%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU379+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:37 PM UTC 2026
% Result : Theorem 12.65s 2.69s
% Output : Refutation 13.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 33
% Syntax : Number of formulae : 286 ( 47 unt; 10 def)
% Number of atoms : 1263 ( 106 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1645 ( 668 ~; 766 |; 146 &)
% ( 24 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 10 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 5 con; 0-4 aty)
% Number of variables : 384 ( 0 sgn 365 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f10,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& net_str(X1,X0) )
=> ! [X2] :
( is_eventually_in(X0,X1,X2)
<=> ? [X3] :
( element(X3,the_carrier(X1))
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( related(X1,X3,X4)
=> in(apply_netmap(X0,X1,X4),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_waybel_0) ).
fof(f11,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f12,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( net_str(X1,X0)
=> ! [X2,X3] :
( ( strict_net_str(X3,X0)
& subnetstr(X3,X0,X1) )
=> ( X3 = preimage_subnetstr(X0,X1,X2)
<=> ( full_subrelstr(X3,X1)
& subrelstr(X3,X1)
& the_carrier(X3) = function_invverse_img_as_carrier_subset(X1,X0,the_mapping(X0,X1),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_yellow_6) ).
fof(f13,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& net_str(X1,X0) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> apply_netmap(X0,X1,X2) = apply_on_structs(X1,X0,the_mapping(X0,X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_waybel_0) ).
fof(f14,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( net_str(X1,X0)
=> ! [X2] :
( net_str(X2,X0)
=> ( subnetstr(X2,X0,X1)
<=> ( subrelstr(X2,X1)
& the_mapping(X0,X2) = relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_yellow_6) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( one_sorted_str(X0)
& net_str(X1,X0) )
=> ( strict_net_str(preimage_subnetstr(X0,X1,X2),X0)
& subnetstr(preimage_subnetstr(X0,X1,X2),X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_yellow_6) ).
fof(f28,axiom,
! [X0] :
( rel_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(f30,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( net_str(X1,X0)
=> rel_str(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
fof(f34,axiom,
! [X0,X1] :
( ( one_sorted_str(X0)
& net_str(X1,X0) )
=> ! [X2] :
( subnetstr(X2,X0,X1)
=> net_str(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_yellow_6) ).
fof(f35,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f36,axiom,
! [X0,X1] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0)
& ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
=> ! [X2] :
( subnet(X2,X0,X1)
=> ( ~ empty_carrier(X2)
& transitive_relstr(X2)
& directed_relstr(X2)
& net_str(X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_yellow_6) ).
fof(f39,axiom,
! [X0,X1] :
( ( one_sorted_str(X0)
& net_str(X1,X0) )
=> ( function(the_mapping(X0,X1))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_waybel_0) ).
fof(f44,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f52,axiom,
! [X0,X1] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0)
& ~ empty_carrier(X1)
& net_str(X1,X0) )
=> ( ~ empty(the_mapping(X0,X1))
& relation(the_mapping(X0,X1))
& function(the_mapping(X0,X1))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc15_yellow_6) ).
fof(f54,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f78,axiom,
! [X0,X1,X2,X3] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0)
& ~ empty_carrier(X1)
& one_sorted_str(X1)
& function(X2)
& quasi_total(X2,the_carrier(X0),the_carrier(X1))
& relation_of2(X2,the_carrier(X0),the_carrier(X1))
& element(X3,the_carrier(X0)) )
=> apply_on_structs(X0,X1,X2,X3) = apply(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_waybel_0) ).
fof(f79,axiom,
! [X0,X1,X2,X3] :
( ( one_sorted_str(X0)
& one_sorted_str(X1)
& function(X2)
& quasi_total(X2,the_carrier(X0),the_carrier(X1))
& relation_of2(X2,the_carrier(X0),the_carrier(X1)) )
=> function_invverse_img_as_carrier_subset(X0,X1,X2,X3) = relation_inverse_image(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_pre_topc) ).
fof(f80,axiom,
! [X0,X1,X2,X3] :
( relation_of2(X2,X0,X1)
=> relation_dom_restr_as_relation_of(X0,X1,X2,X3) = relation_dom_restriction(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_relset_1) ).
fof(f81,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f84,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f85,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
=> ! [X2,X3] :
( subnet(X3,X0,X1)
=> ( X3 = preimage_subnetstr(X0,X1,X2)
=> is_eventually_in(X0,X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_yellow_6) ).
fof(f86,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
=> ! [X2,X3] :
( subnet(X3,X0,X1)
=> ( X3 = preimage_subnetstr(X0,X1,X2)
=> is_eventually_in(X0,X3,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f85]) ).
fof(f91,axiom,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
fof(f109,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f5]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( is_eventually_in(X0,X1,X2)
<=> ? [X3] :
( element(X3,the_carrier(X1))
& ! [X4] :
( in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) ) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( is_eventually_in(X0,X1,X2)
<=> ? [X3] :
( element(X3,the_carrier(X1))
& ! [X4] :
( in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) ) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f114]) ).
fof(f116,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f117,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f116]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( ( X3 = preimage_subnetstr(X0,X1,X2)
<=> ( full_subrelstr(X3,X1)
& subrelstr(X3,X1)
& the_carrier(X3) = function_invverse_img_as_carrier_subset(X1,X0,the_mapping(X0,X1),X2) ) )
| ~ strict_net_str(X3,X0)
| ~ subnetstr(X3,X0,X1) )
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( ( X3 = preimage_subnetstr(X0,X1,X2)
<=> ( full_subrelstr(X3,X1)
& subrelstr(X3,X1)
& the_carrier(X3) = function_invverse_img_as_carrier_subset(X1,X0,the_mapping(X0,X1),X2) ) )
| ~ strict_net_str(X3,X0)
| ~ subnetstr(X3,X0,X1) )
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f118]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( apply_netmap(X0,X1,X2) = apply_on_structs(X1,X0,the_mapping(X0,X1),X2)
| ~ element(X2,the_carrier(X1)) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( apply_netmap(X0,X1,X2) = apply_on_structs(X1,X0,the_mapping(X0,X1),X2)
| ~ element(X2,the_carrier(X1)) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f120]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subnetstr(X2,X0,X1)
<=> ( subrelstr(X2,X1)
& the_mapping(X0,X2) = relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X2)) ) )
| ~ net_str(X2,X0) )
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ( strict_net_str(preimage_subnetstr(X0,X1,X2),X0)
& subnetstr(preimage_subnetstr(X0,X1,X2),X0,X1) )
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ( strict_net_str(preimage_subnetstr(X0,X1,X2),X0)
& subnetstr(preimage_subnetstr(X0,X1,X2),X0,X1) )
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) ),
inference(flattening,[],[f131]) ).
fof(f135,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( rel_str(X1)
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f138,plain,
! [X0,X1] :
( ! [X2] :
( net_str(X2,X0)
| ~ subnetstr(X2,X0,X1) )
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f139,plain,
! [X0,X1] :
( ! [X2] :
( net_str(X2,X0)
| ~ subnetstr(X2,X0,X1) )
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) ),
inference(flattening,[],[f138]) ).
fof(f140,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f141,plain,
! [X0,X1] :
( ! [X2] :
( ( ~ empty_carrier(X2)
& transitive_relstr(X2)
& directed_relstr(X2)
& net_str(X2,X0) )
| ~ subnet(X2,X0,X1) )
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f142,plain,
! [X0,X1] :
( ! [X2] :
( ( ~ empty_carrier(X2)
& transitive_relstr(X2)
& directed_relstr(X2)
& net_str(X2,X0) )
| ~ subnet(X2,X0,X1) )
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) ),
inference(flattening,[],[f141]) ).
fof(f144,plain,
! [X0,X1] :
( ( function(the_mapping(X0,X1))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0)) )
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f145,plain,
! [X0,X1] :
( ( function(the_mapping(X0,X1))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0)) )
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) ),
inference(flattening,[],[f144]) ).
fof(f154,plain,
! [X0,X1] :
( ( ~ empty(the_mapping(X0,X1))
& relation(the_mapping(X0,X1))
& function(the_mapping(X0,X1))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0)) )
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| empty_carrier(X1)
| ~ net_str(X1,X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f155,plain,
! [X0,X1] :
( ( ~ empty(the_mapping(X0,X1))
& relation(the_mapping(X0,X1))
& function(the_mapping(X0,X1))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0)) )
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| empty_carrier(X1)
| ~ net_str(X1,X0) ),
inference(flattening,[],[f154]) ).
fof(f158,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f159,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f158]) ).
fof(f179,plain,
! [X0,X1,X2,X3] :
( apply_on_structs(X0,X1,X2,X3) = apply(X2,X3)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ function(X2)
| ~ quasi_total(X2,the_carrier(X0),the_carrier(X1))
| ~ relation_of2(X2,the_carrier(X0),the_carrier(X1))
| ~ element(X3,the_carrier(X0)) ),
inference(ennf_transformation,[],[f78]) ).
fof(f180,plain,
! [X0,X1,X2,X3] :
( apply_on_structs(X0,X1,X2,X3) = apply(X2,X3)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ function(X2)
| ~ quasi_total(X2,the_carrier(X0),the_carrier(X1))
| ~ relation_of2(X2,the_carrier(X0),the_carrier(X1))
| ~ element(X3,the_carrier(X0)) ),
inference(flattening,[],[f179]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( function_invverse_img_as_carrier_subset(X0,X1,X2,X3) = relation_inverse_image(X2,X3)
| ~ one_sorted_str(X0)
| ~ one_sorted_str(X1)
| ~ function(X2)
| ~ quasi_total(X2,the_carrier(X0),the_carrier(X1))
| ~ relation_of2(X2,the_carrier(X0),the_carrier(X1)) ),
inference(ennf_transformation,[],[f79]) ).
