X2381,X2382))) != esk106_3(X2380,X2381,X2382) ) )
& ( 'inj_on$a'(X2382,X2380)
| 'member$b'(esk106_3(X2380,X2381,X2382),X2380) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom111])])])])]) ).
tff(c_0_85,plain,
! [X2364: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( ( 'image$e'(X2364,'top$a') = 'top$' )
| ( 'fun_app$i'('comp$b'(X2364),'inv_into$c'('top$a',X2364)) != 'id$a' ) )
& ( ( 'fun_app$i'('comp$b'(X2364),'inv_into$c'('top$a',X2364)) = 'id$a' )
| ( 'image$e'(X2364,'top$a') != 'top$' ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom517])])]) ).
tff(c_0_86,plain,
! [X1789: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1790: 'B_ell2_b_ell2_cblinfun_set$',X1791: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1792: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( ( X1791 = X1792 )
| ( 'image$e'(X1789,X1790) != 'top$' )
| ( 'fun_app$b'('fun_app$a'('comp$'(X1791),X1789),esk25_4(X1789,X1790,X1791,X1792)) != 'fun_app$b'('fun_app$a'('comp$'(X1792),X1789),esk25_4(X1789,X1790,X1791,X1792)) ) )
& ( ( X1791 = X1792 )
| ( 'image$e'(X1789,X1790) != 'top$' )
| 'member$b'(esk25_4(X1789,X1790,X1791,X1792),X1790) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom385])])])])]) ).
tff(c_0_87,plain,
! [X1651: 'C_ell2_c_ell2_cblinfun$',X1652: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X1653: 'A_ell2_a_ell2_cblinfun_set$'] :
( ( 'fun_app$c'(X1652,'fun_app$l'('inv_into$'(X1653,X1652),X1651)) = X1651 )
| ~ 'member$'(X1651,'image$'(X1652,X1653)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom341])])]) ).
tff(c_0_88,plain,
! [X1617: 'B_ell2_b_ell2_cblinfun$'] : ( 'fun_app$d'('i$',X1617) = 'fun_app$l'('inv_into$'('top$','f$'),'fun_app$b'('g$',X1617)) ),
inference(variable_rename,[status(thm)],[axiom9]) ).
tff(c_0_89,plain,
! [X2400: 'B_ell2_b_ell2_cblinfun_set$',X2401: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X2402: 'C_ell2_c_ell2_cblinfun$',X2403: 'C_ell2_c_ell2_cblinfun$'] :
( ( X2402 = X2403 )
| ~ 'member$'(X2403,'image$a'(X2401,X2400))
| ~ 'member$'(X2402,'image$a'(X2401,X2400))
| ( 'fun_app$n'('inv_into$a'(X2400,X2401),X2402) != 'fun_app$n'('inv_into$a'(X2400,X2401),X2403) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom347])])]) ).
tff(c_0_90,plain,
! [X2072: 'A_ell2_a_ell2_cblinfun$'] : ( 'fun_app$g'('j$',X2072) = 'fun_app$n'('inv_into$a'('top$a','g$'),'fun_app$c'('f$',X2072)) ),
inference(variable_rename,[status(thm)],[axiom96]) ).
tcf(c_0_91,plain,
! [X5: 'B_ell2_b_ell2_cblinfun$',X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ~ 'inj_on$a'(X28,'top$a')
| ( 'fun_app$n'('inv_into$a'('top$a',X28),'fun_app$b'(X28,X5)) = X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
tcf(c_0_92,plain,
! [X3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X5: 'B_ell2_b_ell2_cblinfun$'] : 'fun_app$b'('fun_app$a'('comp$'(X3),X4),X5) = 'fun_app$c'(X3,'fun_app$d'(X4,X5)),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
tcf(c_0_93,plain,
! [X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'fun_app$i'('comp$b'('i$'),X6) != 'id$a' )
| ( 'fun_app$f'('comp$a'(X6),'i$') = 'id$' ) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
tcf(c_0_94,plain,
! [X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : 'comp$j'(X28,'id$') = X28,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_60]),c_0_79]),c_0_61])]) ).
