TSTP Solution File: SEU323-10 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU323-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 : Tue Sep 20 07:28:55 EDT 2022
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 82
% Syntax : Number of formulae : 204 ( 133 unt; 18 typ; 0 def)
% Number of atoms : 275 ( 256 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 97 ( 26 ~; 13 |; 0 &)
% ( 58 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 25 ( 13 >; 12 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-4 aty)
% Number of variables : 266 ( 228 !; 0 ?; 266 :)
% Comments :
%------------------------------------------------------------------------------
tff(topological_space_type,type,
topological_space: $i > $i ).
tff(sK2_t51_tops_1_A_type,type,
sK2_t51_tops_1_A: $i ).
tff(open_subset_type,type,
open_subset: ( $i * $i ) > $i ).
tff(interior_type,type,
interior: ( $i * $i ) > $i ).
tff(sK1_t51_tops_1_B_type,type,
sK1_t51_tops_1_B: $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(subset_complement_type,type,
subset_complement: ( $i * $i ) > $i ).
tff(topstr_closure_type,type,
topstr_closure: ( $i * $i ) > $i ).
tff(the_carrier_type,type,
the_carrier: $i > $i ).
tff(top_str_type,type,
top_str: $i > $i ).
tff(closed_subset_type,type,
closed_subset: ( $i * $i ) > $i ).
tff(element_type,type,
element: ( $i * $i ) > $i ).
tff(powerset_type,type,
powerset: $i > $i ).
tff(one_sorted_str_type,type,
one_sorted_str: $i > $i ).
tff(sK6_existence_l1_struct_0_A_type,type,
sK6_existence_l1_struct_0_A: $i ).
tff(true_type,type,
true: $i ).
tff(sK5_existence_l1_pre_topc_A_type,type,
sK5_existence_l1_pre_topc_A: $i ).
tff(ifeq2_type,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(closed_subset(B,A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(A),B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) )
<=> ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(closed_subset(B,A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(A),B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(closed_subset(B,A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(A),B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(closed_subset(B,A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(A),B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [B: $i,A: $i] :
rewrite(
( ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(closed_subset(B,A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),open_subset(subset_complement(the_carrier(A),B),A),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) )
<=> ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(closed_subset(B,A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(A),B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(closed_subset(B,A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),open_subset(subset_complement(the_carrier(A),B),A),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(closed_subset(B,A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(A),B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [B: $i,A: $i] :
rewrite(
( ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(closed_subset(B,A),true,ifeq(topological_space(A),true,ifeq(top_str(A),true,open_subset(subset_complement(the_carrier(A),B),A),true),true),true),true) = true )
<=> ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(closed_subset(B,A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),open_subset(subset_complement(the_carrier(A),B),A),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(closed_subset(B,A),true,ifeq(topological_space(A),true,ifeq(top_str(A),true,open_subset(subset_complement(the_carrier(A),B),A),true),true),true),true) = true )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(closed_subset(B,A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),open_subset(subset_complement(the_carrier(A),B),A),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(closed_subset(B,A),true,ifeq(topological_space(A),true,ifeq(top_str(A),true,open_subset(subset_complement(the_carrier(A),B),A),true),true),true),true) = true )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(closed_subset(B,A),true,ifeq(topological_space(A),true,ifeq(top_str(A),true,open_subset(subset_complement(the_carrier(A),B),A),true),true),true),true) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(closed_subset(B,A),true,ifeq(topological_space(A),true,ifeq(top_str(A),true,open_subset(subset_complement(the_carrier(A),B),A),true),true),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_tops_1) ).
tff(9,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(closed_subset(B,A),true,ifeq(topological_space(A),true,ifeq(top_str(A),true,open_subset(subset_complement(the_carrier(A),B),A),true),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(closed_subset(B,A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),open_subset(subset_complement(the_carrier(A),B),A),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) ),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(closed_subset(B,A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(A),B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ),
inference(modus_ponens,[status(thm)],[10,4]) ).
tff(12,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(closed_subset(B,A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(A),B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(closed_subset(B,A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(A),B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ),
inference(modus_ponens,[status(thm)],[12,2]) ).