fof(f182,plain,
! [X0,X1,X2,X3] :
( function_invverse_img_as_carrier_subset(X0,X1,X2,X3) = relation_inverse_image(X2,X3)
| ~ one_sorted_str(X0)
| ~ one_sorted_str(X1)
| ~ function(X2)
| ~ quasi_total(X2,the_carrier(X0),the_carrier(X1))
| ~ relation_of2(X2,the_carrier(X0),the_carrier(X1)) ),
inference(flattening,[],[f181]) ).
fof(f183,plain,
! [X0,X1,X2,X3] :
( relation_dom_restr_as_relation_of(X0,X1,X2,X3) = relation_dom_restriction(X2,X3)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f80]) ).
fof(f185,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f84]) ).
fof(f186,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f185]) ).
fof(f187,plain,
? [X0] :
( ? [X1] :
( ? [X2,X3] :
( ~ is_eventually_in(X0,X3,X2)
& X3 = preimage_subnetstr(X0,X1,X2)
& subnet(X3,X0,X1) )
& ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f188,plain,
? [X0] :
( ? [X1] :
( ? [X2,X3] :
( ~ is_eventually_in(X0,X3,X2)
& X3 = preimage_subnetstr(X0,X1,X2)
& subnet(X3,X0,X1) )
& ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(flattening,[],[f187]) ).
fof(f194,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ relation(X2)
| ~ function(X2) ),
inference(ennf_transformation,[],[f91]) ).
fof(f195,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f194]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_eventually_in(X0,X1,X2)
| ! [X3] :
( ~ element(X3,the_carrier(X1))
| ? [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) ) ) )
& ( ? [X3] :
( element(X3,the_carrier(X1))
& ! [X4] :
( in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) ) )
| ~ is_eventually_in(X0,X1,X2) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(nnf_transformation,[],[f115]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_eventually_in(X0,X1,X2)
| ! [X3] :
( ~ element(X3,the_carrier(X1))
| ? [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) ) ) )
& ( ? [X5] :
( element(X5,the_carrier(X1))
& ! [X6] :
( in(apply_netmap(X0,X1,X6),X2)
| ~ related(X1,X5,X6)
| ~ element(X6,the_carrier(X1)) ) )
| ~ is_eventually_in(X0,X1,X2) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(rectify,[],[f198]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_eventually_in(X0,X1,X2)
| ! [X3] :
( ~ element(X3,the_carrier(X1))
| ( ~ in(apply_netmap(X0,X1,sK0(X0,X1,X2,X3)),X2)
& related(X1,X3,sK0(X0,X1,X2,X3))
& element(sK0(X0,X1,X2,X3),the_carrier(X1)) ) ) )
& ( ( element(sK1(X0,X1,X2),the_carrier(X1))
& ! [X6] :
( in(apply_netmap(X0,X1,X6),X2)
| ~ related(X1,sK1(X0,X1,X2),X6)
| ~ element(X6,the_carrier(X1)) ) )
| ~ is_eventually_in(X0,X1,X2) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X4,sK0(X0,X1,X2,X3)),skolemize(X5,sK1(X0,X1,X2))],[f199]) ).
fof(f201,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f117]) ).
fof(f202,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f201]) ).
fof(f203,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f202]) ).
fof(f204,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ~ in(sK2(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK2(X0,X1,X2)),X1)
| ~ in(sK2(X0,X1,X2),X2) )
& ( ( in(sK2(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK2(X0,X1,X2)),X1) )
| in(sK2(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f203]) ).
fof(f205,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( ( ( X3 = preimage_subnetstr(X0,X1,X2)
| ~ full_subrelstr(X3,X1)
| ~ subrelstr(X3,X1)
| the_carrier(X3) != function_invverse_img_as_carrier_subset(X1,X0,the_mapping(X0,X1),X2) )
& ( ( full_subrelstr(X3,X1)
& subrelstr(X3,X1)
& the_carrier(X3) = function_invverse_img_as_carrier_subset(X1,X0,the_mapping(X0,X1),X2) )
| preimage_subnetstr(X0,X1,X2) != X3 ) )
| ~ strict_net_str(X3,X0)
| ~ subnetstr(X3,X0,X1) )
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f206,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( ( ( X3 = preimage_subnetstr(X0,X1,X2)
| ~ full_subrelstr(X3,X1)
| ~ subrelstr(X3,X1)
| the_carrier(X3) != function_invverse_img_as_carrier_subset(X1,X0,the_mapping(X0,X1),X2) )
& ( ( full_subrelstr(X3,X1)
& subrelstr(X3,X1)
& the_carrier(X3) = function_invverse_img_as_carrier_subset(X1,X0,the_mapping(X0,X1),X2) )
| preimage_subnetstr(X0,X1,X2) != X3 ) )
| ~ strict_net_str(X3,X0)
| ~ subnetstr(X3,X0,X1) )
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f205]) ).
fof(f207,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( subnetstr(X2,X0,X1)
| ~ subrelstr(X2,X1)
| the_mapping(X0,X2) != relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X2)) )
& ( ( subrelstr(X2,X1)
& the_mapping(X0,X2) = relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X2)) )
| ~ subnetstr(X2,X0,X1) ) )
| ~ net_str(X2,X0) )
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(nnf_transformation,[],[f122]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( subnetstr(X2,X0,X1)
| ~ subrelstr(X2,X1)
| the_mapping(X0,X2) != relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X2)) )
& ( ( subrelstr(X2,X1)
& the_mapping(X0,X2) = relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X2)) )
| ~ subnetstr(X2,X0,X1) ) )
| ~ net_str(X2,X0) )
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f207]) ).
fof(f213,plain,
! [X0] : element(sK7(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f44]) ).
fof(f233,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f234,plain,
( ~ is_eventually_in(sK27,sK30,sK29)
& sK30 = preimage_subnetstr(sK27,sK28,sK29)
& subnet(sK30,sK27,sK28)
& ~ empty_carrier(sK28)
& transitive_relstr(sK28)
& directed_relstr(sK28)
& net_str(sK28,sK27)
& ~ empty_carrier(sK27)
& one_sorted_str(sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27,sK28,sK29,sK30]),skolemize(X0,sK27),skolemize(X1,sK28),skolemize(X2,sK29),skolemize(X3,sK30)],[f188]) ).
fof(f239,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f246,plain,
! [X2,X3,X0,X1] :
( element(sK0(X0,X1,X2,X3),the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| is_eventually_in(X0,X1,X2)
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f200]) ).
fof(f248,plain,
! [X2,X3,X0,X1] :
( ~ in(apply_netmap(X0,X1,sK0(X0,X1,X2,X3)),X2)
| ~ element(X3,the_carrier(X1))
| is_eventually_in(X0,X1,X2)
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f200]) ).
fof(f249,plain,
! [X2,X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f255,plain,
! [X2,X3,X0,X1] :
( the_carrier(X3) = function_invverse_img_as_carrier_subset(X1,X0,the_mapping(X0,X1),X2)
| preimage_subnetstr(X0,X1,X2) != X3
| ~ strict_net_str(X3,X0)
| ~ subnetstr(X3,X0,X1)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f259,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| apply_netmap(X0,X1,X2) = apply_on_structs(X1,X0,the_mapping(X0,X1),X2)
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f260,plain,
! [X2,X0,X1] :
( the_mapping(X0,X2) = relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X2))
| ~ subnetstr(X2,X0,X1)
| ~ net_str(X2,X0)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f268,plain,
! [X2,X0,X1] :
( subnetstr(preimage_subnetstr(X0,X1,X2),X0,X1)
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f269,plain,
! [X2,X0,X1] :
( strict_net_str(preimage_subnetstr(X0,X1,X2),X0)
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f272,plain,
! [X0] :
( ~ rel_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f273,plain,
! [X0,X1] :
( ~ net_str(X1,X0)
| rel_str(X1)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f275,plain,
! [X2,X0,X1] :
( ~ subnetstr(X2,X0,X1)
| net_str(X2,X0)
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f276,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
fof(f277,plain,
! [X2,X0,X1] :
( ~ subnet(X2,X0,X1)
| net_str(X2,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f280,plain,
! [X2,X0,X1] :
( ~ subnet(X2,X0,X1)
| ~ empty_carrier(X2)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| empty_carrier(X1)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ net_str(X1,X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f282,plain,
! [X0,X1] :
( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f289,plain,
! [X0] : element(sK7(X0),X0),
inference(cnf_transformation,[],[f213]) ).
fof(f299,plain,
! [X0,X1] :
( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| empty_carrier(X1)
| ~ net_str(X1,X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f300,plain,
! [X0,X1] :
( function(the_mapping(X0,X1))
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| empty_carrier(X1)
| ~ net_str(X1,X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f305,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f159]) ).
fof(f355,plain,
! [X2,X3,X0,X1] :
( ~ quasi_total(X2,the_carrier(X0),the_carrier(X1))
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ function(X2)
| apply_on_structs(X0,X1,X2,X3) = apply(X2,X3)
| ~ relation_of2(X2,the_carrier(X0),the_carrier(X1))
| ~ element(X3,the_carrier(X0)) ),
inference(cnf_transformation,[],[f180]) ).
