TSTP Solution File: SEU379+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU379+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 16:25:16 EDT 2023
% Result : Theorem 220.15s 220.22s
% Output : CNFRefutation 220.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 110
% Syntax : Number of formulae : 306 ( 48 unt; 73 typ; 0 def)
% Number of atoms : 905 ( 94 equ)
% Maximal formula atoms : 35 ( 3 avg)
% Number of connectives : 1161 ( 489 ~; 487 |; 120 &)
% ( 8 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 114 ( 57 >; 57 *; 0 +; 0 <<)
% Number of predicates : 28 ( 26 usr; 1 prp; 0-3 aty)
% Number of functors : 47 ( 47 usr; 16 con; 0-4 aty)
% Number of variables : 480 ( 39 sgn; 191 !; 8 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
one_sorted_str: $i > $o ).
tff(decl_23,type,
net_str: ( $i * $i ) > $o ).
tff(decl_24,type,
strict_net_str: ( $i * $i ) > $o ).
tff(decl_25,type,
the_carrier: $i > $i ).
tff(decl_26,type,
the_InternalRel: $i > $i ).
tff(decl_27,type,
the_mapping: ( $i * $i ) > $i ).
tff(decl_28,type,
net_str_of: ( $i * $i * $i * $i ) > $i ).
tff(decl_29,type,
in: ( $i * $i ) > $o ).
tff(decl_30,type,
empty: $i > $o ).
tff(decl_31,type,
function: $i > $o ).
tff(decl_32,type,
relation: $i > $o ).
tff(decl_33,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_34,type,
powerset: $i > $i ).
tff(decl_35,type,
element: ( $i * $i ) > $o ).
tff(decl_36,type,
rel_str: $i > $o ).
tff(decl_37,type,
empty_carrier: $i > $o ).
tff(decl_38,type,
v1_yellow_3: $i > $o ).
tff(decl_39,type,
one_to_one: $i > $o ).
tff(decl_40,type,
transitive_relstr: $i > $o ).
tff(decl_41,type,
subrelstr: ( $i * $i ) > $o ).
tff(decl_42,type,
full_subrelstr: ( $i * $i ) > $o ).
tff(decl_43,type,
is_eventually_in: ( $i * $i * $i ) > $o ).
tff(decl_44,type,
related: ( $i * $i * $i ) > $o ).
tff(decl_45,type,
apply_netmap: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff(decl_47,type,
relation_dom: $i > $i ).
tff(decl_48,type,
apply: ( $i * $i ) > $i ).
tff(decl_49,type,
subnetstr: ( $i * $i * $i ) > $o ).
tff(decl_50,type,
preimage_subnetstr: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
function_invverse_img_as_carrier_subset: ( $i * $i * $i * $i ) > $i ).
tff(decl_52,type,
apply_on_structs: ( $i * $i * $i * $i ) > $i ).
tff(decl_53,type,
relation_dom_restr_as_relation_of: ( $i * $i * $i * $i ) > $i ).
tff(decl_54,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_55,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_56,type,
relation_dom_restriction: ( $i * $i ) > $i ).
tff(decl_57,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_58,type,
directed_relstr: $i > $o ).
tff(decl_59,type,
subnet: ( $i * $i * $i ) > $o ).
tff(decl_60,type,
empty_set: $i ).
tff(decl_61,type,
relation_empty_yielding: $i > $o ).
tff(decl_62,type,
full_subnetstr: ( $i * $i * $i ) > $o ).
tff(decl_63,type,
subset: ( $i * $i ) > $o ).
tff(decl_64,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
esk2_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_66,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_67,type,
esk4_0: $i ).
tff(decl_68,type,
esk5_0: $i ).
tff(decl_69,type,
esk6_1: $i > $i ).
tff(decl_70,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_71,type,
esk8_1: $i > $i ).
tff(decl_72,type,
esk9_1: $i > $i ).
tff(decl_73,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_74,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_75,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_76,type,
esk13_0: $i ).
tff(decl_77,type,
esk14_0: $i ).
tff(decl_78,type,
esk15_0: $i ).
tff(decl_79,type,
esk16_1: $i > $i ).
tff(decl_80,type,
esk17_0: $i ).
tff(decl_81,type,
esk18_0: $i ).
tff(decl_82,type,
esk19_1: $i > $i ).
tff(decl_83,type,
esk20_0: $i ).
tff(decl_84,type,
esk21_0: $i ).
tff(decl_85,type,
esk22_0: $i ).
tff(decl_86,type,
esk23_0: $i ).
tff(decl_87,type,
esk24_1: $i > $i ).
tff(decl_88,type,
esk25_1: $i > $i ).
tff(decl_89,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_90,type,
esk27_2: ( $i * $i ) > $i ).
tff(decl_91,type,
esk28_0: $i ).
tff(decl_92,type,
esk29_0: $i ).
tff(decl_93,type,
esk30_0: $i ).
tff(decl_94,type,
esk31_0: $i ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(d13_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(fc7_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_funct_1,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(d8_yellow_6,axiom,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( net_str(X2,X1)
=> ! [X3] :
( net_str(X3,X1)
=> ( subnetstr(X3,X1,X2)
<=> ( subrelstr(X3,X2)
& the_mapping(X1,X3) = relation_dom_restr_as_relation_of(the_carrier(X2),the_carrier(X1),the_mapping(X1,X2),the_carrier(X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_yellow_6) ).
fof(dt_m1_yellow_6,axiom,
! [X1,X2] :
( ( one_sorted_str(X1)
& net_str(X2,X1) )
=> ! [X3] :
( subnetstr(X3,X1,X2)
=> net_str(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_6) ).