tff(14,plain,
( ~ ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(closed_subset(B,A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(A),B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) )
| ( ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ifeq(A,A,B,C) = B )
<=> ( ifeq(A,A,B,C) = B ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
tff(20,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ( top_str(sK5_existence_l1_pre_topc_A) = one_sorted_str(sK6_existence_l1_struct_0_A) )
<=> ( topological_space(sK2_t51_tops_1_A) = one_sorted_str(sK6_existence_l1_struct_0_A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ( top_str(sK5_existence_l1_pre_topc_A) = true )
<=> ( top_str(sK5_existence_l1_pre_topc_A) = one_sorted_str(sK6_existence_l1_struct_0_A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( top_str(sK5_existence_l1_pre_topc_A) = true )
<=> ( top_str(sK5_existence_l1_pre_topc_A) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
top_str(sK5_existence_l1_pre_topc_A) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
tff(29,plain,
top_str(sK5_existence_l1_pre_topc_A) = true,
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
top_str(sK5_existence_l1_pre_topc_A) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(modus_ponens,[status(thm)],[29,26]) ).
tff(31,plain,
topological_space(sK2_t51_tops_1_A) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(modus_ponens,[status(thm)],[30,25]) ).
tff(32,plain,
one_sorted_str(sK6_existence_l1_struct_0_A) = topological_space(sK2_t51_tops_1_A),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),
inference(monotonicity,[status(thm)],[32,32,32]) ).
tff(34,plain,
ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),
inference(transitivity,[status(thm)],[34,24]) ).
tff(36,plain,
^ [B: $i,A: $i] :
refl(
( ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(A,B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) )
<=> ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(A,B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(A,B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(A,B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
^ [B: $i,A: $i] :
rewrite(
( ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(A,B),A),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) )
<=> ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(A,B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(A,B),A),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(A,B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
^ [B: $i,A: $i] :
rewrite(
( ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(topological_space(A),true,ifeq(top_str(A),true,closed_subset(topstr_closure(A,B),A),true),true),true) = true )
<=> ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(A,B),A),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(topological_space(A),true,ifeq(top_str(A),true,closed_subset(topstr_closure(A,B),A),true),true),true) = true )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(A,B),A),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(topological_space(A),true,ifeq(top_str(A),true,closed_subset(topstr_closure(A,B),A),true),true),true) = true )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(topological_space(A),true,ifeq(top_str(A),true,closed_subset(topstr_closure(A,B),A),true),true),true) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(topological_space(A),true,ifeq(top_str(A),true,closed_subset(topstr_closure(A,B),A),true),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tops_1) ).
tff(44,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(topological_space(A),true,ifeq(top_str(A),true,closed_subset(topstr_closure(A,B),A),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(A,B),A),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) ),
inference(modus_ponens,[status(thm)],[44,41]) ).
tff(46,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(A,B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ),
inference(modus_ponens,[status(thm)],[45,39]) ).
tff(47,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(A,B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(A,B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ),
inference(modus_ponens,[status(thm)],[47,37]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(A,B),A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) )
| ( ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),
inference(monotonicity,[status(thm)],[32,32,32]) ).
tff(52,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),
inference(unit_resolution,[status(thm)],[52,22]) ).
tff(54,plain,
ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)) = ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)) = ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),
inference(transitivity,[status(thm)],[54,51]) ).
tff(56,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),one_sorted_str(sK6_existence_l1_struct_0_A)) = element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),one_sorted_str(sK6_existence_l1_struct_0_A)) = element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),
inference(unit_resolution,[status(thm)],[56,22]) ).
tff(58,plain,
( ( element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = top_str(sK5_existence_l1_pre_topc_A) )
<=> ( element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = topological_space(sK2_t51_tops_1_A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = one_sorted_str(sK6_existence_l1_struct_0_A) )
<=> ( element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = top_str(sK5_existence_l1_pre_topc_A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = true )
<=> ( element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = one_sorted_str(sK6_existence_l1_struct_0_A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ( element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = true )
<=> ( element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1_2) ).
tff(63,plain,
element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = true,
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(modus_ponens,[status(thm)],[63,60]) ).
tff(65,plain,
element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = top_str(sK5_existence_l1_pre_topc_A),
inference(modus_ponens,[status(thm)],[64,59]) ).
tff(66,plain,
element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = topological_space(sK2_t51_tops_1_A),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
topological_space(sK2_t51_tops_1_A) = element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
one_sorted_str(sK6_existence_l1_struct_0_A) = element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),
inference(transitivity,[status(thm)],[32,67]) ).
tff(69,plain,
ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),one_sorted_str(sK6_existence_l1_struct_0_A)) = ifeq(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)),
inference(monotonicity,[status(thm)],[68,32,32]) ).