fof(f356,plain,
! [X2,X3,X0,X1] :
( ~ quasi_total(X2,the_carrier(X0),the_carrier(X1))
| ~ one_sorted_str(X0)
| ~ one_sorted_str(X1)
| ~ function(X2)
| function_invverse_img_as_carrier_subset(X0,X1,X2,X3) = relation_inverse_image(X2,X3)
| ~ relation_of2(X2,the_carrier(X0),the_carrier(X1)) ),
inference(cnf_transformation,[],[f182]) ).
fof(f357,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_restr_as_relation_of(X0,X1,X2,X3) = relation_dom_restriction(X2,X3) ),
inference(cnf_transformation,[],[f183]) ).
fof(f358,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f233]) ).
fof(f359,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f233]) ).
fof(f362,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f186]) ).
fof(f363,plain,
one_sorted_str(sK27),
inference(cnf_transformation,[],[f234]) ).
fof(f364,plain,
~ empty_carrier(sK27),
inference(cnf_transformation,[],[f234]) ).
fof(f365,plain,
net_str(sK28,sK27),
inference(cnf_transformation,[],[f234]) ).
fof(f366,plain,
directed_relstr(sK28),
inference(cnf_transformation,[],[f234]) ).
fof(f367,plain,
transitive_relstr(sK28),
inference(cnf_transformation,[],[f234]) ).
fof(f368,plain,
~ empty_carrier(sK28),
inference(cnf_transformation,[],[f234]) ).
fof(f369,plain,
subnet(sK30,sK27,sK28),
inference(cnf_transformation,[],[f234]) ).
fof(f370,plain,
sK30 = preimage_subnetstr(sK27,sK28,sK29),
inference(cnf_transformation,[],[f234]) ).
fof(f371,plain,
~ is_eventually_in(sK27,sK30,sK29),
inference(cnf_transformation,[],[f234]) ).
fof(f376,plain,
! [X2,X0,X1] :
( ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f195]) ).
fof(f381,plain,
! [X0,X1,X4] :
( ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f249]) ).
fof(f384,plain,
! [X2,X0,X1] :
( function_invverse_img_as_carrier_subset(X1,X0,the_mapping(X0,X1),X2) = the_carrier(preimage_subnetstr(X0,X1,X2))
| ~ strict_net_str(preimage_subnetstr(X0,X1,X2),X0)
| ~ subnetstr(preimage_subnetstr(X0,X1,X2),X0,X1)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(equality_resolution,[],[f255]) ).
fof(f385,definition,
sF31 = preimage_subnetstr(sK27,sK28,sK29),
introduced(definition,[new_symbols(definition,[sF31])],[function_definition]) ).
fof(f386,plain,
preimage_subnetstr(sK27,sK28,sK29) = sF31,
inference(reorient_equations,[],[f385]) ).
fof(f387,plain,
sK30 = sF31,
inference(definition_folding,[],[f370,f386]) ).
fof(f388,plain,
! [X2,X0,X1] :
( ~ subnetstr(X2,X0,X1)
| the_mapping(X0,X2) = relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X2))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(forward_subsumption_resolution,[],[f260,f275]) ).
fof(f390,plain,
! [X2,X0,X1] :
( function_invverse_img_as_carrier_subset(X1,X0,the_mapping(X0,X1),X2) = the_carrier(preimage_subnetstr(X0,X1,X2))
| ~ subnetstr(preimage_subnetstr(X0,X1,X2),X0,X1)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(forward_subsumption_resolution,[],[f384,f269]) ).
fof(f393,plain,
sK30 = preimage_subnetstr(sK27,sK28,sK29),
inference(forward_demodulation,[],[f386,f387]) ).
fof(f394,plain,
! [X2,X0,X1] :
( ~ net_str(X1,X0)
| function_invverse_img_as_carrier_subset(X1,X0,the_mapping(X0,X1),X2) = the_carrier(preimage_subnetstr(X0,X1,X2))
| ~ one_sorted_str(X0) ),
inference(forward_subsumption_resolution,[],[f390,f268]) ).
fof(f396,plain,
! [X0] :
( function_invverse_img_as_carrier_subset(sK28,sK27,the_mapping(sK27,sK28),X0) = the_carrier(preimage_subnetstr(sK27,sK28,X0))
| ~ one_sorted_str(sK27) ),
inference(resolution,[],[f394,f365]) ).
fof(f397,plain,
! [X0] : function_invverse_img_as_carrier_subset(sK28,sK27,the_mapping(sK27,sK28),X0) = the_carrier(preimage_subnetstr(sK27,sK28,X0)),
inference(forward_subsumption_resolution,[],[f396,f363]) ).
fof(f401,plain,
( subnetstr(sK30,sK27,sK28)
| ~ one_sorted_str(sK27)
| ~ net_str(sK28,sK27) ),
inference(superposition,[],[f268,f393]) ).
fof(f402,plain,
( subnetstr(sK30,sK27,sK28)
| ~ net_str(sK28,sK27) ),
inference(forward_subsumption_resolution,[],[f401,f363]) ).
fof(f403,plain,
subnetstr(sK30,sK27,sK28),
inference(forward_subsumption_resolution,[],[f402,f365]) ).
fof(f414,plain,
( ~ empty_carrier(sK30)
| empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| empty_carrier(sK28)
| ~ transitive_relstr(sK28)
| ~ directed_relstr(sK28)
| ~ net_str(sK28,sK27) ),
inference(resolution,[],[f280,f369]) ).
fof(f415,plain,
( ~ empty_carrier(sK30)
| ~ one_sorted_str(sK27)
| empty_carrier(sK28)
| ~ transitive_relstr(sK28)
| ~ directed_relstr(sK28)
| ~ net_str(sK28,sK27) ),
inference(forward_subsumption_resolution,[],[f414,f364]) ).
fof(f416,plain,
( ~ empty_carrier(sK30)
| empty_carrier(sK28)
| ~ transitive_relstr(sK28)
| ~ directed_relstr(sK28)
| ~ net_str(sK28,sK27) ),
inference(forward_subsumption_resolution,[],[f415,f363]) ).
fof(f417,plain,
( ~ empty_carrier(sK30)
| ~ transitive_relstr(sK28)
| ~ directed_relstr(sK28)
| ~ net_str(sK28,sK27) ),
inference(forward_subsumption_resolution,[],[f416,f368]) ).
fof(f418,plain,
( ~ empty_carrier(sK30)
| ~ directed_relstr(sK28)
| ~ net_str(sK28,sK27) ),
inference(forward_subsumption_resolution,[],[f417,f367]) ).
fof(f419,plain,
( ~ empty_carrier(sK30)
| ~ net_str(sK28,sK27) ),
inference(forward_subsumption_resolution,[],[f418,f366]) ).
fof(f420,plain,
~ empty_carrier(sK30),
inference(forward_subsumption_resolution,[],[f419,f365]) ).
fof(f431,plain,
( net_str(sK30,sK27)
| empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| empty_carrier(sK28)
| ~ transitive_relstr(sK28)
| ~ directed_relstr(sK28)
| ~ net_str(sK28,sK27) ),
inference(resolution,[],[f277,f369]) ).
fof(f432,plain,
( net_str(sK30,sK27)
| ~ one_sorted_str(sK27)
| empty_carrier(sK28)
| ~ transitive_relstr(sK28)
| ~ directed_relstr(sK28)
| ~ net_str(sK28,sK27) ),
inference(forward_subsumption_resolution,[],[f431,f364]) ).
fof(f433,plain,
( net_str(sK30,sK27)
| empty_carrier(sK28)
| ~ transitive_relstr(sK28)
| ~ directed_relstr(sK28)
| ~ net_str(sK28,sK27) ),
inference(forward_subsumption_resolution,[],[f432,f363]) ).
fof(f434,plain,
( net_str(sK30,sK27)
| ~ transitive_relstr(sK28)
| ~ directed_relstr(sK28)
| ~ net_str(sK28,sK27) ),
inference(forward_subsumption_resolution,[],[f433,f368]) ).
fof(f435,plain,
( net_str(sK30,sK27)
| ~ directed_relstr(sK28)
| ~ net_str(sK28,sK27) ),
inference(forward_subsumption_resolution,[],[f434,f367]) ).
fof(f436,plain,
( net_str(sK30,sK27)
| ~ net_str(sK28,sK27) ),
inference(forward_subsumption_resolution,[],[f435,f366]) ).
fof(f437,plain,
net_str(sK30,sK27),
inference(forward_subsumption_resolution,[],[f436,f365]) ).
fof(f440,plain,
( rel_str(sK28)
| ~ one_sorted_str(sK27) ),
inference(resolution,[],[f273,f365]) ).
fof(f441,plain,
( rel_str(sK30)
| ~ one_sorted_str(sK27) ),
inference(resolution,[],[f273,f437]) ).
fof(f442,plain,
rel_str(sK30),
inference(forward_subsumption_resolution,[],[f441,f363]) ).
fof(f443,plain,
rel_str(sK28),
inference(forward_subsumption_resolution,[],[f440,f363]) ).
fof(f444,plain,
! [X2,X3,X0,X1,X4] :
( apply_netmap(X0,X1,sK0(X2,X1,X3,X4)) = apply_on_structs(X1,X0,the_mapping(X0,X1),sK0(X2,X1,X3,X4))
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ element(X4,the_carrier(X1))
| is_eventually_in(X2,X1,X3)
| empty_carrier(X1)
| ~ net_str(X1,X2)
| empty_carrier(X2)
| ~ one_sorted_str(X2) ),
inference(resolution,[],[f259,f246]) ).