fof(t32_yellow_6,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& transitive_relstr(X2)
& directed_relstr(X2)
& net_str(X2,X1) )
=> ! [X3,X4] :
( subnet(X4,X1,X2)
=> ( X4 = preimage_subnetstr(X1,X2,X3)
=> is_eventually_in(X1,X4,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_yellow_6) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(d13_yellow_6,axiom,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( net_str(X2,X1)
=> ! [X3,X4] :
( ( strict_net_str(X4,X1)
& subnetstr(X4,X1,X2) )
=> ( X4 = preimage_subnetstr(X1,X2,X3)
<=> ( full_subrelstr(X4,X2)
& subrelstr(X4,X2)
& the_carrier(X4) = function_invverse_img_as_carrier_subset(X2,X1,the_mapping(X1,X2),X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_yellow_6) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_u1_waybel_0,axiom,
! [X1,X2] :
( ( one_sorted_str(X1)
& net_str(X2,X1) )
=> ( function(the_mapping(X1,X2))
& quasi_total(the_mapping(X1,X2),the_carrier(X2),the_carrier(X1))
& relation_of2_as_subset(the_mapping(X1,X2),the_carrier(X2),the_carrier(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_waybel_0) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(dt_k6_yellow_6,axiom,
! [X1,X2,X3] :
( ( one_sorted_str(X1)
& net_str(X2,X1) )
=> ( strict_net_str(preimage_subnetstr(X1,X2,X3),X1)
& subnetstr(preimage_subnetstr(X1,X2,X3),X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_yellow_6) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(redefinition_k5_pre_topc,axiom,
! [X1,X2,X3,X4] :
( ( one_sorted_str(X1)
& one_sorted_str(X2)
& function(X3)
& quasi_total(X3,the_carrier(X1),the_carrier(X2))
& relation_of2(X3,the_carrier(X1),the_carrier(X2)) )
=> function_invverse_img_as_carrier_subset(X1,X2,X3,X4) = relation_inverse_image(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_pre_topc) ).
fof(dt_l1_waybel_0,axiom,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( net_str(X2,X1)
=> rel_str(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
fof(redefinition_k8_relset_1,axiom,
! [X1,X2,X3,X4] :
( relation_of2(X3,X1,X2)
=> relation_dom_restr_as_relation_of(X1,X2,X3,X4) = relation_dom_restriction(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_relset_1) ).
fof(dt_l1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(d8_waybel_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> apply_netmap(X1,X2,X3) = apply_on_structs(X2,X1,the_mapping(X1,X2),X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_waybel_0) ).
fof(redefinition_k1_waybel_0,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ~ empty_carrier(X2)
& one_sorted_str(X2)
& function(X3)
& quasi_total(X3,the_carrier(X1),the_carrier(X2))
& relation_of2(X3,the_carrier(X1),the_carrier(X2))
& element(X4,the_carrier(X1)) )
=> apply_on_structs(X1,X2,X3,X4) = apply(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_waybel_0) ).
fof(t72_funct_1,axiom,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
fof(dt_m2_yellow_6,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ~ empty_carrier(X2)
& transitive_relstr(X2)
& directed_relstr(X2)
& net_str(X2,X1) )
=> ! [X3] :
( subnet(X3,X1,X2)
=> ( ~ empty_carrier(X3)
& transitive_relstr(X3)
& directed_relstr(X3)
& net_str(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_yellow_6) ).
fof(rc4_funct_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(d11_waybel_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ! [X3] :
( is_eventually_in(X1,X2,X3)
<=> ? [X4] :
( element(X4,the_carrier(X2))
& ! [X5] :
( element(X5,the_carrier(X2))
=> ( related(X2,X4,X5)
=> in(apply_netmap(X1,X2,X5),X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_waybel_0) ).
fof(c_0_37,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(c_0_38,plain,
! [X190,X191,X192] :
( ~ in(X190,X191)
| ~ element(X191,powerset(X192))
| ~ empty(X192) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(c_0_39,plain,
! [X97] : element(esk8_1(X97),X97),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_40,plain,
! [X31,X32,X33,X34,X35,X36,X37] :
( ( in(X34,relation_dom(X31))
| ~ in(X34,X33)
| X33 != relation_inverse_image(X31,X32)
| ~ relation(X31)
| ~ function(X31) )
& ( in(apply(X31,X34),X32)
| ~ in(X34,X33)
| X33 != relation_inverse_image(X31,X32)
| ~ relation(X31)
| ~ function(X31) )
& ( ~ in(X35,relation_dom(X31))
| ~ in(apply(X31,X35),X32)
| in(X35,X33)
| X33 != relation_inverse_image(X31,X32)
| ~ relation(X31)
| ~ function(X31) )
& ( ~ in(esk3_3(X31,X36,X37),X37)
| ~ in(esk3_3(X31,X36,X37),relation_dom(X31))
| ~ in(apply(X31,esk3_3(X31,X36,X37)),X36)
| X37 = relation_inverse_image(X31,X36)
| ~ relation(X31)
| ~ function(X31) )
& ( in(esk3_3(X31,X36,X37),relation_dom(X31))
| in(esk3_3(X31,X36,X37),X37)
| X37 = relation_inverse_image(X31,X36)
| ~ relation(X31)
| ~ function(X31) )
& ( in(apply(X31,esk3_3(X31,X36,X37)),X36)
| in(esk3_3(X31,X36,X37),X37)
| X37 = relation_inverse_image(X31,X36)
| ~ relation(X31)
| ~ function(X31) ) ),
inference(distribute,[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)],[d13_funct_1])])])])])]) ).
fof(c_0_41,plain,
! [X187,X188,X189] :
( ~ in(X187,X188)
| ~ element(X188,powerset(X189))
| element(X187,X189) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_42,plain,
! [X141] :
( ( element(esk16_1(X141),powerset(X141))
| empty(X141) )
& ( ~ empty(esk16_1(X141))
| empty(X141) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).