tff(70,plain,
ifeq(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)) = ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
^ [B: $i,A: $i] :
refl(
( ( ifeq(element(B,powerset(A)),topological_space(sK2_t51_tops_1_A),element(subset_complement(A,B),powerset(A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) )
<=> ( ifeq(element(B,powerset(A)),topological_space(sK2_t51_tops_1_A),element(subset_complement(A,B),powerset(A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),topological_space(sK2_t51_tops_1_A),element(subset_complement(A,B),powerset(A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),topological_space(sK2_t51_tops_1_A),element(subset_complement(A,B),powerset(A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
^ [B: $i,A: $i] :
rewrite(
( ( ifeq(element(B,powerset(A)),one_sorted_str(sK6_existence_l1_struct_0_A),element(subset_complement(A,B),powerset(A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) )
<=> ( ifeq(element(B,powerset(A)),topological_space(sK2_t51_tops_1_A),element(subset_complement(A,B),powerset(A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),one_sorted_str(sK6_existence_l1_struct_0_A),element(subset_complement(A,B),powerset(A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),topological_space(sK2_t51_tops_1_A),element(subset_complement(A,B),powerset(A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
^ [B: $i,A: $i] :
rewrite(
( ( ifeq(element(B,powerset(A)),true,element(subset_complement(A,B),powerset(A)),true) = true )
<=> ( ifeq(element(B,powerset(A)),one_sorted_str(sK6_existence_l1_struct_0_A),element(subset_complement(A,B),powerset(A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) ) )),
inference(bind,[status(th)],]) ).
tff(76,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),true,element(subset_complement(A,B),powerset(A)),true) = true )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),one_sorted_str(sK6_existence_l1_struct_0_A),element(subset_complement(A,B),powerset(A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),true,element(subset_complement(A,B),powerset(A)),true) = true )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),true,element(subset_complement(A,B),powerset(A)),true) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),true,element(subset_complement(A,B),powerset(A)),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
tff(79,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),true,element(subset_complement(A,B),powerset(A)),true) = true ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),one_sorted_str(sK6_existence_l1_struct_0_A),element(subset_complement(A,B),powerset(A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) ),
inference(modus_ponens,[status(thm)],[79,76]) ).
tff(81,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),topological_space(sK2_t51_tops_1_A),element(subset_complement(A,B),powerset(A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ),
inference(modus_ponens,[status(thm)],[80,74]) ).
tff(82,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),topological_space(sK2_t51_tops_1_A),element(subset_complement(A,B),powerset(A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),topological_space(sK2_t51_tops_1_A),element(subset_complement(A,B),powerset(A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ),
inference(modus_ponens,[status(thm)],[82,72]) ).
tff(84,plain,
( ~ ! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),topological_space(sK2_t51_tops_1_A),element(subset_complement(A,B),powerset(A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) )
| ( ifeq(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
ifeq(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
topological_space(sK2_t51_tops_1_A) = ifeq(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
topological_space(sK2_t51_tops_1_A) = element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),
inference(transitivity,[status(thm)],[86,70,57]) ).
tff(88,plain,
ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),
inference(monotonicity,[status(thm)],[87,55]) ).
tff(89,plain,
( ( top_str(sK2_t51_tops_1_A) = top_str(sK5_existence_l1_pre_topc_A) )
<=> ( top_str(sK2_t51_tops_1_A) = topological_space(sK2_t51_tops_1_A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( top_str(sK2_t51_tops_1_A) = one_sorted_str(sK6_existence_l1_struct_0_A) )
<=> ( top_str(sK2_t51_tops_1_A) = top_str(sK5_existence_l1_pre_topc_A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ( top_str(sK2_t51_tops_1_A) = true )
<=> ( top_str(sK2_t51_tops_1_A) = one_sorted_str(sK6_existence_l1_struct_0_A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ( top_str(sK2_t51_tops_1_A) = true )
<=> ( top_str(sK2_t51_tops_1_A) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,axiom,
top_str(sK2_t51_tops_1_A) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
tff(94,plain,
top_str(sK2_t51_tops_1_A) = true,
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
top_str(sK2_t51_tops_1_A) = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(modus_ponens,[status(thm)],[94,91]) ).
tff(96,plain,
top_str(sK2_t51_tops_1_A) = top_str(sK5_existence_l1_pre_topc_A),
inference(modus_ponens,[status(thm)],[95,90]) ).