fof(f445,plain,
! [X2,X3,X0,X1,X4] :
( ~ element(X4,the_carrier(X1))
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| apply_netmap(X0,X1,sK0(X2,X1,X3,X4)) = apply_on_structs(X1,X0,the_mapping(X0,X1),sK0(X2,X1,X3,X4))
| is_eventually_in(X2,X1,X3)
| ~ net_str(X1,X2)
| empty_carrier(X2)
| ~ one_sorted_str(X2) ),
inference(duplicate_literal_removal,[],[f444]) ).
fof(f462,plain,
! [X0,X1] :
( relation_of2(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f282,f358]) ).
fof(f465,plain,
( the_mapping(sK27,sK30) = relation_dom_restr_as_relation_of(the_carrier(sK28),the_carrier(sK27),the_mapping(sK27,sK28),the_carrier(sK30))
| ~ net_str(sK28,sK27)
| ~ one_sorted_str(sK27) ),
inference(resolution,[],[f388,f403]) ).
fof(f467,plain,
( the_mapping(sK27,sK30) = relation_dom_restr_as_relation_of(the_carrier(sK28),the_carrier(sK27),the_mapping(sK27,sK28),the_carrier(sK30))
| ~ one_sorted_str(sK27) ),
inference(forward_subsumption_resolution,[],[f465,f365]) ).
fof(f468,plain,
the_mapping(sK27,sK30) = relation_dom_restr_as_relation_of(the_carrier(sK28),the_carrier(sK27),the_mapping(sK27,sK28),the_carrier(sK30)),
inference(forward_subsumption_resolution,[],[f467,f363]) ).
fof(f477,definition,
( spl32_1
<=> relation_of2(the_mapping(sK27,sK28),the_carrier(sK28),the_carrier(sK27)) ),
introduced(definition,[new_symbols(definition,[spl32_1])],[avatar_definition]) ).
fof(f478,plain,
( relation_of2(the_mapping(sK27,sK28),the_carrier(sK28),the_carrier(sK27))
| ~ spl32_1 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f479,plain,
( ~ relation_of2(the_mapping(sK27,sK28),the_carrier(sK28),the_carrier(sK27))
| spl32_1 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f481,definition,
( spl32_2
<=> quasi_total(the_mapping(sK27,sK28),the_carrier(sK28),the_carrier(sK27)) ),
introduced(definition,[new_symbols(definition,[spl32_2])],[avatar_definition]) ).
fof(f482,plain,
( quasi_total(the_mapping(sK27,sK28),the_carrier(sK28),the_carrier(sK27))
| ~ spl32_2 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f483,plain,
( ~ quasi_total(the_mapping(sK27,sK28),the_carrier(sK28),the_carrier(sK27))
| spl32_2 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f485,definition,
( spl32_3
<=> function(the_mapping(sK27,sK28)) ),
introduced(definition,[new_symbols(definition,[spl32_3])],[avatar_definition]) ).
fof(f486,plain,
( function(the_mapping(sK27,sK28))
| ~ spl32_3 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f487,plain,
( ~ function(the_mapping(sK27,sK28))
| spl32_3 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f489,definition,
( spl32_4
<=> one_sorted_str(sK28) ),
introduced(definition,[new_symbols(definition,[spl32_4])],[avatar_definition]) ).
fof(f490,plain,
( one_sorted_str(sK28)
| ~ spl32_4 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f491,plain,
( ~ one_sorted_str(sK28)
| spl32_4 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f496,plain,
( ~ net_str(sK28,sK27)
| ~ one_sorted_str(sK27)
| spl32_1 ),
inference(resolution,[],[f479,f462]) ).
fof(f497,plain,
( ~ one_sorted_str(sK27)
| spl32_1 ),
inference(forward_subsumption_resolution,[],[f496,f365]) ).
fof(f498,plain,
( $false
| spl32_1 ),
inference(forward_subsumption_resolution,[],[f497,f363]) ).
fof(f499,plain,
spl32_1,
inference(avatar_contradiction_clause,[],[f498]) ).
fof(f500,plain,
( relation_of2_as_subset(the_mapping(sK27,sK28),the_carrier(sK28),the_carrier(sK27))
| ~ spl32_1 ),
inference(resolution,[],[f478,f359]) ).
fof(f501,plain,
( ! [X0] : relation_dom_restr_as_relation_of(the_carrier(sK28),the_carrier(sK27),the_mapping(sK27,sK28),X0) = relation_dom_restriction(the_mapping(sK27,sK28),X0)
| ~ spl32_1 ),
inference(resolution,[],[f478,f357]) ).
fof(f503,plain,
( empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| empty_carrier(sK28)
| ~ net_str(sK28,sK27)
| spl32_2 ),
inference(resolution,[],[f483,f299]) ).
fof(f504,plain,
( ~ one_sorted_str(sK27)
| empty_carrier(sK28)
| ~ net_str(sK28,sK27)
| spl32_2 ),
inference(forward_subsumption_resolution,[],[f503,f364]) ).
fof(f506,plain,
( empty_carrier(sK28)
| ~ net_str(sK28,sK27)
| spl32_2 ),
inference(forward_subsumption_resolution,[],[f504,f363]) ).
fof(f509,plain,
( ~ net_str(sK28,sK27)
| spl32_2 ),
inference(forward_subsumption_resolution,[],[f506,f368]) ).
fof(f510,plain,
( $false
| spl32_2 ),
inference(forward_subsumption_resolution,[],[f509,f365]) ).
fof(f511,plain,
spl32_2,
inference(avatar_contradiction_clause,[],[f510]) ).
fof(f513,plain,
( ! [X0] :
( ~ one_sorted_str(sK28)
| ~ one_sorted_str(sK27)
| ~ function(the_mapping(sK27,sK28))
| function_invverse_img_as_carrier_subset(sK28,sK27,the_mapping(sK27,sK28),X0) = relation_inverse_image(the_mapping(sK27,sK28),X0)
| ~ relation_of2(the_mapping(sK27,sK28),the_carrier(sK28),the_carrier(sK27)) )
| ~ spl32_2 ),
inference(resolution,[],[f482,f356]) ).
fof(f534,plain,
( empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| empty_carrier(sK28)
| ~ net_str(sK28,sK27)
| spl32_3 ),
inference(resolution,[],[f487,f300]) ).
fof(f537,plain,
( ~ one_sorted_str(sK27)
| empty_carrier(sK28)
| ~ net_str(sK28,sK27)
| spl32_3 ),
inference(forward_subsumption_resolution,[],[f534,f364]) ).
fof(f540,plain,
( empty_carrier(sK28)
| ~ net_str(sK28,sK27)
| spl32_3 ),
inference(forward_subsumption_resolution,[],[f537,f363]) ).
fof(f541,plain,
( ~ net_str(sK28,sK27)
| spl32_3 ),
inference(forward_subsumption_resolution,[],[f540,f368]) ).
fof(f542,plain,
( $false
| spl32_3 ),
inference(forward_subsumption_resolution,[],[f541,f365]) ).
fof(f543,plain,
spl32_3,
inference(avatar_contradiction_clause,[],[f542]) ).
fof(f553,plain,
( the_mapping(sK27,sK30) = relation_dom_restriction(the_mapping(sK27,sK28),the_carrier(sK30))
| ~ spl32_1 ),
inference(superposition,[],[f468,f501]) ).
fof(f569,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f276,f239]) ).
fof(f571,plain,
( relation(the_mapping(sK27,sK28))
| ~ spl32_1 ),
inference(resolution,[],[f569,f500]) ).
fof(f572,plain,
one_sorted_str(sK30),
inference(resolution,[],[f272,f442]) ).
fof(f573,plain,
one_sorted_str(sK28),
inference(resolution,[],[f272,f443]) ).
fof(f574,plain,
( $false
| spl32_4 ),
inference(forward_subsumption_resolution,[],[f573,f491]) ).
fof(f575,plain,
spl32_4,
inference(avatar_contradiction_clause,[],[f574]) ).
fof(f576,plain,
( ! [X0] :
( ~ one_sorted_str(sK27)
| ~ function(the_mapping(sK27,sK28))
| function_invverse_img_as_carrier_subset(sK28,sK27,the_mapping(sK27,sK28),X0) = relation_inverse_image(the_mapping(sK27,sK28),X0)
| ~ relation_of2(the_mapping(sK27,sK28),the_carrier(sK28),the_carrier(sK27)) )
| ~ spl32_2
| ~ spl32_4 ),
inference(forward_subsumption_resolution,[],[f513,f490]) ).
fof(f578,plain,
( ! [X0] :
( ~ function(the_mapping(sK27,sK28))
| function_invverse_img_as_carrier_subset(sK28,sK27,the_mapping(sK27,sK28),X0) = relation_inverse_image(the_mapping(sK27,sK28),X0)
| ~ relation_of2(the_mapping(sK27,sK28),the_carrier(sK28),the_carrier(sK27)) )
| ~ spl32_2
| ~ spl32_4 ),
inference(forward_subsumption_resolution,[],[f576,f363]) ).
fof(f580,plain,
( ! [X0] :
( function_invverse_img_as_carrier_subset(sK28,sK27,the_mapping(sK27,sK28),X0) = relation_inverse_image(the_mapping(sK27,sK28),X0)
| ~ relation_of2(the_mapping(sK27,sK28),the_carrier(sK28),the_carrier(sK27)) )
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4 ),
inference(forward_subsumption_resolution,[],[f578,f486]) ).