tcf(c_0_95,plain,
! [X5: 'B_ell2_b_ell2_cblinfun$'] : 'member$'('fun_app$b'('g$',X5),'image$'('f$','top$')),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
tcf(c_0_96,plain,
! [X2: 'C_ell2_c_ell2_cblinfun$',X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X207: 'B_ell2_b_ell2_cblinfun_set$'] :
( ~ 'member$'(X2,'image$a'(X28,X207))
| ( X2 = 'fun_app$b'(X28,esk14_3(X2,X28,X207)) ) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
tcf(c_0_97,plain,
! [X10: 'A_ell2_a_ell2_cblinfun$',X3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : 'member$'('fun_app$c'(X3,X10),'image$'(X3,'top$')),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
tcf(c_0_98,plain,
! [X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X204: 'A_ell2_a_ell2_cblinfun_set$'] : 'image$a'(X28,'image$f'(X6,X204)) = 'image$'('comp$k'(X28,X6),X204),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
tcf(c_0_99,plain,
! [X22: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X207: 'B_ell2_b_ell2_cblinfun_set$',X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ( 'fun_app$n'(X22,'fun_app$b'(X28,esk106_3(X207,X22,X28))) != esk106_3(X207,X22,X28) )
| 'inj_on$a'(X28,X207) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
tcf(c_0_100,plain,
! [X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'fun_app$i'('comp$b'(X4),'inv_into$c'('top$a',X4)) != 'id$a' )
| ( 'image$e'(X4,'top$a') = 'top$' ) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
tff(c_0_101,plain,
! [X2129: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2130: 'B_ell2_b_ell2_cblinfun$',X2132: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2134: 'B_ell2_b_ell2_cblinfun$'] :
( ( ( 'fun_app$p'('image$d'(X2132),'top$a') = 'top$a' )
| ( esk83_1(X2132) != 'fun_app$e'(X2132,X2134) ) )
& ( ( X2130 = 'fun_app$e'(X2129,esk82_2(X2129,X2130)) )
| ( 'fun_app$p'('image$d'(X2129),'top$a') != 'top$a' ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom196])])])])])]) ).
tff(c_0_102,plain,
! [X2024: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X2025: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2026: 'B_ell2_b_ell2_cblinfun_set$'] : ( 'image$f'(X2024,'image$e'(X2025,X2026)) = 'fun_app$p'('image$d'('fun_app$f'('comp$a'(X2024),X2025)),X2026) ),
inference(variable_rename,[status(thm)],[axiom215]) ).
tcf(c_0_103,plain,
! [X3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X20: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X207: 'B_ell2_b_ell2_cblinfun_set$'] :
( ( 'image$e'(X4,X207) != 'top$' )
| ( 'fun_app$b'('fun_app$a'('comp$'(X3),X4),esk25_4(X4,X207,X3,X20)) != 'fun_app$b'('fun_app$a'('comp$'(X20),X4),esk25_4(X4,X207,X3,X20)) )
| ( X3 = X20 ) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
tcf(c_0_104,plain,
! [X2: 'C_ell2_c_ell2_cblinfun$',X3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X204: 'A_ell2_a_ell2_cblinfun_set$'] :
( ~ 'member$'(X2,'image$'(X3,X204))
| ( 'fun_app$c'(X3,'fun_app$l'('inv_into$'(X204,X3),X2)) = X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
tcf(c_0_105,plain,
! [X5: 'B_ell2_b_ell2_cblinfun$'] : 'fun_app$d'('i$',X5) = 'fun_app$l'('inv_into$'('top$','f$'),'fun_app$b'('g$',X5)),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
tcf(c_0_106,plain,
! [X2: 'C_ell2_c_ell2_cblinfun$',X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X155: 'C_ell2_c_ell2_cblinfun$',X207: 'B_ell2_b_ell2_cblinfun_set$'] :
( ~ 'member$'(X155,'image$a'(X28,X207))
| ~ 'member$'(X2,'image$a'(X28,X207))
| ( 'fun_app$n'('inv_into$a'(X207,X28),X2) != 'fun_app$n'('inv_into$a'(X207,X28),X155) )
| ( X2 = X155 ) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
tcf(c_0_107,plain,
! [X10: 'A_ell2_a_ell2_cblinfun$'] : 'fun_app$g'('j$',X10) = 'fun_app$n'('inv_into$a'('top$a','g$'),'fun_app$c'('f$',X10)),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
tcf(c_0_108,plain,
'image$'('f$','top$') = 'image$a'('g$','top$a'),
inference(split_conjunct,[status(thm)],[axiom97]) ).
