TSTP Solution File: SEU379+1 by Enigma---0.5.1
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%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SEU379+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:41:41 EDT 2022
% Result : Theorem 11.78s 2.90s
% Output : CNFRefutation 11.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 63
% Syntax : Number of clauses : 223 ( 60 unt; 36 nHn; 182 RR)
% Number of literals : 670 ( 85 equ; 419 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 7 con; 0-4 aty)
% Number of variables : 417 ( 55 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_160,plain,
( ~ empty(X1)
| ~ in(X2,X3)
| ~ element(X3,powerset(X1)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_160) ).
cnf(i_0_157,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_157) ).
cnf(i_0_147,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_147) ).
cnf(i_0_68,plain,
element(esk8_1(X1),X1),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_68) ).
cnf(i_0_158,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_158) ).
cnf(i_0_164,plain,
( X1 = X2
| ~ empty(X2)
| ~ empty(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_164) ).
cnf(i_0_161,plain,
( X1 = empty_set
| ~ empty(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_161) ).
cnf(i_0_113,plain,
empty(esk17_0),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_113) ).
cnf(i_0_98,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_98) ).
cnf(i_0_112,plain,
function(esk17_0),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_112) ).
cnf(i_0_19,plain,
( X1 = relation_inverse_image(X2,X3)
| in(esk3_3(X2,X3,X1),X1)
| in(esk3_3(X2,X3,X1),relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_19) ).
cnf(i_0_74,plain,
relation(empty_set),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_74) ).
cnf(i_0_118,plain,
element(esk19_1(X1),powerset(X1)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_118) ).
cnf(i_0_117,plain,
empty(esk19_1(X1)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_117) ).
cnf(i_0_75,plain,
empty(empty_set),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_75) ).
cnf(i_0_21,plain,
( in(X1,X2)
| X2 != relation_inverse_image(X3,X4)
| ~ function(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(apply(X3,X1),X4) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_21) ).
cnf(i_0_88,plain,
~ empty(powerset(X1)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_88) ).
cnf(i_0_145,plain,
subset(X1,X1),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_145) ).
cnf(i_0_23,plain,
( in(X1,relation_dom(X2))
| X3 != relation_inverse_image(X2,X4)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_23) ).
cnf(i_0_31,plain,
( subrelstr(X1,X2)
| ~ one_sorted_str(X3)
| ~ net_str(X2,X3)
| ~ net_str(X1,X3)
| ~ subnetstr(X1,X3,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_31) ).
cnf(i_0_53,plain,
( net_str(X1,X2)
| ~ one_sorted_str(X2)
| ~ net_str(X3,X2)
| ~ subnetstr(X1,X2,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_53) ).
cnf(i_0_159,plain,
( element(X1,X2)
| ~ in(X1,X3)
| ~ element(X3,powerset(X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_159) ).
cnf(i_0_111,plain,
( empty(X1)
| element(esk16_1(X1),powerset(X1)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_111) ).
cnf(i_0_24,plain,
( X1 = preimage_subnetstr(X2,X3,X4)
| the_carrier(X1) != function_invverse_img_as_carrier_subset(X3,X2,the_mapping(X2,X3),X4)
| ~ one_sorted_str(X2)
| ~ net_str(X3,X2)
| ~ strict_net_str(X1,X2)
| ~ subrelstr(X1,X3)
| ~ full_subrelstr(X1,X3)
| ~ subnetstr(X1,X2,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_24) ).
cnf(i_0_25,plain,
( the_carrier(X1) = function_invverse_img_as_carrier_subset(X2,X3,the_mapping(X3,X2),X4)
| X1 != preimage_subnetstr(X3,X2,X4)
| ~ one_sorted_str(X3)
| ~ net_str(X2,X3)
| ~ strict_net_str(X1,X3)
| ~ subnetstr(X1,X3,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_25) ).
cnf(i_0_44,plain,
( strict_net_str(preimage_subnetstr(X1,X2,X3),X1)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_44) ).
cnf(i_0_43,plain,
( subnetstr(preimage_subnetstr(X1,X2,X3),X1,X2)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_43) ).
cnf(i_0_110,plain,
( empty(X1)
| ~ empty(esk16_1(X1)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_110) ).
cnf(i_0_18,plain,
( X1 = relation_inverse_image(X2,X3)
| in(esk3_3(X2,X3,X1),X1)
| in(apply(X2,esk3_3(X2,X3,X1)),X3)
| ~ function(X2)
| ~ relation(X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_18) ).
cnf(i_0_128,plain,
relation(esk23_0),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_128) ).
cnf(i_0_126,plain,
function(esk23_0),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_126) ).
cnf(i_0_22,plain,
( in(apply(X1,X2),X3)
| X4 != relation_inverse_image(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,X4) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_22) ).
cnf(i_0_144,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_144) ).
cnf(i_0_61,plain,
( relation_of2_as_subset(the_mapping(X1,X2),the_carrier(X2),the_carrier(X1))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_61) ).
cnf(i_0_5,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_5) ).
cnf(i_0_54,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_54) ).
cnf(i_0_149,negated_conjecture,
preimage_subnetstr(esk28_0,esk29_0,esk30_0) = esk31_0,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_149) ).