fof(f582,plain,
( ! [X0] : function_invverse_img_as_carrier_subset(sK28,sK27,the_mapping(sK27,sK28),X0) = relation_inverse_image(the_mapping(sK27,sK28),X0)
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4 ),
inference(forward_subsumption_resolution,[],[f580,f478]) ).
fof(f584,plain,
( ! [X0] : the_carrier(preimage_subnetstr(sK27,sK28,X0)) = relation_inverse_image(the_mapping(sK27,sK28),X0)
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4 ),
inference(forward_demodulation,[],[f582,f397]) ).
fof(f588,plain,
( ! [X0,X1] :
( ~ in(X1,the_carrier(preimage_subnetstr(sK27,sK28,X0)))
| in(apply(the_mapping(sK27,sK28),X1),X0)
| ~ relation(the_mapping(sK27,sK28))
| ~ function(the_mapping(sK27,sK28)) )
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4 ),
inference(superposition,[],[f381,f584]) ).
fof(f589,plain,
( ! [X0,X1] :
( ~ in(X1,the_carrier(preimage_subnetstr(sK27,sK28,X0)))
| in(apply(the_mapping(sK27,sK28),X1),X0)
| ~ function(the_mapping(sK27,sK28)) )
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4 ),
inference(forward_subsumption_resolution,[],[f588,f571]) ).
fof(f591,plain,
( ! [X0,X1] :
( ~ in(X1,the_carrier(preimage_subnetstr(sK27,sK28,X0)))
| in(apply(the_mapping(sK27,sK28),X1),X0) )
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4 ),
inference(forward_subsumption_resolution,[],[f589,f486]) ).
fof(f594,plain,
( ! [X0] :
( in(apply(the_mapping(sK27,sK28),X0),sK29)
| ~ in(X0,the_carrier(sK30)) )
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4 ),
inference(superposition,[],[f591,f393]) ).
fof(f605,definition,
( spl32_6
<=> relation_of2(the_mapping(sK27,sK30),the_carrier(sK30),the_carrier(sK27)) ),
introduced(definition,[new_symbols(definition,[spl32_6])],[avatar_definition]) ).
fof(f606,plain,
( relation_of2(the_mapping(sK27,sK30),the_carrier(sK30),the_carrier(sK27))
| ~ spl32_6 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f607,plain,
( ~ relation_of2(the_mapping(sK27,sK30),the_carrier(sK30),the_carrier(sK27))
| spl32_6 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f609,definition,
( spl32_7
<=> quasi_total(the_mapping(sK27,sK30),the_carrier(sK30),the_carrier(sK27)) ),
introduced(definition,[new_symbols(definition,[spl32_7])],[avatar_definition]) ).
fof(f610,plain,
( quasi_total(the_mapping(sK27,sK30),the_carrier(sK30),the_carrier(sK27))
| ~ spl32_7 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f611,plain,
( ~ quasi_total(the_mapping(sK27,sK30),the_carrier(sK30),the_carrier(sK27))
| spl32_7 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f613,definition,
( spl32_8
<=> function(the_mapping(sK27,sK30)) ),
introduced(definition,[new_symbols(definition,[spl32_8])],[avatar_definition]) ).
fof(f614,plain,
( function(the_mapping(sK27,sK30))
| ~ spl32_8 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f615,plain,
( ~ function(the_mapping(sK27,sK30))
| spl32_8 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f620,plain,
( ~ net_str(sK30,sK27)
| ~ one_sorted_str(sK27)
| spl32_6 ),
inference(resolution,[],[f607,f462]) ).
fof(f621,plain,
( ~ one_sorted_str(sK27)
| spl32_6 ),
inference(forward_subsumption_resolution,[],[f620,f437]) ).
fof(f622,plain,
( $false
| spl32_6 ),
inference(forward_subsumption_resolution,[],[f621,f363]) ).
fof(f623,plain,
spl32_6,
inference(avatar_contradiction_clause,[],[f622]) ).
fof(f642,plain,
( empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| empty_carrier(sK30)
| ~ net_str(sK30,sK27)
| spl32_7 ),
inference(resolution,[],[f611,f299]) ).
fof(f643,plain,
( ~ one_sorted_str(sK27)
| empty_carrier(sK30)
| ~ net_str(sK30,sK27)
| spl32_7 ),
inference(forward_subsumption_resolution,[],[f642,f364]) ).
fof(f645,plain,
( empty_carrier(sK30)
| ~ net_str(sK30,sK27)
| spl32_7 ),
inference(forward_subsumption_resolution,[],[f643,f363]) ).
fof(f648,plain,
( ~ net_str(sK30,sK27)
| spl32_7 ),
inference(forward_subsumption_resolution,[],[f645,f420]) ).
fof(f649,plain,
( $false
| spl32_7 ),
inference(forward_subsumption_resolution,[],[f648,f437]) ).
fof(f650,plain,
spl32_7,
inference(avatar_contradiction_clause,[],[f649]) ).
fof(f651,plain,
( ! [X0] :
( empty_carrier(sK30)
| ~ one_sorted_str(sK30)
| empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| ~ function(the_mapping(sK27,sK30))
| apply_on_structs(sK30,sK27,the_mapping(sK27,sK30),X0) = apply(the_mapping(sK27,sK30),X0)
| ~ relation_of2(the_mapping(sK27,sK30),the_carrier(sK30),the_carrier(sK27))
| ~ element(X0,the_carrier(sK30)) )
| ~ spl32_7 ),
inference(resolution,[],[f610,f355]) ).
fof(f737,definition,
( spl32_13
<=> empty(the_carrier(sK30)) ),
introduced(definition,[new_symbols(definition,[spl32_13])],[avatar_definition]) ).
fof(f738,plain,
( ~ empty(the_carrier(sK30))
| spl32_13 ),
inference(avatar_component_clause,[],[f737]) ).
fof(f739,plain,
( empty(the_carrier(sK30))
| ~ spl32_13 ),
inference(avatar_component_clause,[],[f737]) ).
fof(f744,plain,
( empty_carrier(sK30)
| ~ one_sorted_str(sK30)
| ~ spl32_13 ),
inference(resolution,[],[f739,f305]) ).
fof(f745,plain,
( ~ one_sorted_str(sK30)
| ~ spl32_13 ),
inference(forward_subsumption_resolution,[],[f744,f420]) ).
fof(f746,plain,
( $false
| ~ spl32_13 ),
inference(forward_subsumption_resolution,[],[f745,f572]) ).
fof(f747,plain,
~ spl32_13,
inference(avatar_contradiction_clause,[],[f746]) ).
fof(f922,plain,
( empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| empty_carrier(sK30)
| ~ net_str(sK30,sK27)
| spl32_8 ),
inference(resolution,[],[f615,f300]) ).
fof(f925,plain,
( ~ one_sorted_str(sK27)
| empty_carrier(sK30)
| ~ net_str(sK30,sK27)
| spl32_8 ),
inference(forward_subsumption_resolution,[],[f922,f364]) ).
fof(f928,plain,
( empty_carrier(sK30)
| ~ net_str(sK30,sK27)
| spl32_8 ),
inference(forward_subsumption_resolution,[],[f925,f363]) ).
fof(f929,plain,
( ~ net_str(sK30,sK27)
| spl32_8 ),
inference(forward_subsumption_resolution,[],[f928,f420]) ).
fof(f930,plain,
( $false
| spl32_8 ),
inference(forward_subsumption_resolution,[],[f929,f437]) ).
fof(f931,plain,
spl32_8,
inference(avatar_contradiction_clause,[],[f930]) ).
fof(f933,plain,
( ! [X0] :
( ~ one_sorted_str(sK30)
| empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| ~ function(the_mapping(sK27,sK30))
| apply_on_structs(sK30,sK27,the_mapping(sK27,sK30),X0) = apply(the_mapping(sK27,sK30),X0)
| ~ relation_of2(the_mapping(sK27,sK30),the_carrier(sK30),the_carrier(sK27))
| ~ element(X0,the_carrier(sK30)) )
| ~ spl32_7 ),
inference(forward_subsumption_resolution,[],[f651,f420]) ).
fof(f936,plain,
( ! [X0] :
( empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| ~ function(the_mapping(sK27,sK30))
| apply_on_structs(sK30,sK27,the_mapping(sK27,sK30),X0) = apply(the_mapping(sK27,sK30),X0)
| ~ relation_of2(the_mapping(sK27,sK30),the_carrier(sK30),the_carrier(sK27))
| ~ element(X0,the_carrier(sK30)) )
| ~ spl32_7 ),
inference(forward_subsumption_resolution,[],[f933,f572]) ).
fof(f939,plain,
( ! [X0] :
( ~ one_sorted_str(sK27)
| ~ function(the_mapping(sK27,sK30))
| apply_on_structs(sK30,sK27,the_mapping(sK27,sK30),X0) = apply(the_mapping(sK27,sK30),X0)
| ~ relation_of2(the_mapping(sK27,sK30),the_carrier(sK30),the_carrier(sK27))
| ~ element(X0,the_carrier(sK30)) )
| ~ spl32_7 ),
inference(forward_subsumption_resolution,[],[f936,f364]) ).