tcf(c_0_109,plain,
! [X3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X5: 'B_ell2_b_ell2_cblinfun$',X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ~ 'inj_on$a'('fun_app$a'('comp$'(X3),X4),'top$a')
| ( 'fun_app$n'('inv_into$a'('top$a','fun_app$a'('comp$'(X3),X4)),'fun_app$c'(X3,'fun_app$d'(X4,X5))) = X5 ) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
tcf(c_0_110,plain,
! [X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'fun_app$i'('comp$b'('i$'),X6) != 'id$a' )
| ( 'fun_app$a'('comp$'('comp$k'(X28,X6)),'i$') = X28 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_93]),c_0_94]) ).
tcf(c_0_111,plain,
! [X2: 'C_ell2_c_ell2_cblinfun$',X207: 'B_ell2_b_ell2_cblinfun_set$'] :
( ~ 'member$'(X2,'image$a'('g$',X207))
| 'member$'(X2,'image$'('f$','top$')) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
tcf(c_0_112,plain,
! [X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X10: 'A_ell2_a_ell2_cblinfun$',X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : 'member$'('fun_app$c'('comp$k'(X28,X6),X10),'image$a'(X28,'image$f'(X6,'top$'))),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
tcf(c_0_113,plain,
! [X207: 'B_ell2_b_ell2_cblinfun_set$',X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ~ 'inj_on$a'(X28,'top$a')
| 'inj_on$a'(X28,X207) ),
inference(spm,[status(thm)],[c_0_99,c_0_91]) ).
tcf(c_0_114,plain,
'inj_on$a'('g$','top$a'),
inference(split_conjunct,[status(thm)],[axiom336]) ).
tff(c_0_115,plain,
! [X2359: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X2360: 'A_ell2_a_ell2_cblinfun_set$'] :
( ( 'image$e'(X2359,'image$f'('inv_into$c'('top$a',X2359),X2360)) = X2360 )
| ( 'image$e'(X2359,'top$a') != 'top$' ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom368])])]) ).
tcf(c_0_116,plain,
! [X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ~ 'iso_register$'(X4)
| ( 'image$e'(X4,'top$a') = 'top$' ) ),
inference(spm,[status(thm)],[c_0_100,c_0_48]) ).
tcf(c_0_117,plain,
! [X31: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X5: 'B_ell2_b_ell2_cblinfun$'] :
( ( esk83_1(X31) != 'fun_app$e'(X31,X5) )
| ( 'fun_app$p'('image$d'(X31),'top$a') = 'top$a' ) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
tcf(c_0_118,plain,
! [X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X207: 'B_ell2_b_ell2_cblinfun_set$'] : 'image$f'(X6,'image$e'(X4,X207)) = 'fun_app$p'('image$d'('fun_app$f'('comp$a'(X6),X4)),X207),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
tff(c_0_119,plain,
! [X1893: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X1894: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X1895: 'B_ell2_b_ell2_cblinfun$'] :
( ( 'fun_app$g'(X1893,'fun_app$d'(X1894,X1895)) = X1895 )
| ( 'fun_app$f'('comp$a'(X1893),X1894) != 'id$' ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom558])])]) ).
tcf(c_0_120,plain,
! [X3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X20: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X207: 'B_ell2_b_ell2_cblinfun_set$'] :
( ( 'image$e'(X4,X207) != 'top$' )
| ( 'fun_app$c'(X3,'fun_app$d'(X4,esk25_4(X4,X207,X3,X20))) != 'fun_app$c'(X20,'fun_app$d'(X4,esk25_4(X4,X207,X3,X20))) )
| ( X3 = X20 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_92]),c_0_92]) ).