cnf(i_0_151,negated_conjecture,
net_str(esk29_0,esk28_0),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_151) ).
cnf(i_0_155,negated_conjecture,
one_sorted_str(esk28_0),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_155) ).
cnf(i_0_27,plain,
( full_subrelstr(X1,X2)
| X1 != preimage_subnetstr(X3,X2,X4)
| ~ one_sorted_str(X3)
| ~ net_str(X2,X3)
| ~ strict_net_str(X1,X3)
| ~ subnetstr(X1,X3,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_27) ).
cnf(i_0_141,plain,
( function_invverse_img_as_carrier_subset(X1,X2,X3,X4) = relation_inverse_image(X3,X4)
| ~ one_sorted_str(X2)
| ~ one_sorted_str(X1)
| ~ function(X3)
| ~ relation_of2(X3,the_carrier(X1),the_carrier(X2))
| ~ quasi_total(X3,the_carrier(X1),the_carrier(X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_141) ).
cnf(i_0_63,plain,
( function(the_mapping(X1,X2))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_63) ).
cnf(i_0_62,plain,
( quasi_total(the_mapping(X1,X2),the_carrier(X2),the_carrier(X1))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_62) ).
cnf(i_0_49,plain,
( rel_str(X1)
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_49) ).
cnf(i_0_30,plain,
( relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X2),the_mapping(X2,X1),the_carrier(X3)) = the_mapping(X2,X3)
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ net_str(X3,X2)
| ~ subnetstr(X3,X2,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_30) ).
cnf(i_0_47,plain,
( one_sorted_str(X1)
| ~ rel_str(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_47) ).
cnf(i_0_142,plain,
( relation_dom_restr_as_relation_of(X1,X2,X3,X4) = relation_dom_restriction(X3,X4)
| ~ relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_142) ).
cnf(i_0_55,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| net_str(X3,X2)
| ~ one_sorted_str(X2)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X2)
| ~ subnet(X3,X2,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_55) ).
cnf(i_0_150,negated_conjecture,
subnet(esk31_0,esk28_0,esk29_0),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_150) ).
cnf(i_0_152,negated_conjecture,
directed_relstr(esk29_0),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_152) ).
cnf(i_0_153,negated_conjecture,
transitive_relstr(esk29_0),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_153) ).
cnf(i_0_156,negated_conjecture,
~ empty_carrier(esk28_0),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_156) ).
cnf(i_0_154,negated_conjecture,
~ empty_carrier(esk29_0),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_154) ).
cnf(i_0_162,plain,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X3,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_162) ).
cnf(i_0_163,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_163) ).
cnf(i_0_146,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_146) ).
cnf(i_0_28,plain,
( apply_on_structs(X1,X2,the_mapping(X2,X1),X3) = apply_netmap(X2,X1,X3)
| empty_carrier(X1)
| empty_carrier(X2)
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X3,the_carrier(X1)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_28) ).
cnf(i_0_140,plain,
( apply_on_structs(X1,X2,X3,X4) = apply(X3,X4)
| empty_carrier(X2)
| empty_carrier(X1)
| ~ one_sorted_str(X2)
| ~ one_sorted_str(X1)
| ~ function(X3)
| ~ element(X4,the_carrier(X1))
| ~ relation_of2(X3,the_carrier(X1),the_carrier(X2))
| ~ quasi_total(X3,the_carrier(X1),the_carrier(X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_140) ).
cnf(i_0_58,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| ~ one_sorted_str(X2)
| ~ empty_carrier(X3)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X2)
| ~ subnet(X3,X2,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_58) ).
cnf(i_0_87,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_87) ).
cnf(i_0_13,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| is_eventually_in(X2,X1,X3)
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X4,the_carrier(X1))
| ~ in(apply_netmap(X2,X1,esk2_4(X2,X1,X3,X4)),X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_13) ).
cnf(i_0_148,negated_conjecture,
~ is_eventually_in(esk28_0,esk31_0,esk30_0),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_148) ).
cnf(i_0_15,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| is_eventually_in(X2,X1,X3)
| element(esk2_4(X2,X1,X3,X4),the_carrier(X1))
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X4,the_carrier(X1)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-ij8rrexn/input.p',i_0_15) ).
cnf(c_0_228,plain,
( ~ empty(X1)
| ~ in(X2,X3)
| ~ element(X3,powerset(X1)) ),
i_0_160 ).
cnf(c_0_229,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
i_0_157 ).
cnf(c_0_230,plain,
( ~ in(X1,X2)
| ~ subset(X2,X3)
| ~ empty(X3) ),
inference(spm,[status(thm)],[c_0_228,c_0_229]) ).
cnf(c_0_231,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
i_0_147 ).
cnf(c_0_232,plain,
( empty(X1)
| ~ element(X2,X1)
| ~ subset(X1,X3)
| ~ empty(X3) ),
inference(spm,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_233,plain,
element(esk8_1(X1),X1),
i_0_68 ).
cnf(c_0_234,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
i_0_158 ).
cnf(c_0_235,plain,
( empty(X1)
| ~ subset(X1,X2)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_232,c_0_233]) ).