fof(f942,plain,
( ! [X0] :
( ~ function(the_mapping(sK27,sK30))
| apply_on_structs(sK30,sK27,the_mapping(sK27,sK30),X0) = apply(the_mapping(sK27,sK30),X0)
| ~ relation_of2(the_mapping(sK27,sK30),the_carrier(sK30),the_carrier(sK27))
| ~ element(X0,the_carrier(sK30)) )
| ~ spl32_7 ),
inference(forward_subsumption_resolution,[],[f939,f363]) ).
fof(f944,plain,
( ! [X0] :
( apply_on_structs(sK30,sK27,the_mapping(sK27,sK30),X0) = apply(the_mapping(sK27,sK30),X0)
| ~ relation_of2(the_mapping(sK27,sK30),the_carrier(sK30),the_carrier(sK27))
| ~ element(X0,the_carrier(sK30)) )
| ~ spl32_7
| ~ spl32_8 ),
inference(forward_subsumption_resolution,[],[f942,f614]) ).
fof(f945,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK30))
| apply_on_structs(sK30,sK27,the_mapping(sK27,sK30),X0) = apply(the_mapping(sK27,sK30),X0) )
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8 ),
inference(forward_subsumption_resolution,[],[f944,f606]) ).
fof(f1065,plain,
! [X2,X3,X0,X1] :
( ~ net_str(X0,X2)
| ~ net_str(X0,X1)
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| apply_netmap(X1,X0,sK0(X2,X0,X3,sK7(the_carrier(X0)))) = apply_on_structs(X0,X1,the_mapping(X1,X0),sK0(X2,X0,X3,sK7(the_carrier(X0))))
| is_eventually_in(X2,X0,X3)
| empty_carrier(X0)
| empty_carrier(X2)
| ~ one_sorted_str(X2) ),
inference(resolution,[],[f445,f289]) ).
fof(f1345,plain,
! [X0,X1] :
( ~ net_str(sK30,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| apply_netmap(X0,sK30,sK0(sK27,sK30,X1,sK7(the_carrier(sK30)))) = apply_on_structs(sK30,X0,the_mapping(X0,sK30),sK0(sK27,sK30,X1,sK7(the_carrier(sK30))))
| is_eventually_in(sK27,sK30,X1)
| empty_carrier(sK30)
| empty_carrier(sK27)
| ~ one_sorted_str(sK27) ),
inference(resolution,[],[f1065,f437]) ).
fof(f1348,plain,
! [X0,X1] :
( ~ net_str(sK30,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| apply_netmap(X0,sK30,sK0(sK27,sK30,X1,sK7(the_carrier(sK30)))) = apply_on_structs(sK30,X0,the_mapping(X0,sK30),sK0(sK27,sK30,X1,sK7(the_carrier(sK30))))
| is_eventually_in(sK27,sK30,X1)
| empty_carrier(sK27)
| ~ one_sorted_str(sK27) ),
inference(forward_subsumption_resolution,[],[f1345,f420]) ).
fof(f1350,plain,
! [X0,X1] :
( ~ net_str(sK30,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| apply_netmap(X0,sK30,sK0(sK27,sK30,X1,sK7(the_carrier(sK30)))) = apply_on_structs(sK30,X0,the_mapping(X0,sK30),sK0(sK27,sK30,X1,sK7(the_carrier(sK30))))
| is_eventually_in(sK27,sK30,X1)
| ~ one_sorted_str(sK27) ),
inference(forward_subsumption_resolution,[],[f1348,f364]) ).
fof(f1352,plain,
! [X0,X1] :
( ~ net_str(sK30,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0)
| apply_netmap(X0,sK30,sK0(sK27,sK30,X1,sK7(the_carrier(sK30)))) = apply_on_structs(sK30,X0,the_mapping(X0,sK30),sK0(sK27,sK30,X1,sK7(the_carrier(sK30))))
| is_eventually_in(sK27,sK30,X1) ),
inference(forward_subsumption_resolution,[],[f1350,f363]) ).
fof(f1357,plain,
! [X0] :
( empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| apply_netmap(sK27,sK30,sK0(sK27,sK30,X0,sK7(the_carrier(sK30)))) = apply_on_structs(sK30,sK27,the_mapping(sK27,sK30),sK0(sK27,sK30,X0,sK7(the_carrier(sK30))))
| is_eventually_in(sK27,sK30,X0) ),
inference(resolution,[],[f1352,f437]) ).
fof(f1358,plain,
! [X0] :
( ~ one_sorted_str(sK27)
| apply_netmap(sK27,sK30,sK0(sK27,sK30,X0,sK7(the_carrier(sK30)))) = apply_on_structs(sK30,sK27,the_mapping(sK27,sK30),sK0(sK27,sK30,X0,sK7(the_carrier(sK30))))
| is_eventually_in(sK27,sK30,X0) ),
inference(forward_subsumption_resolution,[],[f1357,f364]) ).
fof(f1359,plain,
! [X0] :
( is_eventually_in(sK27,sK30,X0)
| apply_netmap(sK27,sK30,sK0(sK27,sK30,X0,sK7(the_carrier(sK30)))) = apply_on_structs(sK30,sK27,the_mapping(sK27,sK30),sK0(sK27,sK30,X0,sK7(the_carrier(sK30)))) ),
inference(forward_subsumption_resolution,[],[f1358,f363]) ).
fof(f1518,plain,
apply_netmap(sK27,sK30,sK0(sK27,sK30,sK29,sK7(the_carrier(sK30)))) = apply_on_structs(sK30,sK27,the_mapping(sK27,sK30),sK0(sK27,sK30,sK29,sK7(the_carrier(sK30)))),
inference(resolution,[],[f1359,f371]) ).
fof(f1536,definition,
( spl32_44
<=> element(sK0(sK27,sK30,sK29,sK7(the_carrier(sK30))),the_carrier(sK30)) ),
introduced(definition,[new_symbols(definition,[spl32_44])],[avatar_definition]) ).
fof(f1537,plain,
( element(sK0(sK27,sK30,sK29,sK7(the_carrier(sK30))),the_carrier(sK30))
| ~ spl32_44 ),
inference(avatar_component_clause,[],[f1536]) ).
fof(f1538,plain,
( ~ element(sK0(sK27,sK30,sK29,sK7(the_carrier(sK30))),the_carrier(sK30))
| spl32_44 ),
inference(avatar_component_clause,[],[f1536]) ).
fof(f1549,plain,
( ~ element(sK7(the_carrier(sK30)),the_carrier(sK30))
| is_eventually_in(sK27,sK30,sK29)
| empty_carrier(sK30)
| ~ net_str(sK30,sK27)
| empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| spl32_44 ),
inference(resolution,[],[f1538,f246]) ).
fof(f1550,plain,
( is_eventually_in(sK27,sK30,sK29)
| empty_carrier(sK30)
| ~ net_str(sK30,sK27)
| empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| spl32_44 ),
inference(forward_subsumption_resolution,[],[f1549,f289]) ).
fof(f1551,plain,
( empty_carrier(sK30)
| ~ net_str(sK30,sK27)
| empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| spl32_44 ),
inference(forward_subsumption_resolution,[],[f1550,f371]) ).
fof(f1552,plain,
( ~ net_str(sK30,sK27)
| empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| spl32_44 ),
inference(forward_subsumption_resolution,[],[f1551,f420]) ).
fof(f1553,plain,
( empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| spl32_44 ),
inference(forward_subsumption_resolution,[],[f1552,f437]) ).
fof(f1554,plain,
( ~ one_sorted_str(sK27)
| spl32_44 ),
inference(forward_subsumption_resolution,[],[f1553,f364]) ).
fof(f1555,plain,
( $false
| spl32_44 ),
inference(forward_subsumption_resolution,[],[f1554,f363]) ).
fof(f1556,plain,
spl32_44,
inference(avatar_contradiction_clause,[],[f1555]) ).
fof(f1559,plain,
( apply_on_structs(sK30,sK27,the_mapping(sK27,sK30),sK0(sK27,sK30,sK29,sK7(the_carrier(sK30)))) = apply(the_mapping(sK27,sK30),sK0(sK27,sK30,sK29,sK7(the_carrier(sK30))))
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8
| ~ spl32_44 ),
inference(resolution,[],[f1537,f945]) ).
fof(f1564,plain,
( in(sK0(sK27,sK30,sK29,sK7(the_carrier(sK30))),the_carrier(sK30))
| empty(the_carrier(sK30))
| ~ spl32_44 ),
inference(resolution,[],[f1537,f362]) ).
fof(f1565,plain,
( in(sK0(sK27,sK30,sK29,sK7(the_carrier(sK30))),the_carrier(sK30))
| spl32_13
| ~ spl32_44 ),
inference(forward_subsumption_resolution,[],[f1564,f738]) ).
fof(f1568,plain,
( apply_netmap(sK27,sK30,sK0(sK27,sK30,sK29,sK7(the_carrier(sK30)))) = apply(the_mapping(sK27,sK30),sK0(sK27,sK30,sK29,sK7(the_carrier(sK30))))
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8
| ~ spl32_44 ),
inference(forward_demodulation,[],[f1559,f1518]) ).
fof(f1581,plain,
( ! [X0] :
( ~ relation(X0)
| apply(relation_dom_restriction(X0,the_carrier(sK30)),sK0(sK27,sK30,sK29,sK7(the_carrier(sK30)))) = apply(X0,sK0(sK27,sK30,sK29,sK7(the_carrier(sK30))))
| ~ function(X0) )
| spl32_13
| ~ spl32_44 ),
inference(resolution,[],[f1565,f376]) ).