cnf(c_0_43,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
element(esk8_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_45,plain,
! [X179,X180] :
( ~ element(X179,X180)
| empty(X180)
| in(X179,X180) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_46,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,X4)
| X4 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
( element(esk16_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_49,plain,
! [X199,X200] :
( ~ empty(X199)
| X199 = X200
| ~ empty(X200) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(c_0_50,plain,
! [X129] :
( ( empty(relation_dom(X129))
| ~ empty(X129) )
& ( relation(relation_dom(X129))
| ~ empty(X129) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).
cnf(c_0_51,plain,
( ~ empty(X1)
| ~ in(X2,esk8_1(powerset(X1))) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_53,plain,
! [X193] :
( ~ empty(X193)
| X193 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_54,plain,
( relation(esk17_0)
& empty(esk17_0)
& function(esk17_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
cnf(c_0_55,plain,
( in(apply(X1,X2),X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(er,[status(thm)],[c_0_46]) ).
cnf(c_0_56,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,esk16_1(X2)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_57,plain,
( empty(X1)
| ~ empty(esk16_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_58,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
cnf(c_0_59,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_60,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_61,plain,
( empty(esk8_1(powerset(X1)))
| ~ element(X2,esk8_1(powerset(X1)))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_62,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,plain,
empty(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_64,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ empty(X2)
| ~ in(X3,relation_inverse_image(X1,esk8_1(powerset(X2)))) ),
inference(spm,[status(thm)],[c_0_51,c_0_55]) ).
cnf(c_0_65,plain,
( element(X1,X2)
| empty(X2)
| ~ element(X1,esk16_1(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_52]),c_0_57]) ).
fof(c_0_66,plain,
! [X119] : ~ empty(powerset(X119)),
inference(variable_rename,[status(thm)],[c_0_58]) ).
fof(c_0_67,plain,
! [X145] :
( element(esk19_1(X145),powerset(X145))
& empty(esk19_1(X145)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
cnf(c_0_68,plain,
( X1 = relation_dom(X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_69,plain,
( empty(esk8_1(powerset(X1)))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_44]) ).
cnf(c_0_70,plain,
function(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_71,plain,
esk17_0 = empty_set,
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,plain,
( empty(relation_inverse_image(X1,esk8_1(powerset(X2))))
| ~ element(X3,relation_inverse_image(X1,esk8_1(powerset(X2))))
| ~ relation(X1)
| ~ function(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_52]) ).
cnf(c_0_73,plain,
( element(esk8_1(esk16_1(X1)),X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_44]) ).
cnf(c_0_74,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_75,plain,
( in(X1,X4)
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),X3)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_76,plain,
empty(esk19_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,plain,
( esk8_1(powerset(X1)) = relation_dom(X2)
| ~ empty(X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_78,plain,
( in(esk3_3(X1,X2,X3),relation_dom(X1))
| in(esk3_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_79,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_80,plain,
function(empty_set),
inference(rw,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_81,plain,
( empty(relation_inverse_image(X1,esk8_1(powerset(X2))))
| ~ relation(X1)
| ~ function(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_82,plain,
( ~ empty(X1)
| ~ in(X2,esk8_1(esk16_1(powerset(X1)))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_73]),c_0_74]) ).
fof(c_0_83,plain,
! [X197,X198] :
( ~ in(X197,X198)
| ~ empty(X198) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_84,plain,
( in(X1,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| ~ in(apply(X2,X1),X3)
| ~ in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[c_0_75]) ).
cnf(c_0_85,plain,
element(esk19_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_86,plain,
esk19_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_62,c_0_76]) ).
cnf(c_0_87,plain,
( ~ empty(X1)
| ~ empty(X2)
| ~ in(X3,relation_dom(X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_77]) ).
cnf(c_0_88,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_78,c_0_79]),c_0_80])]) ).
cnf(c_0_89,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
fof(c_0_90,plain,
! [X46,X47,X48] :
( ( subrelstr(X48,X47)
| ~ subnetstr(X48,X46,X47)
| ~ net_str(X48,X46)
| ~ net_str(X47,X46)
| ~ one_sorted_str(X46) )
& ( the_mapping(X46,X48) = relation_dom_restr_as_relation_of(the_carrier(X47),the_carrier(X46),the_mapping(X46,X47),the_carrier(X48))
| ~ subnetstr(X48,X46,X47)
| ~ net_str(X48,X46)
| ~ net_str(X47,X46)
| ~ one_sorted_str(X46) )
& ( ~ subrelstr(X48,X47)
| the_mapping(X46,X48) != relation_dom_restr_as_relation_of(the_carrier(X47),the_carrier(X46),the_mapping(X46,X47),the_carrier(X48))
| subnetstr(X48,X46,X47)
| ~ net_str(X48,X46)
| ~ net_str(X47,X46)
| ~ one_sorted_str(X46) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_yellow_6])])])]) ).
fof(c_0_91,plain,
! [X78,X79,X80] :
( ~ one_sorted_str(X78)
| ~ net_str(X79,X78)
| ~ subnetstr(X80,X78,X79)
| net_str(X80,X78) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_yellow_6])])]) ).
cnf(c_0_92,plain,
( empty(relation_inverse_image(X1,relation_dom(X2)))
| ~ relation(X1)
| ~ function(X1)
| ~ empty(X3)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_77]) ).
cnf(c_0_93,plain,
( empty(esk8_1(esk16_1(powerset(X1))))
| ~ element(X2,esk8_1(esk16_1(powerset(X1))))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_52]) ).
fof(c_0_94,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& transitive_relstr(X2)
& directed_relstr(X2)
& net_str(X2,X1) )
=> ! [X3,X4] :
( subnet(X4,X1,X2)
=> ( X4 = preimage_subnetstr(X1,X2,X3)
=> is_eventually_in(X1,X4,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t32_yellow_6])]) ).