cnf(c_0_236,plain,
subset(esk8_1(powerset(X1)),X1),
inference(spm,[status(thm)],[c_0_234,c_0_233]) ).
cnf(c_0_237,plain,
( X1 = X2
| ~ empty(X2)
| ~ empty(X1) ),
i_0_164 ).
cnf(c_0_238,plain,
( empty(esk8_1(powerset(X1)))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_235,c_0_236]) ).
cnf(c_0_239,plain,
( X1 = empty_set
| ~ empty(X1) ),
i_0_161 ).
cnf(c_0_240,plain,
empty(esk17_0),
i_0_113 ).
cnf(c_0_241,plain,
( X1 = esk8_1(powerset(X2))
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_237,c_0_238]) ).
cnf(c_0_242,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
i_0_98 ).
cnf(c_0_243,plain,
function(esk17_0),
i_0_112 ).
cnf(c_0_244,plain,
esk17_0 = empty_set,
inference(spm,[status(thm)],[c_0_239,c_0_240]) ).
cnf(c_0_245,plain,
( ~ in(X1,esk8_1(powerset(X2)))
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_228,c_0_233]) ).
cnf(c_0_246,plain,
( relation_dom(X1) = esk8_1(powerset(X2))
| ~ empty(X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_241,c_0_242]) ).
cnf(c_0_247,plain,
( X1 = relation_inverse_image(X2,X3)
| in(esk3_3(X2,X3,X1),X1)
| in(esk3_3(X2,X3,X1),relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ),
i_0_19 ).
cnf(c_0_248,plain,
relation(empty_set),
i_0_74 ).
cnf(c_0_249,plain,
function(empty_set),
inference(rw,[status(thm)],[c_0_243,c_0_244]) ).
cnf(c_0_250,plain,
element(esk19_1(X1),powerset(X1)),
i_0_118 ).
cnf(c_0_251,plain,
empty(esk19_1(X1)),
i_0_117 ).
cnf(c_0_252,plain,
( ~ in(X1,relation_dom(X2))
| ~ empty(X3)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_245,c_0_246]) ).
cnf(c_0_253,plain,
( X1 = relation_inverse_image(empty_set,X2)
| in(esk3_3(empty_set,X2,X1),relation_dom(empty_set))
| in(esk3_3(empty_set,X2,X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_248]),c_0_249])]) ).
cnf(c_0_254,plain,
empty(empty_set),
i_0_75 ).
cnf(c_0_255,plain,
( ~ in(X1,esk19_1(X2))
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_228,c_0_250]) ).
cnf(c_0_256,plain,
esk19_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_239,c_0_251]) ).
cnf(c_0_257,plain,
( X1 = relation_inverse_image(empty_set,X2)
| in(esk3_3(empty_set,X2,X1),X1)
| ~ empty(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_253]),c_0_254])]) ).
cnf(c_0_258,plain,
( in(X1,X2)
| X2 != relation_inverse_image(X3,X4)
| ~ function(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(apply(X3,X1),X4) ),
i_0_21 ).
cnf(c_0_259,plain,
( ~ in(X1,empty_set)
| ~ empty(X2) ),
inference(rw,[status(thm)],[c_0_255,c_0_256]) ).
cnf(c_0_260,plain,
( X1 = relation_inverse_image(empty_set,X2)
| in(esk3_3(empty_set,X2,X1),X1) ),
inference(spm,[status(thm)],[c_0_257,c_0_254]) ).
cnf(c_0_261,plain,
( in(X1,relation_inverse_image(X2,X3))
| ~ in(apply(X2,X1),X3)
| ~ in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(er,[status(thm)],[c_0_258]) ).
cnf(c_0_262,plain,
( relation_inverse_image(empty_set,X1) = empty_set
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_259,c_0_260]) ).
cnf(c_0_263,plain,
( in(X1,relation_inverse_image(X2,X3))
| empty(X3)
| ~ in(X1,relation_dom(X2))
| ~ element(apply(X2,X1),X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(spm,[status(thm)],[c_0_261,c_0_231]) ).
cnf(c_0_264,plain,
relation_inverse_image(empty_set,X1) = empty_set,
inference(spm,[status(thm)],[c_0_262,c_0_254]) ).
cnf(c_0_265,plain,
( in(X1,empty_set)
| empty(X2)
| ~ in(X1,relation_dom(empty_set))
| ~ element(apply(empty_set,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_263,c_0_264]),c_0_248]),c_0_249])]) ).
cnf(c_0_266,plain,
~ empty(powerset(X1)),
i_0_88 ).
cnf(c_0_267,plain,
( in(X1,empty_set)
| ~ in(X1,relation_dom(empty_set))
| ~ subset(apply(empty_set,X1),X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_265,c_0_229]),c_0_266]) ).
cnf(c_0_268,plain,
subset(X1,X1),
i_0_145 ).
cnf(c_0_269,plain,
( X1 = relation_dom(X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_237,c_0_242]) ).
cnf(c_0_270,plain,
( in(X1,relation_dom(X2))
| X3 != relation_inverse_image(X2,X4)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
i_0_23 ).