tcf(c_0_121,plain,
! [X5: 'B_ell2_b_ell2_cblinfun$'] : 'fun_app$c'('f$','fun_app$d'('i$',X5)) = 'fun_app$b'('g$',X5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_95])]) ).
tcf(c_0_122,plain,
! [X10: 'A_ell2_a_ell2_cblinfun$',X2: 'C_ell2_c_ell2_cblinfun$'] :
( ~ 'member$'(X2,'image$'('f$','top$'))
| ( 'fun_app$n'('inv_into$a'('top$a','g$'),X2) != 'fun_app$g'('j$',X10) )
| ( X2 = 'fun_app$c'('f$',X10) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_97]),c_0_108])]) ).
tcf(c_0_123,plain,
! [X5: 'B_ell2_b_ell2_cblinfun$',X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
( ~ 'inj_on$a'(X28,'top$a')
| ( 'fun_app$i'('comp$b'('i$'),X6) != 'id$a' )
| ( 'fun_app$n'('inv_into$a'('top$a',X28),'fun_app$c'('comp$k'(X28,X6),'fun_app$d'('i$',X5))) = X5 ) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
tcf(c_0_124,plain,
! [X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X10: 'A_ell2_a_ell2_cblinfun$'] : 'member$'('fun_app$c'('comp$k'('g$',X6),X10),'image$'('f$','top$')),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
tcf(c_0_125,plain,
! [X207: 'B_ell2_b_ell2_cblinfun_set$'] : 'inj_on$a'('g$',X207),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
tcf(c_0_126,plain,
! [X204: 'A_ell2_a_ell2_cblinfun_set$',X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'image$e'(X4,'top$a') != 'top$' )
| ( 'image$e'(X4,'image$f'('inv_into$c'('top$a',X4),X204)) = X204 ) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
tcf(c_0_127,plain,
'image$e'('i$','top$a') = 'top$',
inference(spm,[status(thm)],[c_0_116,c_0_49]) ).
tcf(c_0_128,plain,
! [X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X5: 'B_ell2_b_ell2_cblinfun$'] :
( ( esk83_1('fun_app$f'('comp$a'(X6),X4)) != 'fun_app$g'(X6,'fun_app$d'(X4,X5)) )
| ( 'image$f'(X6,'image$e'(X4,'top$a')) = 'top$a' ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_52]),c_0_118]) ).
tcf(c_0_129,plain,
! [X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X5: 'B_ell2_b_ell2_cblinfun$',X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'fun_app$f'('comp$a'(X6),X4) != 'id$' )
| ( 'fun_app$g'(X6,'fun_app$d'(X4,X5)) = X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
tff(c_0_130,negated_conjecture,
'fun_app$a'('comp$'('f$'),'i$') != 'g$',
inference(assume_negation,[status(cth)],[conjecture1]) ).
tcf(c_0_131,plain,
! [X3: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',X207: 'B_ell2_b_ell2_cblinfun_set$'] :
( ( 'image$e'('i$',X207) != 'top$' )
| ( 'fun_app$c'(X3,'fun_app$d'('i$',esk25_4('i$',X207,X3,'f$'))) != 'fun_app$b'('g$',esk25_4('i$',X207,X3,'f$')) )
| ( X3 = 'f$' ) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
tcf(c_0_132,plain,
! [X10: 'A_ell2_a_ell2_cblinfun$',X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'fun_app$i'('comp$b'('i$'),X6) != 'id$a' )
| ( 'fun_app$c'('comp$k'('g$',X6),X10) = 'fun_app$c'('f$',X10) ) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124]),c_0_125])])]),c_0_65]) ).
tcf(c_0_133,plain,
! [X204: 'A_ell2_a_ell2_cblinfun_set$'] : 'image$e'('i$','image$f'('j$',X204)) = X204,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_60]),c_0_127])]) ).