cnf(c_0_95,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_96,plain,
( empty(X1)
| in(X2,relation_inverse_image(X3,X1))
| ~ element(apply(X3,X2),X1)
| ~ relation(X3)
| ~ function(X3)
| ~ in(X2,relation_dom(X3)) ),
inference(spm,[status(thm)],[c_0_84,c_0_52]) ).
fof(c_0_97,plain,
! [X185,X186] :
( ( ~ element(X185,powerset(X186))
| subset(X185,X186) )
& ( ~ subset(X185,X186)
| element(X185,powerset(X186)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_98,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_99,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_87,c_0_88]),c_0_89])]) ).
fof(c_0_100,plain,
! [X39,X40,X41,X42] :
( ( full_subrelstr(X42,X40)
| X42 != preimage_subnetstr(X39,X40,X41)
| ~ strict_net_str(X42,X39)
| ~ subnetstr(X42,X39,X40)
| ~ net_str(X40,X39)
| ~ one_sorted_str(X39) )
& ( subrelstr(X42,X40)
| X42 != preimage_subnetstr(X39,X40,X41)
| ~ strict_net_str(X42,X39)
| ~ subnetstr(X42,X39,X40)
| ~ net_str(X40,X39)
| ~ one_sorted_str(X39) )
& ( the_carrier(X42) = function_invverse_img_as_carrier_subset(X40,X39,the_mapping(X39,X40),X41)
| X42 != preimage_subnetstr(X39,X40,X41)
| ~ strict_net_str(X42,X39)
| ~ subnetstr(X42,X39,X40)
| ~ net_str(X40,X39)
| ~ one_sorted_str(X39) )
& ( ~ full_subrelstr(X42,X40)
| ~ subrelstr(X42,X40)
| the_carrier(X42) != function_invverse_img_as_carrier_subset(X40,X39,the_mapping(X39,X40),X41)
| X42 = preimage_subnetstr(X39,X40,X41)
| ~ strict_net_str(X42,X39)
| ~ subnetstr(X42,X39,X40)
| ~ net_str(X40,X39)
| ~ one_sorted_str(X39) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d13_yellow_6])])])]) ).
cnf(c_0_101,plain,
( subrelstr(X1,X2)
| ~ subnetstr(X1,X3,X2)
| ~ net_str(X1,X3)
| ~ net_str(X2,X3)
| ~ one_sorted_str(X3) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_102,plain,
( net_str(X3,X1)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ subnetstr(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
fof(c_0_103,plain,
! [X173,X174,X175] :
( ( ~ relation_of2_as_subset(X175,X173,X174)
| relation_of2(X175,X173,X174) )
& ( ~ relation_of2(X175,X173,X174)
| relation_of2_as_subset(X175,X173,X174) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_104,plain,
! [X88,X89] :
( ( function(the_mapping(X88,X89))
| ~ one_sorted_str(X88)
| ~ net_str(X89,X88) )
& ( quasi_total(the_mapping(X88,X89),the_carrier(X89),the_carrier(X88))
| ~ one_sorted_str(X88)
| ~ net_str(X89,X88) )
& ( relation_of2_as_subset(the_mapping(X88,X89),the_carrier(X89),the_carrier(X88))
| ~ one_sorted_str(X88)
| ~ net_str(X89,X88) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_waybel_0])])]) ).
cnf(c_0_105,plain,
( empty(relation_inverse_image(X1,relation_dom(X2)))
| ~ relation(X1)
| ~ function(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_92,c_0_89]) ).
cnf(c_0_106,plain,
( empty(esk8_1(esk16_1(powerset(X1))))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_73]) ).
fof(c_0_107,plain,
! [X15,X16,X17] :
( ~ element(X17,powerset(cartesian_product2(X15,X16)))
| relation(X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(c_0_108,plain,
! [X81,X82,X83] :
( ~ relation_of2_as_subset(X83,X81,X82)
| element(X83,powerset(cartesian_product2(X81,X82))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
fof(c_0_109,plain,
! [X64,X65,X66] :
( ( strict_net_str(preimage_subnetstr(X64,X65,X66),X64)
| ~ one_sorted_str(X64)
| ~ net_str(X65,X64) )
& ( subnetstr(preimage_subnetstr(X64,X65,X66),X64,X65)
| ~ one_sorted_str(X64)
| ~ net_str(X65,X64) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_yellow_6])])]) ).
fof(c_0_110,negated_conjecture,
( ~ empty_carrier(esk28_0)
& one_sorted_str(esk28_0)
& ~ empty_carrier(esk29_0)
& transitive_relstr(esk29_0)
& directed_relstr(esk29_0)
& net_str(esk29_0,esk28_0)
& subnet(esk31_0,esk28_0,esk29_0)
& esk31_0 = preimage_subnetstr(esk28_0,esk29_0,esk30_0)
& ~ is_eventually_in(esk28_0,esk31_0,esk30_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_94])])]) ).
cnf(c_0_111,plain,
( empty(X1)
| ~ element(apply(X2,X3),X1)
| ~ relation(X2)
| ~ function(X2)
| ~ empty(relation_inverse_image(X2,X1))
| ~ in(X3,relation_dom(X2)) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_112,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
fof(c_0_113,plain,
! [X176] : subset(X176,X176),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_114,plain,
( ~ empty(X1)
| ~ in(X2,empty_set) ),
inference(spm,[status(thm)],[c_0_43,c_0_98]) ).
cnf(c_0_115,plain,
( X1 = relation_inverse_image(empty_set,X2)
| in(esk3_3(empty_set,X2,X1),X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_89]) ).