cnf(c_0_271,plain,
( subrelstr(X1,X2)
| ~ one_sorted_str(X3)
| ~ net_str(X2,X3)
| ~ net_str(X1,X3)
| ~ subnetstr(X1,X3,X2) ),
i_0_31 ).
cnf(c_0_272,plain,
( net_str(X1,X2)
| ~ one_sorted_str(X2)
| ~ net_str(X3,X2)
| ~ subnetstr(X1,X2,X3) ),
i_0_53 ).
cnf(c_0_273,plain,
( in(X1,empty_set)
| ~ in(X1,relation_dom(empty_set)) ),
inference(spm,[status(thm)],[c_0_267,c_0_268]) ).
cnf(c_0_274,plain,
( relation_dom(X1) = relation_dom(X2)
| ~ empty(X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_269,c_0_242]) ).
cnf(c_0_275,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ function(X2) ),
inference(er,[status(thm)],[c_0_270]) ).
cnf(c_0_276,plain,
( element(X1,X2)
| ~ in(X1,X3)
| ~ element(X3,powerset(X2)) ),
i_0_159 ).
cnf(c_0_277,plain,
( empty(X1)
| element(esk16_1(X1),powerset(X1)) ),
i_0_111 ).
cnf(c_0_278,plain,
( X1 = preimage_subnetstr(X2,X3,X4)
| the_carrier(X1) != function_invverse_img_as_carrier_subset(X3,X2,the_mapping(X2,X3),X4)
| ~ one_sorted_str(X2)
| ~ net_str(X3,X2)
| ~ strict_net_str(X1,X2)
| ~ subrelstr(X1,X3)
| ~ full_subrelstr(X1,X3)
| ~ subnetstr(X1,X2,X3) ),
i_0_24 ).
cnf(c_0_279,plain,
( subrelstr(X1,X2)
| ~ subnetstr(X1,X3,X2)
| ~ net_str(X2,X3)
| ~ one_sorted_str(X3) ),
inference(csr,[status(thm)],[c_0_271,c_0_272]) ).
cnf(c_0_280,plain,
( the_carrier(X1) = function_invverse_img_as_carrier_subset(X2,X3,the_mapping(X3,X2),X4)
| X1 != preimage_subnetstr(X3,X2,X4)
| ~ one_sorted_str(X3)
| ~ net_str(X2,X3)
| ~ strict_net_str(X1,X3)
| ~ subnetstr(X1,X3,X2) ),
i_0_25 ).
cnf(c_0_281,plain,
( strict_net_str(preimage_subnetstr(X1,X2,X3),X1)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
i_0_44 ).
cnf(c_0_282,plain,
( subnetstr(preimage_subnetstr(X1,X2,X3),X1,X2)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
i_0_43 ).
cnf(c_0_283,plain,
( ~ in(X1,relation_dom(X2))
| ~ empty(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_274]),c_0_254])]),c_0_259]) ).
cnf(c_0_284,plain,
( in(X1,relation_dom(empty_set))
| ~ in(X1,empty_set) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_264]),c_0_248]),c_0_249])]) ).
cnf(c_0_285,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,esk16_1(X2)) ),
inference(spm,[status(thm)],[c_0_276,c_0_277]) ).
cnf(c_0_286,plain,
( empty(X1)
| ~ empty(esk16_1(X1)) ),
i_0_110 ).
cnf(c_0_287,plain,
( X1 = relation_inverse_image(X2,X3)
| in(esk3_3(X2,X3,X1),X1)
| in(apply(X2,esk3_3(X2,X3,X1)),X3)
| ~ function(X2)
| ~ relation(X2) ),
i_0_18 ).
cnf(c_0_288,plain,
relation(esk23_0),
i_0_128 ).
cnf(c_0_289,plain,
function(esk23_0),
i_0_126 ).
cnf(c_0_290,plain,
( X1 = preimage_subnetstr(X2,X3,X4)
| the_carrier(X1) != function_invverse_img_as_carrier_subset(X3,X2,the_mapping(X2,X3),X4)
| ~ subnetstr(X1,X2,X3)
| ~ full_subrelstr(X1,X3)
| ~ strict_net_str(X1,X2)
| ~ net_str(X3,X2)
| ~ one_sorted_str(X2) ),
inference(csr,[status(thm)],[c_0_278,c_0_279]) ).
cnf(c_0_291,plain,
( function_invverse_img_as_carrier_subset(X1,X2,the_mapping(X2,X1),X3) = the_carrier(preimage_subnetstr(X2,X1,X3))
| ~ net_str(X1,X2)
| ~ one_sorted_str(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_280]),c_0_281]),c_0_282]) ).
cnf(c_0_292,plain,
( in(apply(X1,X2),X3)
| X4 != relation_inverse_image(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,X4) ),
i_0_22 ).
cnf(c_0_293,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
i_0_144 ).
cnf(c_0_294,plain,
( relation_of2_as_subset(the_mapping(X1,X2),the_carrier(X2),the_carrier(X1))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
i_0_61 ).
cnf(c_0_295,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
i_0_5 ).
cnf(c_0_296,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
i_0_54 ).
cnf(c_0_297,plain,
~ in(X1,empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_283,c_0_284]),c_0_254])]) ).