tcf(c_0_134,plain,
! [X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'fun_app$f'('comp$a'(X6),X4) != 'id$' )
| ( 'image$f'(X6,'image$e'(X4,'top$a')) = 'top$a' ) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129])]) ).
tff(c_0_135,negated_conjecture,
'fun_app$a'('comp$'('f$'),'i$') != 'g$',
inference(fof_simplification,[status(thm)],[c_0_130]) ).
tcf(c_0_136,plain,
! [X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',X207: 'B_ell2_b_ell2_cblinfun_set$'] :
( ( 'image$e'('i$',X207) != 'top$' )
| ( 'fun_app$i'('comp$b'('i$'),X6) != 'id$a' )
| ( 'comp$k'('g$',X6) = 'f$' ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_121])]) ).
tcf(c_0_137,plain,
! [X4: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
( ( 'fun_app$f'('comp$a'('j$'),X4) != 'id$' )
| ( 'image$e'(X4,'top$a') = 'top$' ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_127]) ).
tff(c_0_138,negated_conjecture,
'fun_app$a'('comp$'('f$'),'i$') != 'g$',
inference(fof_nnf,[status(thm)],[c_0_135]) ).
tcf(c_0_139,plain,
! [X28: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] : 'fun_app$a'('comp$'('comp$k'(X28,'j$')),'i$') = X28,
inference(rw,[status(thm)],[c_0_79,c_0_94]) ).
tcf(c_0_140,plain,
! [X6: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
( ( 'fun_app$i'('comp$b'('i$'),X6) != 'id$a' )
| ( 'comp$k'('g$',X6) = 'f$' ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_39])]) ).
tcf(c_0_141,negated_conjecture,
'fun_app$a'('comp$'('f$'),'i$') != 'g$',
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_142,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_56])]),c_0_141]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP397_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n019.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 20 22:36:50 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.53 Running first-order theorem proving
% 0.23/0.53 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 97.80/14.81 % Version: 3.5.1
% 97.80/14.81 % Preprocessing class: FSLMSMSMSSSNFFN.
% 97.80/14.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 97.80/14.81 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 97.80/14.81 % Starting new_bool_3 with 600s (2) cores
% 97.80/14.81 % Starting new_bool_1 with 300s (1) cores
% 97.80/14.81 % Starting sh5l with 300s (1) cores
% 97.80/14.81 % new_bool_3 with pid 1062388 completed with status 0
% 97.80/14.81 % Result found by new_bool_3
% 97.80/14.81 % Preprocessing class: FSLMSMSMSSSNFFN.
% 97.80/14.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 97.80/14.81 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 97.80/14.81 % Starting new_bool_3 with 600s (2) cores
% 97.80/14.81 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 97.80/14.81 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 97.80/14.81 % Search class: FGUSM-FSLM32-MFFFFFNN
% 97.80/14.81 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 97.80/14.81 % Starting SubtermCWHack with 61s (1) cores
% 97.80/14.81 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 97.80/14.81 % SAT001_MinMin_p005000_rr_RG with pid 1062393 completed with status 0
% 97.80/14.81 % Result found by SAT001_MinMin_p005000_rr_RG
% 97.80/14.81 % Preprocessing class: FSLMSMSMSSSNFFN.
% 97.80/14.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 97.80/14.81 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 97.80/14.81 % Starting new_bool_3 with 600s (2) cores
% 97.80/14.81 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 97.80/14.81 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 97.80/14.81 % Search class: FGUSM-FSLM32-MFFFFFNN
% 97.80/14.81 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 97.80/14.81 % Starting SubtermCWHack with 61s (1) cores
% 97.80/14.81 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 97.80/14.81 % Preprocessing time : 0.011 s
% 97.80/14.81 % Presaturation interreduction done
% 97.80/14.81
% 97.80/14.81 % Proof found!