cnf(c_0_116,plain,
( X1 = esk8_1(powerset(X2))
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_69]) ).
cnf(c_0_117,plain,
( X1 = preimage_subnetstr(X3,X2,X4)
| ~ full_subrelstr(X1,X2)
| ~ subrelstr(X1,X2)
| the_carrier(X1) != function_invverse_img_as_carrier_subset(X2,X3,the_mapping(X3,X2),X4)
| ~ strict_net_str(X1,X3)
| ~ subnetstr(X1,X3,X2)
| ~ net_str(X2,X3)
| ~ one_sorted_str(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_118,plain,
( subrelstr(X1,X2)
| ~ subnetstr(X1,X3,X2)
| ~ net_str(X2,X3)
| ~ one_sorted_str(X3) ),
inference(csr,[status(thm)],[c_0_101,c_0_102]) ).
fof(c_0_119,plain,
! [X165,X166,X167,X168] :
( ~ one_sorted_str(X165)
| ~ one_sorted_str(X166)
| ~ function(X167)
| ~ quasi_total(X167,the_carrier(X165),the_carrier(X166))
| ~ relation_of2(X167,the_carrier(X165),the_carrier(X166))
| function_invverse_img_as_carrier_subset(X165,X166,X167,X168) = relation_inverse_image(X167,X168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_pre_topc])]) ).
cnf(c_0_120,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_121,plain,
( relation_of2_as_subset(the_mapping(X1,X2),the_carrier(X2),the_carrier(X1))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_122,plain,
( relation_inverse_image(X1,relation_dom(X2)) = empty_set
| ~ relation(X1)
| ~ function(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_105]) ).
cnf(c_0_123,plain,
( esk8_1(esk16_1(powerset(X1))) = relation_dom(X2)
| ~ empty(X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_106]) ).
cnf(c_0_124,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_125,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
fof(c_0_126,plain,
! [X74,X75] :
( ~ one_sorted_str(X74)
| ~ net_str(X75,X74)
| rel_str(X75) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_waybel_0])])]) ).
fof(c_0_127,plain,
! [X169,X170,X171,X172] :
( ~ relation_of2(X171,X169,X170)
| relation_dom_restr_as_relation_of(X169,X170,X171,X172) = relation_dom_restriction(X171,X172) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k8_relset_1])]) ).
cnf(c_0_128,plain,
( the_mapping(X1,X2) = relation_dom_restr_as_relation_of(the_carrier(X3),the_carrier(X1),the_mapping(X1,X3),the_carrier(X2))
| ~ subnetstr(X2,X1,X3)
| ~ net_str(X2,X1)
| ~ net_str(X3,X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_129,plain,
( subnetstr(preimage_subnetstr(X1,X2,X3),X1,X2)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_130,negated_conjecture,
esk31_0 = preimage_subnetstr(esk28_0,esk29_0,esk30_0),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_131,negated_conjecture,
net_str(esk29_0,esk28_0),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_132,negated_conjecture,
one_sorted_str(esk28_0),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_133,plain,
( ~ subset(apply(X1,X2),X3)
| ~ relation(X1)
| ~ function(X1)
| ~ empty(relation_inverse_image(X1,powerset(X3)))
| ~ in(X2,relation_dom(X1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_74]) ).
cnf(c_0_134,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_135,plain,
( relation_inverse_image(empty_set,X1) = empty_set
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_136,plain,
( esk8_1(esk16_1(powerset(X1))) = esk8_1(powerset(X2))
| ~ empty(X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_106]) ).
cnf(c_0_137,plain,
( the_carrier(X1) = function_invverse_img_as_carrier_subset(X2,X3,the_mapping(X3,X2),X4)
| X1 != preimage_subnetstr(X3,X2,X4)
| ~ strict_net_str(X1,X3)
| ~ subnetstr(X1,X3,X2)
| ~ net_str(X2,X3)
| ~ one_sorted_str(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_138,plain,
( strict_net_str(preimage_subnetstr(X1,X2,X3),X1)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_139,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_117,c_0_118]) ).
cnf(c_0_140,plain,
( function_invverse_img_as_carrier_subset(X1,X2,X3,X4) = relation_inverse_image(X3,X4)
| ~ one_sorted_str(X1)
| ~ one_sorted_str(X2)
| ~ function(X3)
| ~ quasi_total(X3,the_carrier(X1),the_carrier(X2))
| ~ relation_of2(X3,the_carrier(X1),the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_141,plain,
( function(the_mapping(X1,X2))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_142,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_120,c_0_121]) ).
cnf(c_0_143,plain,
( quasi_total(the_mapping(X1,X2),the_carrier(X2),the_carrier(X1))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_144,plain,
( relation_inverse_image(X1,esk8_1(esk16_1(powerset(X2)))) = empty_set
| ~ relation(X1)
| ~ function(X1)
| ~ empty(X3)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_145,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_146,plain,
( full_subrelstr(X1,X2)
| X1 != preimage_subnetstr(X3,X2,X4)
| ~ strict_net_str(X1,X3)
| ~ subnetstr(X1,X3,X2)
| ~ net_str(X2,X3)
| ~ one_sorted_str(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
fof(c_0_147,plain,
! [X73] :
( ~ rel_str(X73)
| one_sorted_str(X73) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_orders_2])]) ).
cnf(c_0_148,plain,
( rel_str(X2)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
fof(c_0_149,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> apply_netmap(X1,X2,X3) = apply_on_structs(X2,X1,the_mapping(X1,X2),X3) ) ) ),
inference(fof_simplification,[status(thm)],[d8_waybel_0]) ).