cnf(c_0_298,plain,
( element(X1,X2)
| empty(X2)
| ~ element(X1,esk16_1(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_285,c_0_231]),c_0_286]) ).
cnf(c_0_299,plain,
( X1 = relation_inverse_image(esk23_0,X2)
| in(apply(esk23_0,esk3_3(esk23_0,X2,X1)),X2)
| in(esk3_3(esk23_0,X2,X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_287,c_0_288]),c_0_289])]) ).
cnf(c_0_300,plain,
( X1 = preimage_subnetstr(X2,X3,X4)
| the_carrier(X1) != the_carrier(preimage_subnetstr(X2,X3,X4))
| ~ subnetstr(X1,X2,X3)
| ~ full_subrelstr(X1,X3)
| ~ strict_net_str(X1,X2)
| ~ net_str(X3,X2)
| ~ one_sorted_str(X2) ),
inference(spm,[status(thm)],[c_0_290,c_0_291]) ).
cnf(c_0_301,negated_conjecture,
preimage_subnetstr(esk28_0,esk29_0,esk30_0) = esk31_0,
i_0_149 ).
cnf(c_0_302,negated_conjecture,
net_str(esk29_0,esk28_0),
i_0_151 ).
cnf(c_0_303,negated_conjecture,
one_sorted_str(esk28_0),
i_0_155 ).
cnf(c_0_304,plain,
( full_subrelstr(X1,X2)
| X1 != preimage_subnetstr(X3,X2,X4)
| ~ one_sorted_str(X3)
| ~ net_str(X2,X3)
| ~ strict_net_str(X1,X3)
| ~ subnetstr(X1,X3,X2) ),
i_0_27 ).
cnf(c_0_305,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_292]) ).
cnf(c_0_306,plain,
( function_invverse_img_as_carrier_subset(X1,X2,X3,X4) = relation_inverse_image(X3,X4)
| ~ one_sorted_str(X2)
| ~ one_sorted_str(X1)
| ~ function(X3)
| ~ relation_of2(X3,the_carrier(X1),the_carrier(X2))
| ~ quasi_total(X3,the_carrier(X1),the_carrier(X2)) ),
i_0_141 ).
cnf(c_0_307,plain,
( function(the_mapping(X1,X2))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
i_0_63 ).
cnf(c_0_308,plain,
( relation_of2(the_mapping(X1,X2),the_carrier(X2),the_carrier(X1))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_293,c_0_294]) ).
cnf(c_0_309,plain,
( quasi_total(the_mapping(X1,X2),the_carrier(X2),the_carrier(X1))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
i_0_62 ).
cnf(c_0_310,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_295,c_0_296]) ).
cnf(c_0_311,plain,
( empty(relation_dom(empty_set))
| ~ element(X1,relation_dom(empty_set)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_231]),c_0_297]) ).
cnf(c_0_312,plain,
( element(esk8_1(esk16_1(X1)),X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_298,c_0_233]) ).
cnf(c_0_313,plain,
( X1 = relation_inverse_image(esk23_0,empty_set)
| in(esk3_3(esk23_0,empty_set,X1),X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_259,c_0_299]) ).
cnf(c_0_314,negated_conjecture,
( X1 = esk31_0
| the_carrier(X1) != the_carrier(esk31_0)
| ~ subnetstr(X1,esk28_0,esk29_0)
| ~ full_subrelstr(X1,esk29_0)
| ~ strict_net_str(X1,esk28_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_301]),c_0_302]),c_0_303])]) ).
cnf(c_0_315,plain,
( full_subrelstr(preimage_subnetstr(X1,X2,X3),X2)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_304]),c_0_281]),c_0_282]) ).
cnf(c_0_316,plain,
( in(apply(X1,X2),relation_dom(X3))
| ~ in(X2,relation_inverse_image(X1,relation_inverse_image(X3,X4)))
| ~ relation(X3)
| ~ relation(X1)
| ~ function(X3)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_275,c_0_305]) ).
cnf(c_0_317,plain,
( relation_inverse_image(the_mapping(X1,X2),X3) = the_carrier(preimage_subnetstr(X1,X2,X3))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1)
| ~ one_sorted_str(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_291,c_0_306]),c_0_307]),c_0_308]),c_0_309]) ).
cnf(c_0_318,plain,
( relation(the_mapping(X1,X2))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_310,c_0_294]) ).
cnf(c_0_319,plain,
empty(relation_dom(empty_set)),
inference(spm,[status(thm)],[c_0_311,c_0_312]) ).
cnf(c_0_320,plain,
( X1 = relation_inverse_image(esk23_0,empty_set)
| in(esk3_3(esk23_0,empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_313,c_0_254]) ).
cnf(c_0_321,plain,
( preimage_subnetstr(X1,esk29_0,X2) = esk31_0
| the_carrier(preimage_subnetstr(X1,esk29_0,X2)) != the_carrier(esk31_0)
| ~ subnetstr(preimage_subnetstr(X1,esk29_0,X2),esk28_0,esk29_0)
| ~ strict_net_str(preimage_subnetstr(X1,esk29_0,X2),esk28_0)
| ~ net_str(esk29_0,X1)
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_314,c_0_315]) ).