fof(f1951,plain,
( apply(the_mapping(sK27,sK28),sK0(sK27,sK30,sK29,sK7(the_carrier(sK30)))) = apply(relation_dom_restriction(the_mapping(sK27,sK28),the_carrier(sK30)),sK0(sK27,sK30,sK29,sK7(the_carrier(sK30))))
| ~ function(the_mapping(sK27,sK28))
| ~ spl32_1
| spl32_13
| ~ spl32_44 ),
inference(resolution,[],[f1581,f571]) ).
fof(f1955,plain,
( apply(the_mapping(sK27,sK28),sK0(sK27,sK30,sK29,sK7(the_carrier(sK30)))) = apply(relation_dom_restriction(the_mapping(sK27,sK28),the_carrier(sK30)),sK0(sK27,sK30,sK29,sK7(the_carrier(sK30))))
| ~ spl32_1
| ~ spl32_3
| spl32_13
| ~ spl32_44 ),
inference(forward_subsumption_resolution,[],[f1951,f486]) ).
fof(f1959,plain,
( apply(the_mapping(sK27,sK30),sK0(sK27,sK30,sK29,sK7(the_carrier(sK30)))) = apply(the_mapping(sK27,sK28),sK0(sK27,sK30,sK29,sK7(the_carrier(sK30))))
| ~ spl32_1
| ~ spl32_3
| spl32_13
| ~ spl32_44 ),
inference(forward_demodulation,[],[f1955,f553]) ).
fof(f1960,plain,
( apply_netmap(sK27,sK30,sK0(sK27,sK30,sK29,sK7(the_carrier(sK30)))) = apply(the_mapping(sK27,sK28),sK0(sK27,sK30,sK29,sK7(the_carrier(sK30))))
| ~ spl32_1
| ~ spl32_3
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8
| spl32_13
| ~ spl32_44 ),
inference(forward_demodulation,[],[f1959,f1568]) ).
fof(f1961,plain,
( in(apply_netmap(sK27,sK30,sK0(sK27,sK30,sK29,sK7(the_carrier(sK30)))),sK29)
| ~ in(sK0(sK27,sK30,sK29,sK7(the_carrier(sK30))),the_carrier(sK30))
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8
| spl32_13
| ~ spl32_44 ),
inference(superposition,[],[f594,f1960]) ).
fof(f1966,plain,
( in(apply_netmap(sK27,sK30,sK0(sK27,sK30,sK29,sK7(the_carrier(sK30)))),sK29)
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8
| spl32_13
| ~ spl32_44 ),
inference(forward_subsumption_resolution,[],[f1961,f1565]) ).
fof(f1983,plain,
( ~ element(sK7(the_carrier(sK30)),the_carrier(sK30))
| is_eventually_in(sK27,sK30,sK29)
| empty_carrier(sK30)
| ~ net_str(sK30,sK27)
| empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8
| spl32_13
| ~ spl32_44 ),
inference(resolution,[],[f1966,f248]) ).
fof(f1988,plain,
( is_eventually_in(sK27,sK30,sK29)
| empty_carrier(sK30)
| ~ net_str(sK30,sK27)
| empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8
| spl32_13
| ~ spl32_44 ),
inference(forward_subsumption_resolution,[],[f1983,f289]) ).
fof(f1989,plain,
( empty_carrier(sK30)
| ~ net_str(sK30,sK27)
| empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8
| spl32_13
| ~ spl32_44 ),
inference(forward_subsumption_resolution,[],[f1988,f371]) ).
fof(f1990,plain,
( ~ net_str(sK30,sK27)
| empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8
| spl32_13
| ~ spl32_44 ),
inference(forward_subsumption_resolution,[],[f1989,f420]) ).
fof(f1991,plain,
( empty_carrier(sK27)
| ~ one_sorted_str(sK27)
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8
| spl32_13
| ~ spl32_44 ),
inference(forward_subsumption_resolution,[],[f1990,f437]) ).
fof(f1992,plain,
( ~ one_sorted_str(sK27)
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8
| spl32_13
| ~ spl32_44 ),
inference(forward_subsumption_resolution,[],[f1991,f364]) ).
fof(f1993,plain,
( $false
| ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8
| spl32_13
| ~ spl32_44 ),
inference(forward_subsumption_resolution,[],[f1992,f363]) ).
fof(f1994,plain,
( ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8
| spl32_13
| ~ spl32_44 ),
inference(avatar_contradiction_clause,[],[f1993]) ).
cnf(s2,plain,
spl32_1,
inference(sat_conversion,[],[f499]) ).
cnf(s4,plain,
spl32_2,
inference(sat_conversion,[],[f511]) ).
cnf(s6,plain,
spl32_3,
inference(sat_conversion,[],[f543]) ).
cnf(s7,plain,
spl32_4,
inference(sat_conversion,[],[f575]) ).
cnf(s9,plain,
spl32_6,
inference(sat_conversion,[],[f623]) ).
cnf(s11,plain,
spl32_7,
inference(sat_conversion,[],[f650]) ).
cnf(s15,plain,
~ spl32_13,
inference(sat_conversion,[],[f747]) ).
cnf(s23,plain,
spl32_8,
inference(sat_conversion,[],[f931]) ).
cnf(s35,plain,
spl32_44,
inference(sat_conversion,[],[f1556]) ).
cnf(s46,plain,
( ~ spl32_1
| ~ spl32_2
| ~ spl32_3
| ~ spl32_4
| ~ spl32_6
| ~ spl32_7
| ~ spl32_8
| spl32_13
| ~ spl32_44 ),
inference(sat_conversion,[],[f1994]) ).
cnf(s60,plain,
~ spl32_1,
inference(rat,[],[s46,s35,s15,s23,s11,s9,s7,s6,s4]) ).
cnf(s61,plain,
$false,
inference(rat,[],[s2,s60]) ).
fof(f1995,plain,
$false,
inference(avatar_sat_refutation,[],[s61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU379+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n009.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 05:01:15 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.45 Running first-order theorem proving
% 0.16/0.45 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.63/2.47 % (2670775)Detected formulas, will run a generic FOF schedule.
% 11.63/2.47 % (2670786)dis-21_1_sil=8000:lcm=predicate:random_seed=996172659:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 11.63/2.47 % (2670780)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1865250404:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.63/2.47 % (2670782)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2788700475:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.63/2.47 % (2670785)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3504582371:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.63/2.47 % (2670783)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=616626067:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.63/2.47 % (2670781)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3554635159:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.63/2.47 % (2670784)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1683096691:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.63/2.47 % (2670786)Instruction limit reached!
% 11.63/2.47 % (2670786)------------------------------
% 11.63/2.47 % (2670786)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.47 % (2670786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.47 % (2670786)CaDiCaL version: 2.1.3
% 11.63/2.47 % (2670786)Termination reason: Instruction limit
% 11.63/2.47 % (2670786)Termination phase: Saturation
% 11.63/2.47 % (2670786)Time elapsed: 0.040 s
% 11.63/2.47 % (2670786)Peak memory usage: 90 MB
% 11.63/2.47 % (2670786)Instructions burned: 130 (million)
% 11.63/2.47 % (2670783)Refutation not found, incomplete strategy
% 11.63/2.47 % (2670783)------------------------------
% 11.63/2.47 % (2670783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.47 % (2670783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.47 % (2670783)CaDiCaL version: 2.1.3
% 11.63/2.47 % (2670783)Termination reason: Refutation not found, incomplete strategy
% 11.63/2.47 % (2670783)Time elapsed: 0.002 s
% 11.63/2.47 % (2670783)Peak memory usage: 88 MB
% 11.63/2.47 % (2670783)Instructions burned: 2 (million)
% 11.63/2.47 % (2670784)Refutation not found, incomplete strategy
% 11.63/2.47 % (2670784)------------------------------
% 11.63/2.47 % (2670784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.47 % (2670784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.47 % (2670784)CaDiCaL version: 2.1.3
% 11.63/2.47 % (2670784)Termination reason: Refutation not found, incomplete strategy
% 11.63/2.47 % (2670784)Time elapsed: 0.003 s
% 11.63/2.47 % (2670784)Peak memory usage: 88 MB
% 11.63/2.47 % (2670784)Instructions burned: 2 (million)
% 11.63/2.47 % (2670785)Instruction limit reached!
% 11.63/2.47 % (2670785)------------------------------
% 11.63/2.47 % (2670785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.47 % (2670785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.47 % (2670785)CaDiCaL version: 2.1.3
% 11.63/2.47 % (2670785)Termination reason: Instruction limit
% 11.63/2.47 % (2670785)Termination phase: Saturation
% 11.63/2.47 % (2670785)Time elapsed: 0.101 s
% 11.63/2.47 % (2670785)Peak memory usage: 90 MB
% 11.63/2.47 % (2670785)Instructions burned: 140 (million)
% 11.63/2.47 % (2670794)lrs+10_1_sil=8000:sp=occurrence:random_seed=4050271576:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 11.63/2.47 % (2670794)Instruction limit reached!
% 11.63/2.47 % (2670794)------------------------------
% 11.63/2.47 % (2670794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.63/2.47 % (2670794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.63/2.47 % (2670794)CaDiCaL version: 2.1.3
% 11.63/2.47 % (2670794)Termination reason: Instruction limit
% 11.63/2.47 % (2670794)Termination phase: Saturation
% 11.63/2.47 % (2670794)Time elapsed: 0.095 s
% 11.63/2.47 % (2670794)Peak memory usage: 92 MB
% 11.63/2.47 % (2670794)Instructions burned: 285 (million)
% 11.63/2.47 % (2670783)------------------------------
% 12.65/2.69 % (2670783)------------------------------
% 12.65/2.69 % (2670784)------------------------------
% 12.65/2.69 % (2670784)------------------------------
% 12.65/2.69 % (2670795)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1309033249:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 12.65/2.69 % (2670795)Instruction limit reached!