fof(c_0_150,plain,
! [X1,X2,X3,X4] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ~ empty_carrier(X2)
& one_sorted_str(X2)
& function(X3)
& quasi_total(X3,the_carrier(X1),the_carrier(X2))
& relation_of2(X3,the_carrier(X1),the_carrier(X2))
& element(X4,the_carrier(X1)) )
=> apply_on_structs(X1,X2,X3,X4) = apply(X3,X4) ),
inference(fof_simplification,[status(thm)],[redefinition_k1_waybel_0]) ).
fof(c_0_151,plain,
! [X194,X195,X196] :
( ~ relation(X196)
| ~ function(X196)
| ~ in(X195,X194)
| apply(relation_dom_restriction(X196,X194),X195) = apply(X196,X195) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t72_funct_1])]) ).
cnf(c_0_152,plain,
( relation_dom_restr_as_relation_of(X2,X3,X1,X4) = relation_dom_restriction(X1,X4)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_153,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_128,c_0_102]) ).
cnf(c_0_154,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_129,c_0_130]),c_0_131]),c_0_132])]) ).
fof(c_0_155,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ~ empty_carrier(X2)
& transitive_relstr(X2)
& directed_relstr(X2)
& net_str(X2,X1) )
=> ! [X3] :
( subnet(X3,X1,X2)
=> ( ~ empty_carrier(X3)
& transitive_relstr(X3)
& directed_relstr(X3)
& net_str(X3,X1) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_yellow_6]) ).
cnf(c_0_156,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ empty(relation_inverse_image(X1,powerset(apply(X1,X2))))
| ~ in(X2,relation_dom(X1)) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_157,plain,
relation_inverse_image(empty_set,X1) = empty_set,
inference(spm,[status(thm)],[c_0_135,c_0_89]) ).
fof(c_0_158,plain,
( relation(esk23_0)
& relation_empty_yielding(esk23_0)
& function(esk23_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_funct_1])]) ).
cnf(c_0_159,plain,
( empty(relation_inverse_image(X1,esk8_1(esk16_1(powerset(X2)))))
| ~ relation(X1)
| ~ function(X1)
| ~ empty(X3)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_136]) ).
cnf(c_0_160,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_137]),c_0_138]),c_0_129]) ).
cnf(c_0_161,plain,
( X1 = preimage_subnetstr(X2,X3,X4)
| the_carrier(X1) != relation_inverse_image(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)
| ~ one_sorted_str(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_141]),c_0_142]),c_0_143]) ).
cnf(c_0_162,plain,
( relation_inverse_image(X1,esk8_1(esk16_1(powerset(X2)))) = empty_set
| ~ relation(X1)
| ~ function(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_144,c_0_89]) ).
cnf(c_0_163,plain,
( relation(the_mapping(X1,X2))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_145,c_0_121]) ).
cnf(c_0_164,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_146]),c_0_138]),c_0_129]) ).
cnf(c_0_165,plain,
( one_sorted_str(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_166,negated_conjecture,
rel_str(esk29_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_131]),c_0_132])]) ).
fof(c_0_167,plain,
! [X177,X178] :
( ~ in(X177,X178)
| element(X177,X178) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(c_0_168,plain,
! [X43,X44,X45] :
( empty_carrier(X43)
| ~ one_sorted_str(X43)
| empty_carrier(X44)
| ~ net_str(X44,X43)
| ~ element(X45,the_carrier(X44))
| apply_netmap(X43,X44,X45) = apply_on_structs(X44,X43,the_mapping(X43,X44),X45) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])])]) ).
fof(c_0_169,plain,
! [X161,X162,X163,X164] :
( empty_carrier(X161)
| ~ one_sorted_str(X161)
| empty_carrier(X162)
| ~ one_sorted_str(X162)
| ~ function(X163)
| ~ quasi_total(X163,the_carrier(X161),the_carrier(X162))
| ~ relation_of2(X163,the_carrier(X161),the_carrier(X162))
| ~ element(X164,the_carrier(X161))
| apply_on_structs(X161,X162,X163,X164) = apply(X163,X164) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_150])]) ).
cnf(c_0_170,plain,
( apply(relation_dom_restriction(X1,X3),X2) = apply(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_171,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_152,c_0_153]),c_0_142]) ).
cnf(c_0_172,negated_conjecture,
net_str(esk31_0,esk28_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_154]),c_0_131]),c_0_132])]) ).
fof(c_0_173,plain,
! [X84,X85,X86] :
( ( ~ empty_carrier(X86)
| ~ subnet(X86,X84,X85)
| empty_carrier(X84)
| ~ one_sorted_str(X84)
| empty_carrier(X85)
| ~ transitive_relstr(X85)
| ~ directed_relstr(X85)
| ~ net_str(X85,X84) )
& ( transitive_relstr(X86)
| ~ subnet(X86,X84,X85)
| empty_carrier(X84)
| ~ one_sorted_str(X84)
| empty_carrier(X85)
| ~ transitive_relstr(X85)
| ~ directed_relstr(X85)
| ~ net_str(X85,X84) )
& ( directed_relstr(X86)
| ~ subnet(X86,X84,X85)
| empty_carrier(X84)
| ~ one_sorted_str(X84)
| empty_carrier(X85)
| ~ transitive_relstr(X85)
| ~ directed_relstr(X85)
| ~ net_str(X85,X84) )
& ( net_str(X86,X84)
| ~ subnet(X86,X84,X85)
| empty_carrier(X84)
| ~ one_sorted_str(X84)
| empty_carrier(X85)
| ~ transitive_relstr(X85)
| ~ directed_relstr(X85)
| ~ net_str(X85,X84) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_155])])])]) ).
cnf(c_0_174,plain,
~ in(X1,relation_dom(empty_set)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_79]),c_0_80]),c_0_89])]) ).
cnf(c_0_175,plain,
( relation_dom(X1) = empty_set
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_60]) ).