cnf(c_0_322,plain,
( in(apply(the_mapping(X1,X2),X3),relation_dom(X4))
| ~ in(X3,the_carrier(preimage_subnetstr(X1,X2,relation_inverse_image(X4,X5))))
| ~ net_str(X2,X1)
| ~ relation(X4)
| ~ function(X4)
| ~ one_sorted_str(X1)
| ~ one_sorted_str(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_316,c_0_317]),c_0_307]),c_0_318]) ).
cnf(c_0_323,plain,
relation_dom(empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_239,c_0_319]) ).
cnf(c_0_324,plain,
relation_inverse_image(esk23_0,empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_297,c_0_320]) ).
cnf(c_0_325,plain,
( rel_str(X1)
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2) ),
i_0_49 ).
cnf(c_0_326,plain,
( relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X2),the_mapping(X2,X1),the_carrier(X3)) = the_mapping(X2,X3)
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ net_str(X3,X2)
| ~ subnetstr(X3,X2,X1) ),
i_0_30 ).
cnf(c_0_327,plain,
( preimage_subnetstr(esk28_0,esk29_0,X1) = esk31_0
| the_carrier(preimage_subnetstr(esk28_0,esk29_0,X1)) != the_carrier(esk31_0)
| ~ strict_net_str(preimage_subnetstr(esk28_0,esk29_0,X1),esk28_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_321,c_0_282]),c_0_302]),c_0_303])]) ).
cnf(c_0_328,plain,
( ~ in(X1,the_carrier(preimage_subnetstr(X2,X3,empty_set)))
| ~ net_str(X3,X2)
| ~ one_sorted_str(X2)
| ~ one_sorted_str(X3) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_322,c_0_264]),c_0_323]),c_0_248]),c_0_249])]),c_0_297]) ).
cnf(c_0_329,plain,
( X1 = empty_set
| in(esk3_3(esk23_0,empty_set,X1),X1) ),
inference(rw,[status(thm)],[c_0_320,c_0_324]) ).
cnf(c_0_330,plain,
( one_sorted_str(X1)
| ~ rel_str(X1) ),
i_0_47 ).
cnf(c_0_331,negated_conjecture,
rel_str(esk29_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_325,c_0_302]),c_0_303])]) ).
cnf(c_0_332,plain,
( relation_dom_restr_as_relation_of(X1,X2,X3,X4) = relation_dom_restriction(X3,X4)
| ~ relation_of2(X3,X1,X2) ),
i_0_142 ).
cnf(c_0_333,plain,
( relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X2),the_mapping(X2,X1),the_carrier(X3)) = the_mapping(X2,X3)
| ~ subnetstr(X3,X2,X1)
| ~ net_str(X1,X2)
| ~ one_sorted_str(X2) ),
inference(csr,[status(thm)],[c_0_326,c_0_272]) ).
cnf(c_0_334,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| net_str(X3,X2)
| ~ one_sorted_str(X2)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X2)
| ~ subnet(X3,X2,X1) ),
i_0_55 ).
cnf(c_0_335,negated_conjecture,
subnet(esk31_0,esk28_0,esk29_0),
i_0_150 ).
cnf(c_0_336,negated_conjecture,
directed_relstr(esk29_0),
i_0_152 ).
cnf(c_0_337,negated_conjecture,
transitive_relstr(esk29_0),
i_0_153 ).
cnf(c_0_338,negated_conjecture,
~ empty_carrier(esk28_0),
i_0_156 ).
cnf(c_0_339,negated_conjecture,
~ empty_carrier(esk29_0),
i_0_154 ).
cnf(c_0_340,plain,
( ~ in(X1,relation_inverse_image(X2,empty_set))
| ~ relation(X2)
| ~ function(X2)
| ~ empty(X3) ),
inference(spm,[status(thm)],[c_0_259,c_0_305]) ).
cnf(c_0_341,plain,
( preimage_subnetstr(esk28_0,esk29_0,X1) = esk31_0
| the_carrier(preimage_subnetstr(esk28_0,esk29_0,X1)) != the_carrier(esk31_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_327,c_0_281]),c_0_302]),c_0_303])]) ).
cnf(c_0_342,plain,
( the_carrier(preimage_subnetstr(X1,X2,empty_set)) = empty_set
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1)
| ~ one_sorted_str(X2) ),
inference(spm,[status(thm)],[c_0_328,c_0_329]) ).
cnf(c_0_343,plain,
one_sorted_str(esk29_0),
inference(spm,[status(thm)],[c_0_330,c_0_331]) ).
cnf(c_0_344,plain,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X3,X2) ),
i_0_162 ).
cnf(c_0_345,plain,
( relation_dom_restriction(the_mapping(X1,X2),the_carrier(X3)) = the_mapping(X1,X3)
| ~ subnetstr(X3,X1,X2)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_332,c_0_333]),c_0_308]) ).
cnf(c_0_346,negated_conjecture,
net_str(esk31_0,esk28_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_334,c_0_335]),c_0_302]),c_0_336]),c_0_337]),c_0_303])]),c_0_338]),c_0_339]) ).