% 97.80/14.81 % SZS status Theorem
% 97.80/14.81 % SZS output start CNFRefutation
% See solution above
% 97.80/14.81 % Parsed axioms : 928
% 97.80/14.81 % Removed by relevancy pruning/SinE : 668
% 97.80/14.81 % Initial clauses : 381
% 97.80/14.81 % Removed in clause preprocessing : 20
% 97.80/14.81 % Initial clauses in saturation : 361
% 97.80/14.81 % Processed clauses : 41198
% 97.80/14.81 % ...of these trivial : 148
% 97.80/14.81 % ...subsumed : 35064
% 97.80/14.81 % ...remaining for further processing : 5986
% 97.80/14.81 % Other redundant clauses eliminated : 9469
% 97.80/14.81 % Clauses deleted for lack of memory : 0
% 97.80/14.81 % Backward-subsumed : 228
% 97.80/14.81 % Backward-rewritten : 107
% 97.80/14.81 % Generated clauses : 354390
% 97.80/14.81 % ...of the previous two non-redundant : 326979
% 97.80/14.81 % ...aggressively subsumed : 0
% 97.80/14.81 % Contextual simplify-reflections : 302
% 97.80/14.81 % Paramodulations : 344663
% 97.80/14.81 % Factorizations : 0
% 97.80/14.81 % NegExts : 0
% 97.80/14.81 % Equation resolutions : 9727
% 97.80/14.81 % Disequality decompositions : 0
% 97.80/14.81 % Total rewrite steps : 185471
% 97.80/14.81 % ...of those cached : 180751
% 97.80/14.81 % Propositional unsat checks : 1
% 97.80/14.81 % Propositional check models : 0
% 97.80/14.81 % Propositional check unsatisfiable : 0
% 97.80/14.81 % Propositional clauses : 0
% 97.80/14.81 % Propositional clauses after purity: 0
% 97.80/14.81 % Propositional unsat core size : 0
% 97.80/14.81 % Propositional preprocessing time : 0.000
% 97.80/14.81 % Propositional encoding time : 0.482
% 97.80/14.81 % Propositional solver time : 0.257
% 97.80/14.81 % Success case prop preproc time : 0.000
% 97.80/14.81 % Success case prop encoding time : 0.000
% 97.80/14.81 % Success case prop solver time : 0.000
% 97.80/14.81 % Current number of processed clauses : 5340
% 97.80/14.81 % Positive orientable unit clauses : 119
% 97.80/14.81 % Positive unorientable unit clauses: 0
% 97.80/14.81 % Negative unit clauses : 1
% 97.80/14.81 % Non-unit-clauses : 5220
% 97.80/14.81 % Current number of unprocessed clauses: 285334
% 97.80/14.81 % ...number of literals in the above : 1246497
% 97.80/14.81 % Current number of archived formulas : 0
% 97.80/14.81 % Current number of archived clauses : 603
% 97.80/14.81 % Clause-clause subsumption calls (NU) : 3977671
% 97.80/14.81 % Rec. Clause-clause subsumption calls : 2650799
% 97.80/14.81 % Non-unit clause-clause subsumptions : 35593
% 97.80/14.81 % Unit Clause-clause subsumption calls : 8708
% 97.80/14.81 % Rewrite failures with RHS unbound : 0
% 97.80/14.81 % BW rewrite match attempts : 92
% 97.80/14.81 % BW rewrite match successes : 61
% 97.80/14.81 % Condensation attempts : 0
% 97.80/14.81 % Condensation successes : 0
% 97.80/14.81 % Termbank termtop insertions : 9810857
% 97.80/14.81 % Search garbage collected termcells : 11401
% 97.80/14.81
% 97.80/14.81 % -------------------------------------------------
% 97.80/14.81 % User time : 12.831 s
% 97.80/14.81 % System time : 0.353 s
% 97.80/14.81 % Total time : 13.184 s
% 97.80/14.81 % Maximum resident set size: 6660 pages
% 97.80/14.81
% 97.80/14.81 % -------------------------------------------------
% 97.80/14.81 % User time : 26.530 s
% 97.80/14.81 % System time : 0.717 s
% 97.80/14.81 % Total time : 27.247 s
% 97.80/14.81 % Maximum resident set size: 6656 pages
% 97.80/14.81 % E exiting
%------------------------------------------------------------------------------