cnf(c_0_176,plain,
( in(apply(X1,esk3_3(X1,X2,X3)),X2)
| in(esk3_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_177,plain,
relation(esk23_0),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_178,plain,
function(esk23_0),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_179,plain,
( empty(relation_inverse_image(X1,esk8_1(esk16_1(powerset(X2)))))
| ~ relation(X1)
| ~ function(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_159,c_0_89]) ).
cnf(c_0_180,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_140,c_0_160]),c_0_141]),c_0_142]),c_0_143]) ).
cnf(c_0_181,plain,
( X1 = preimage_subnetstr(X2,X3,esk8_1(esk16_1(powerset(X4))))
| the_carrier(X1) != empty_set
| ~ subnetstr(X1,X2,X3)
| ~ full_subrelstr(X1,X3)
| ~ empty(X4)
| ~ strict_net_str(X1,X2)
| ~ net_str(X3,X2)
| ~ one_sorted_str(X2)
| ~ one_sorted_str(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_141]),c_0_163]) ).
cnf(c_0_182,negated_conjecture,
full_subrelstr(esk31_0,esk29_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_130]),c_0_131]),c_0_132])]) ).
cnf(c_0_183,negated_conjecture,
strict_net_str(esk31_0,esk28_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_130]),c_0_131]),c_0_132])]) ).
cnf(c_0_184,negated_conjecture,
one_sorted_str(esk29_0),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_185,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_186,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| apply_netmap(X1,X2,X3) = apply_on_structs(X2,X1,the_mapping(X1,X2),X3)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ element(X3,the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
cnf(c_0_187,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| apply_on_structs(X1,X2,X3,X4) = apply(X3,X4)
| ~ one_sorted_str(X1)
| ~ one_sorted_str(X2)
| ~ function(X3)
| ~ quasi_total(X3,the_carrier(X1),the_carrier(X2))
| ~ relation_of2(X3,the_carrier(X1),the_carrier(X2))
| ~ element(X4,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_188,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_170,c_0_171]),c_0_141]),c_0_163]) ).
cnf(c_0_189,negated_conjecture,
rel_str(esk31_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_172]),c_0_132])]) ).
cnf(c_0_190,plain,
( empty_carrier(X2)
| empty_carrier(X3)
| ~ empty_carrier(X1)
| ~ subnet(X1,X2,X3)
| ~ one_sorted_str(X2)
| ~ transitive_relstr(X3)
| ~ directed_relstr(X3)
| ~ net_str(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_191,negated_conjecture,
subnet(esk31_0,esk28_0,esk29_0),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_192,negated_conjecture,
directed_relstr(esk29_0),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_193,negated_conjecture,
transitive_relstr(esk29_0),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_194,negated_conjecture,
~ empty_carrier(esk29_0),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_195,negated_conjecture,
~ empty_carrier(esk28_0),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_196,plain,
~ in(X1,empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_89])]) ).
cnf(c_0_197,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_176,c_0_177]),c_0_178])]) ).
fof(c_0_198,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
cnf(c_0_199,plain,
( empty(the_carrier(preimage_subnetstr(X1,X2,esk8_1(esk16_1(powerset(X3))))))
| ~ empty(X3)
| ~ 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_179,c_0_180]),c_0_141]),c_0_163]) ).
cnf(c_0_200,negated_conjecture,
( preimage_subnetstr(esk28_0,esk29_0,esk8_1(esk16_1(powerset(X1)))) = esk31_0
| the_carrier(esk31_0) != empty_set
| ~ empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_154]),c_0_182]),c_0_183]),c_0_131]),c_0_132]),c_0_184])]) ).
fof(c_0_201,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ! [X3] :
( is_eventually_in(X1,X2,X3)
<=> ? [X4] :
( element(X4,the_carrier(X2))
& ! [X5] :
( element(X5,the_carrier(X2))
=> ( related(X2,X4,X5)
=> in(apply_netmap(X1,X2,X5),X3) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d11_waybel_0]) ).
cnf(c_0_202,plain,
( element(apply(X1,X2),X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(spm,[status(thm)],[c_0_185,c_0_55]) ).
cnf(c_0_203,plain,
( apply(the_mapping(X1,X2),X3) = apply_netmap(X1,X2,X3)
| empty_carrier(X1)
| empty_carrier(X2)
| ~ 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_186,c_0_187]),c_0_141]),c_0_142]),c_0_143]) ).
cnf(c_0_204,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_188,c_0_154]),c_0_131]),c_0_132])]) ).
cnf(c_0_205,negated_conjecture,
one_sorted_str(esk31_0),
inference(spm,[status(thm)],[c_0_165,c_0_189]) ).
cnf(c_0_206,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_190,c_0_191]),c_0_192]),c_0_193]),c_0_131]),c_0_132])]),c_0_194]),c_0_195]) ).
cnf(c_0_207,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ empty(X2)
| ~ in(X3,relation_inverse_image(X1,X2)) ),
inference(spm,[status(thm)],[c_0_95,c_0_55]) ).
cnf(c_0_208,plain,
( X1 = relation_inverse_image(esk23_0,empty_set)
| in(esk3_3(esk23_0,empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_196,c_0_197]) ).
fof(c_0_209,plain,
! [X118] :
( empty_carrier(X118)
| ~ one_sorted_str(X118)
| ~ empty(the_carrier(X118)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_198])]) ).
cnf(c_0_210,negated_conjecture,
( empty(the_carrier(esk31_0))
| the_carrier(esk31_0) != empty_set
| ~ empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_131]),c_0_132]),c_0_184])]) ).