cnf(c_0_347,plain,
( empty(relation_inverse_image(X1,empty_set))
| ~ element(X2,relation_inverse_image(X1,empty_set))
| ~ relation(X1)
| ~ function(X1)
| ~ empty(X3) ),
inference(spm,[status(thm)],[c_0_340,c_0_231]) ).
cnf(c_0_348,plain,
( preimage_subnetstr(esk28_0,esk29_0,empty_set) = esk31_0
| the_carrier(esk31_0) != empty_set ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_341,c_0_342]),c_0_302]),c_0_303]),c_0_343])]) ).
cnf(c_0_349,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
i_0_163 ).
cnf(c_0_350,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
i_0_146 ).
cnf(c_0_351,plain,
( apply_on_structs(X1,X2,the_mapping(X2,X1),X3) = apply_netmap(X2,X1,X3)
| empty_carrier(X1)
| empty_carrier(X2)
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X3,the_carrier(X1)) ),
i_0_28 ).
cnf(c_0_352,plain,
( apply_on_structs(X1,X2,X3,X4) = apply(X3,X4)
| empty_carrier(X2)
| empty_carrier(X1)
| ~ one_sorted_str(X2)
| ~ one_sorted_str(X1)
| ~ function(X3)
| ~ element(X4,the_carrier(X1))
| ~ relation_of2(X3,the_carrier(X1),the_carrier(X2))
| ~ quasi_total(X3,the_carrier(X1),the_carrier(X2)) ),
i_0_140 ).
cnf(c_0_353,plain,
( apply(the_mapping(X1,X2),X3) = apply(the_mapping(X1,X4),X3)
| ~ subnetstr(X2,X1,X4)
| ~ in(X3,the_carrier(X2))
| ~ net_str(X4,X1)
| ~ one_sorted_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_344,c_0_345]),c_0_307]),c_0_318]) ).
cnf(c_0_354,negated_conjecture,
subnetstr(esk31_0,esk28_0,esk29_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_282,c_0_301]),c_0_302]),c_0_303])]) ).
cnf(c_0_355,plain,
rel_str(esk31_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_325,c_0_346]),c_0_303])]) ).
cnf(c_0_356,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| ~ one_sorted_str(X2)
| ~ empty_carrier(X3)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X2)
| ~ subnet(X3,X2,X1) ),
i_0_58 ).
cnf(c_0_357,plain,
( empty(relation_inverse_image(X1,empty_set))
| ~ relation(X1)
| ~ function(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_347,c_0_312]) ).
cnf(c_0_358,plain,
( the_carrier(esk31_0) != empty_set
| ~ in(X1,the_carrier(esk31_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_328,c_0_348]),c_0_302]),c_0_303]),c_0_343])]) ).
cnf(c_0_359,plain,
( X1 = relation_inverse_image(esk23_0,X2)
| in(esk3_3(esk23_0,X2,X1),X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_349,c_0_299]) ).
cnf(c_0_360,plain,
( element(apply(X1,X2),X3)
| ~ in(X2,relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_350,c_0_305]) ).
cnf(c_0_361,plain,
( apply(the_mapping(X1,X2),X3) = apply_netmap(X1,X2,X3)
| empty_carrier(X2)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X2))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1)
| ~ one_sorted_str(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_351,c_0_352]),c_0_307]),c_0_308]),c_0_309]) ).
cnf(c_0_362,negated_conjecture,
( apply(the_mapping(esk28_0,esk31_0),X1) = apply(the_mapping(esk28_0,esk29_0),X1)
| ~ in(X1,the_carrier(esk31_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_353,c_0_354]),c_0_302]),c_0_303])]) ).
cnf(c_0_363,plain,
one_sorted_str(esk31_0),
inference(spm,[status(thm)],[c_0_330,c_0_355]) ).
cnf(c_0_364,negated_conjecture,
~ empty_carrier(esk31_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_356,c_0_335]),c_0_302]),c_0_336]),c_0_337]),c_0_303])]),c_0_338]),c_0_339]) ).
cnf(c_0_365,plain,
( ~ in(X1,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| ~ empty(X3) ),
inference(spm,[status(thm)],[c_0_349,c_0_305]) ).
cnf(c_0_366,plain,
( empty(relation_inverse_image(X1,empty_set))
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_357,c_0_254]) ).
cnf(c_0_367,plain,
( relation_inverse_image(esk23_0,X1) = the_carrier(esk31_0)
| the_carrier(esk31_0) != empty_set
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_358,c_0_359]) ).
cnf(c_0_368,plain,
( element(apply(the_mapping(X1,X2),X3),X4)
| ~ in(X3,the_carrier(preimage_subnetstr(X1,X2,X4)))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1)
| ~ one_sorted_str(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_360,c_0_317]),c_0_307]),c_0_318]) ).
cnf(c_0_369,plain,
( apply(the_mapping(esk28_0,esk29_0),X1) = apply_netmap(esk28_0,esk31_0,X1)
| ~ in(X1,the_carrier(esk31_0)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_361,c_0_362]),c_0_346]),c_0_303]),c_0_363])]),c_0_364]),c_0_338]),c_0_350]) ).