% 12.65/2.69 % (2670795)------------------------------
% 12.65/2.69 % (2670795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.65/2.69 % (2670795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.65/2.69 % (2670795)CaDiCaL version: 2.1.3
% 12.65/2.69 % (2670795)Termination reason: Instruction limit
% 12.65/2.69 % (2670795)Termination phase: Saturation
% 12.65/2.69 % (2670795)Time elapsed: 0.087 s
% 12.65/2.69 % (2670795)Peak memory usage: 89 MB
% 12.65/2.69 % (2670795)Instructions burned: 157 (million)
% 12.65/2.69 % (2670798)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3926177611:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 12.65/2.69 % (2670797)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1127579376:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 12.65/2.69 % (2670799)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3112285144:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 12.65/2.69 % (2670799)Refutation not found, incomplete strategy
% 12.65/2.69 % (2670799)------------------------------
% 12.65/2.69 % (2670799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.65/2.69 % (2670799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.65/2.69 % (2670799)CaDiCaL version: 2.1.3
% 12.65/2.69 % (2670799)Termination reason: Refutation not found, incomplete strategy
% 12.65/2.69 % (2670799)Time elapsed: 0.005 s
% 12.65/2.69 % (2670799)Peak memory usage: 88 MB
% 12.65/2.69 % (2670799)Instructions burned: 6 (million)
% 12.65/2.69 % (2670798)Instruction limit reached!
% 12.65/2.69 % (2670798)------------------------------
% 12.65/2.69 % (2670798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.65/2.69 % (2670798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.65/2.69 % (2670798)CaDiCaL version: 2.1.3
% 12.65/2.69 % (2670798)Termination reason: Instruction limit
% 12.65/2.69 % (2670798)Termination phase: Saturation
% 12.65/2.69 % (2670798)Time elapsed: 0.084 s
% 12.65/2.69 % (2670798)Peak memory usage: 91 MB
% 12.65/2.69 % (2670798)Instructions burned: 250 (million)
% 12.65/2.69 % (2670802)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1664009813:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 12.65/2.69 % (2670797)Instruction limit reached!
% 12.65/2.69 % (2670797)------------------------------
% 12.65/2.69 % (2670797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.65/2.69 % (2670797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.65/2.69 % (2670797)CaDiCaL version: 2.1.3
% 12.65/2.69 % (2670797)Termination reason: Instruction limit
% 12.65/2.69 % (2670797)Termination phase: Saturation
% 12.65/2.69 % (2670797)Time elapsed: 0.184 s
% 12.65/2.69 % (2670797)Peak memory usage: 91 MB
% 12.65/2.69 % (2670797)Instructions burned: 325 (million)
% 12.65/2.69 % (2670805)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3515773652:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 12.65/2.69 % (2670805)Instruction limit reached!
% 12.65/2.69 % (2670805)------------------------------
% 12.65/2.69 % (2670805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.65/2.69 % (2670805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.65/2.69 % (2670805)CaDiCaL version: 2.1.3
% 12.65/2.69 % (2670805)Termination reason: Instruction limit
% 12.65/2.69 % (2670805)Termination phase: Saturation
% 12.65/2.69 % (2670805)Time elapsed: 0.044 s
% 12.65/2.69 % (2670805)Peak memory usage: 91 MB
% 12.65/2.69 % (2670805)Instructions burned: 115 (million)
% 12.65/2.69 % (2670799)------------------------------
% 12.65/2.69 % (2670799)------------------------------
% 12.65/2.69 % (2670807)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1125243055:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 12.65/2.69 % (2670809)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2248027191:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 12.65/2.69 % (2670809)Instruction limit reached!
% 12.65/2.69 % (2670809)------------------------------
% 12.65/2.69 % (2670809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.65/2.69 % (2670809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.65/2.69 % (2670809)CaDiCaL version: 2.1.3
% 12.65/2.69 % (2670809)Termination reason: Instruction limit
% 12.65/2.69 % (2670809)Termination phase: Saturation
% 12.65/2.69 % (2670809)Time elapsed: 0.037 s
% 12.65/2.69 % (2670809)Peak memory usage: 89 MB
% 12.65/2.69 % (2670809)Instructions burned: 116 (million)
% 12.65/2.69 % (2670807)Instruction limit reached!
% 12.65/2.69 % (2670807)------------------------------
% 12.65/2.69 % (2670807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.65/2.69 % (2670807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.65/2.69 % (2670807)CaDiCaL version: 2.1.3
% 12.65/2.69 % (2670807)Termination reason: Instruction limit
% 12.65/2.69 % (2670807)Termination phase: Saturation
% 12.65/2.69 % (2670807)Time elapsed: 0.070 s
% 12.65/2.69 % (2670807)Peak memory usage: 89 MB
% 12.65/2.69 % (2670807)Instructions burned: 128 (million)
% 12.65/2.69 % (2670810)lrs+10_1_sil=8000:sp=occurrence:random_seed=319019581:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 12.65/2.69 % (2670814)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1563312478:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 12.65/2.69 % (2670813)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=166337758:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 12.65/2.69 % (2670813)Refutation not found, incomplete strategy
% 12.65/2.69 % (2670813)------------------------------
% 12.65/2.69 % (2670813)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.65/2.69 % (2670813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.65/2.69 % (2670813)CaDiCaL version: 2.1.3
% 12.65/2.69 % (2670813)Termination reason: Refutation not found, incomplete strategy
% 12.65/2.69 % (2670813)Time elapsed: 0.006 s
% 12.65/2.69 % (2670813)Peak memory usage: 88 MB
% 12.65/2.69 % (2670813)Instructions burned: 8 (million)
% 12.65/2.69 % (2670813)------------------------------
% 12.65/2.69 % (2670813)------------------------------
% 12.65/2.69 % (2670818)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1440820146:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2986 on theBenchmark for (2986ds/134Mi)
% 12.65/2.69 % (2670810)Instruction limit reached!
% 12.65/2.69 % (2670810)------------------------------
% 12.65/2.69 % (2670810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.65/2.69 % (2670810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.65/2.69 % (2670810)CaDiCaL version: 2.1.3
% 12.65/2.69 % (2670810)Termination reason: Instruction limit
% 12.65/2.69 % (2670810)Termination phase: Saturation
% 12.65/2.69 % (2670810)Time elapsed: 0.556 s
% 12.65/2.69 % (2670810)Peak memory usage: 100 MB
% 12.65/2.69 % (2670810)Instructions burned: 908 (million)
% 12.65/2.69 % (2670818)Instruction limit reached!
% 12.65/2.69 % (2670818)------------------------------
% 12.65/2.69 % (2670818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.65/2.69 % (2670818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.65/2.69 % (2670818)CaDiCaL version: 2.1.3
% 12.65/2.69 % (2670818)Termination reason: Instruction limit
% 12.65/2.69 % (2670818)Termination phase: Saturation
% 12.65/2.69 % (2670818)Time elapsed: 0.072 s
% 12.65/2.69 % (2670818)Peak memory usage: 90 MB
% 12.65/2.69 % (2670818)Instructions burned: 135 (million)
% 12.65/2.69 % (2670802)First to succeed.
% 12.65/2.69 % (2670802)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2670775"
% 12.65/2.69 % (2670820)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=809042452:st=8:i=592:sd=3:ep=RST:ss=axioms_2984 on theBenchmark for (2984ds/592Mi)
% 12.65/2.69 % (2670820)Refutation not found, incomplete strategy
% 12.65/2.69 % (2670820)------------------------------
% 12.65/2.69 % (2670820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.65/2.69 % (2670820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.65/2.69 % (2670820)CaDiCaL version: 2.1.3
% 12.65/2.69 % (2670820)Termination reason: Refutation not found, incomplete strategy
% 12.65/2.69 % (2670820)Time elapsed: 0.005 s
% 12.65/2.69 % (2670820)Peak memory usage: 88 MB
% 12.65/2.69 % (2670820)Instructions burned: 8 (million)
% 12.65/2.69 % (2670821)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2725968826:st=3:i=13193:sd=3:ss=axioms_2984 on theBenchmark for (2984ds/13193Mi)
% 12.65/2.69 % (2670802)Refutation found. Thanks to Tanya!
% 12.65/2.69 % SZS status Theorem for theBenchmark
% 12.65/2.69 % SZS output start Proof for theBenchmark
% See solution above
% 13.94/2.89 % (2670802)------------------------------
% 13.94/2.89 % (2670802)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.94/2.89 % (2670802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.94/2.89 % (2670802)CaDiCaL version: 2.1.3
% 13.94/2.89 % (2670802)Termination reason: Refutation
% 13.94/2.89 % (2670802)Time elapsed: 0.971 s
% 13.94/2.89 % (2670802)Peak memory usage: 134 MB
% 13.94/2.89 % (2670802)Instructions burned: 1433 (million)
% 13.94/2.89 % (2670802)------------------------------
% 13.94/2.89 % (2670802)------------------------------
% 13.94/2.89 % (2670775)Success in time 1.903 s
% 13.94/2.89 % Vampire exiting
%------------------------------------------------------------------------------