fof(c_0_211,plain,
! [X23,X24,X25,X27,X28,X29] :
( ( element(esk1_3(X23,X24,X25),the_carrier(X24))
| ~ is_eventually_in(X23,X24,X25)
| empty_carrier(X24)
| ~ net_str(X24,X23)
| empty_carrier(X23)
| ~ one_sorted_str(X23) )
& ( ~ element(X27,the_carrier(X24))
| ~ related(X24,esk1_3(X23,X24,X25),X27)
| in(apply_netmap(X23,X24,X27),X25)
| ~ is_eventually_in(X23,X24,X25)
| empty_carrier(X24)
| ~ net_str(X24,X23)
| empty_carrier(X23)
| ~ one_sorted_str(X23) )
& ( element(esk2_4(X23,X24,X28,X29),the_carrier(X24))
| ~ element(X29,the_carrier(X24))
| is_eventually_in(X23,X24,X28)
| empty_carrier(X24)
| ~ net_str(X24,X23)
| empty_carrier(X23)
| ~ one_sorted_str(X23) )
& ( related(X24,X29,esk2_4(X23,X24,X28,X29))
| ~ element(X29,the_carrier(X24))
| is_eventually_in(X23,X24,X28)
| empty_carrier(X24)
| ~ net_str(X24,X23)
| empty_carrier(X23)
| ~ one_sorted_str(X23) )
& ( ~ in(apply_netmap(X23,X24,esk2_4(X23,X24,X28,X29)),X28)
| ~ element(X29,the_carrier(X24))
| is_eventually_in(X23,X24,X28)
| empty_carrier(X24)
| ~ net_str(X24,X23)
| empty_carrier(X23)
| ~ one_sorted_str(X23) ) ),
inference(distribute,[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)],[c_0_201])])])])])]) ).
cnf(c_0_212,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_202,c_0_180]),c_0_141]),c_0_163]) ).
cnf(c_0_213,negated_conjecture,
( 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_203,c_0_204]),c_0_172]),c_0_132]),c_0_205])]),c_0_195]),c_0_206]),c_0_185]) ).
cnf(c_0_214,plain,
( ~ empty(X1)
| ~ in(X2,the_carrier(preimage_subnetstr(X3,X4,X1)))
| ~ net_str(X4,X3)
| ~ one_sorted_str(X3)
| ~ one_sorted_str(X4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_180]),c_0_141]),c_0_163]) ).
cnf(c_0_215,plain,
relation_inverse_image(esk23_0,empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_196,c_0_208]) ).
cnf(c_0_216,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_209]) ).
cnf(c_0_217,negated_conjecture,
( empty(the_carrier(esk31_0))
| the_carrier(esk31_0) != empty_set ),
inference(spm,[status(thm)],[c_0_210,c_0_89]) ).
cnf(c_0_218,plain,
( is_eventually_in(X1,X2,X3)
| empty_carrier(X2)
| empty_carrier(X1)
| ~ in(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(split_conjunct,[status(thm)],[c_0_211]) ).
cnf(c_0_219,negated_conjecture,
( 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_212,c_0_213]),c_0_131]),c_0_132]),c_0_184])]) ).
cnf(c_0_220,negated_conjecture,
( ~ empty(esk30_0)
| ~ 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_214,c_0_130]),c_0_131]),c_0_132]),c_0_184])]) ).
cnf(c_0_221,plain,
( X1 = empty_set
| in(esk3_3(esk23_0,empty_set,X1),X1) ),
inference(rw,[status(thm)],[c_0_208,c_0_215]) ).
cnf(c_0_222,negated_conjecture,
the_carrier(esk31_0) != empty_set,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_217]),c_0_205])]),c_0_206]) ).
cnf(c_0_223,plain,
( is_eventually_in(X1,X2,X3)
| empty_carrier(X1)
| empty_carrier(X2)
| 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_218,c_0_52]) ).
cnf(c_0_224,negated_conjecture,
( element(apply_netmap(esk28_0,esk31_0,X1),esk30_0)
| ~ in(X1,the_carrier(esk31_0)) ),
inference(spm,[status(thm)],[c_0_219,c_0_130]) ).
cnf(c_0_225,negated_conjecture,
~ is_eventually_in(esk28_0,esk31_0,esk30_0),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_226,negated_conjecture,
~ empty(esk30_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_221]),c_0_222]) ).
cnf(c_0_227,negated_conjecture,
( ~ element(X1,the_carrier(esk31_0))
| ~ in(esk2_4(esk28_0,esk31_0,esk30_0,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_223,c_0_224]),c_0_172]),c_0_132])]),c_0_225]),c_0_195]),c_0_206]),c_0_226]) ).
cnf(c_0_228,negated_conjecture,
( 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_227,c_0_52]) ).
cnf(c_0_229,plain,
( element(esk2_4(X1,X2,X3,X4),the_carrier(X2))
| is_eventually_in(X1,X2,X3)
| empty_carrier(X2)
| empty_carrier(X1)
| ~ element(X4,the_carrier(X2))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_211]) ).
cnf(c_0_230,negated_conjecture,
( 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_228,c_0_229]),c_0_172]),c_0_132])]),c_0_225]),c_0_206]),c_0_195]) ).
cnf(c_0_231,negated_conjecture,
empty(the_carrier(esk31_0)),
inference(spm,[status(thm)],[c_0_230,c_0_73]) ).
cnf(c_0_232,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_231]),c_0_222]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU379+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 15:51:07 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 220.15/220.22 % Version : CSE_E---1.5
% 220.15/220.22 % Problem : theBenchmark.p
% 220.15/220.22 % Proof found
% 220.15/220.22 % SZS status Theorem for theBenchmark.p
% 220.15/220.22 % SZS output start Proof
% See solution above
% 220.15/220.24 % Total time : 219.545000 s
% 220.15/220.24 % SZS output end Proof
% 220.15/220.24 % Total time : 219.560000 s
%------------------------------------------------------------------------------