cnf(c_0_370,plain,
( ~ in(X1,the_carrier(preimage_subnetstr(X2,X3,X4)))
| ~ net_str(X3,X2)
| ~ empty(X4)
| ~ one_sorted_str(X2)
| ~ one_sorted_str(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_365,c_0_317]),c_0_307]),c_0_318]) ).
cnf(c_0_371,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
i_0_87 ).
cnf(c_0_372,plain,
( empty(the_carrier(esk31_0))
| the_carrier(esk31_0) != empty_set ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_366,c_0_367]),c_0_288]),c_0_289]),c_0_254])]) ).
cnf(c_0_373,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| is_eventually_in(X2,X1,X3)
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X4,the_carrier(X1))
| ~ in(apply_netmap(X2,X1,esk2_4(X2,X1,X3,X4)),X3) ),
i_0_13 ).
cnf(c_0_374,plain,
( element(apply_netmap(esk28_0,esk31_0,X1),X2)
| ~ in(X1,the_carrier(preimage_subnetstr(esk28_0,esk29_0,X2)))
| ~ in(X1,the_carrier(esk31_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_368,c_0_369]),c_0_302]),c_0_303]),c_0_343])]) ).
cnf(c_0_375,negated_conjecture,
( ~ in(X1,the_carrier(esk31_0))
| ~ empty(esk30_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_370,c_0_301]),c_0_302]),c_0_303]),c_0_343])]) ).
cnf(c_0_376,plain,
the_carrier(esk31_0) != empty_set,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_371,c_0_372]),c_0_363])]),c_0_364]) ).
cnf(c_0_377,plain,
( is_eventually_in(X1,X2,X3)
| empty_carrier(X2)
| empty_carrier(X1)
| empty(X3)
| ~ element(apply_netmap(X1,X2,esk2_4(X1,X2,X3,X4)),X3)
| ~ element(X4,the_carrier(X2))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_373,c_0_231]) ).
cnf(c_0_378,negated_conjecture,
( element(apply_netmap(esk28_0,esk31_0,X1),esk30_0)
| ~ in(X1,the_carrier(esk31_0)) ),
inference(spm,[status(thm)],[c_0_374,c_0_301]) ).
cnf(c_0_379,negated_conjecture,
~ is_eventually_in(esk28_0,esk31_0,esk30_0),
i_0_148 ).
cnf(c_0_380,plain,
~ empty(esk30_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_375,c_0_329]),c_0_376]) ).
cnf(c_0_381,plain,
( ~ in(esk2_4(esk28_0,esk31_0,esk30_0,X1),the_carrier(esk31_0))
| ~ element(X1,the_carrier(esk31_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_377,c_0_378]),c_0_346]),c_0_303])]),c_0_379]),c_0_364]),c_0_338]),c_0_380]) ).
cnf(c_0_382,plain,
( empty(the_carrier(esk31_0))
| ~ element(esk2_4(esk28_0,esk31_0,esk30_0,X1),the_carrier(esk31_0))
| ~ element(X1,the_carrier(esk31_0)) ),
inference(spm,[status(thm)],[c_0_381,c_0_231]) ).
cnf(c_0_383,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| is_eventually_in(X2,X1,X3)
| element(esk2_4(X2,X1,X3,X4),the_carrier(X1))
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X4,the_carrier(X1)) ),
i_0_15 ).
cnf(c_0_384,plain,
( empty(the_carrier(esk31_0))
| ~ element(X1,the_carrier(esk31_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_382,c_0_383]),c_0_346]),c_0_303])]),c_0_379]),c_0_338]),c_0_364]) ).
cnf(c_0_385,plain,
( X1 = empty_set
| element(esk3_3(esk23_0,empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_350,c_0_329]) ).
cnf(c_0_386,plain,
empty(the_carrier(esk31_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_384,c_0_385]),c_0_376]) ).
cnf(c_0_387,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_386]),c_0_376]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU379+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : enigmatic-eprover.py %s %d 1
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 19 09:48:55 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.45 # ENIGMATIC: Selected complete mode:
% 11.78/2.90 # ENIGMATIC: Solved by autoschedule:
% 11.78/2.90 # No SInE strategy applied
% 11.78/2.90 # Trying AutoSched0 for 150 seconds
% 11.78/2.90 # AutoSched0-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S0Y
% 11.78/2.90 # and selection function SelectMaxLComplexAvoidPosPred.
% 11.78/2.90 #
% 11.78/2.90 # Preprocessing time : 0.027 s
% 11.78/2.90 # Presaturation interreduction done
% 11.78/2.90
% 11.78/2.90 # Proof found!
% 11.78/2.90 # SZS status Theorem
% 11.78/2.90 # SZS output start CNFRefutation
% See solution above
% 11.78/2.90 # Training examples: 0 positive, 0 negative
% 11.78/2.90
% 11.78/2.90 # -------------------------------------------------
% 11.78/2.90 # User time : 0.487 s
% 11.78/2.90 # System time : 0.018 s
% 11.78/2.90 # Total time : 0.505 s
% 11.78/2.90 # Maximum resident set size: 7116 pages
% 11.78/2.90
%------------------------------------------------------------------------------