tff(97,plain,
top_str(sK2_t51_tops_1_A) = topological_space(sK2_t51_tops_1_A),
inference(modus_ponens,[status(thm)],[96,89]) ).
tff(98,plain,
topological_space(sK2_t51_tops_1_A) = top_str(sK2_t51_tops_1_A),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
one_sorted_str(sK6_existence_l1_struct_0_A) = top_str(sK2_t51_tops_1_A),
inference(transitivity,[status(thm)],[32,98]) ).
tff(100,plain,
ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),one_sorted_str(sK6_existence_l1_struct_0_A)) = ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),
inference(monotonicity,[status(thm)],[99,32,32]) ).
tff(101,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),one_sorted_str(sK6_existence_l1_struct_0_A)) = closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),one_sorted_str(sK6_existence_l1_struct_0_A)) = closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),
inference(unit_resolution,[status(thm)],[101,22]) ).
tff(103,plain,
closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A) = ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A) = topological_space(sK2_t51_tops_1_A),
inference(transitivity,[status(thm)],[103,100,54,51,88,50]) ).
tff(105,plain,
ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),
inference(monotonicity,[status(thm)],[104,35]) ).
tff(106,plain,
ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)) = ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(symmetry,[status(thm)],[24]) ).
tff(108,plain,
ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)) = ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),
inference(transitivity,[status(thm)],[107,33,106]) ).
tff(109,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),one_sorted_str(sK6_existence_l1_struct_0_A)) = element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),one_sorted_str(sK6_existence_l1_struct_0_A)) = element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),
inference(unit_resolution,[status(thm)],[109,22]) ).
tff(111,plain,
ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),one_sorted_str(sK6_existence_l1_struct_0_A)) = ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)),
inference(monotonicity,[status(thm)],[99,32,32]) ).
tff(112,plain,
ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)) = ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))) = ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(symmetry,[status(thm)],[110]) ).
tff(114,plain,
element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))) = ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)),
inference(transitivity,[status(thm)],[113,111]) ).
tff(115,plain,
top_str(sK2_t51_tops_1_A) = element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),
inference(transitivity,[status(thm)],[97,86,70,57]) ).
tff(116,plain,
ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)) = ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),
inference(monotonicity,[status(thm)],[115,114]) ).
tff(117,plain,
ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
^ [B: $i,A: $i] :
refl(
( ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(A,B),powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) )
<=> ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(A,B),powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) )),
inference(bind,[status(th)],]) ).
tff(119,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(A,B),powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(A,B),powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
^ [B: $i,A: $i] :
rewrite(
( ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(A,B),powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) )
<=> ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(A,B),powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(A,B),powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(A,B),powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
^ [B: $i,A: $i] :
rewrite(
( ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(top_str(A),true,element(topstr_closure(A,B),powerset(the_carrier(A))),true),true) = true )
<=> ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(A,B),powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(top_str(A),true,element(topstr_closure(A,B),powerset(the_carrier(A))),true),true) = true )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(A,B),powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(top_str(A),true,element(topstr_closure(A,B),powerset(the_carrier(A))),true),true) = true )
<=> ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(top_str(A),true,element(topstr_closure(A,B),powerset(the_carrier(A))),true),true) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,axiom,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(top_str(A),true,element(topstr_closure(A,B),powerset(the_carrier(A))),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
tff(126,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),true,ifeq(top_str(A),true,element(topstr_closure(A,B),powerset(the_carrier(A))),true),true) = true ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(A,B),powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)) = one_sorted_str(sK6_existence_l1_struct_0_A) ),
inference(modus_ponens,[status(thm)],[126,123]) ).
tff(128,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(A,B),powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ),
inference(modus_ponens,[status(thm)],[127,121]) ).
tff(129,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(A,B),powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ),
inference(skolemize,[status(sab)],[128]) ).
tff(130,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(A,B),powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ),
inference(modus_ponens,[status(thm)],[129,119]) ).
tff(131,plain,
( ~ ! [B: $i,A: $i] : ( ifeq(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(A,B),powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) )
| ( ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(132,plain,
ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = topological_space(sK2_t51_tops_1_A),
inference(unit_resolution,[status(thm)],[131,130]) ).
tff(133,plain,
topological_space(sK2_t51_tops_1_A) = ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
topological_space(sK2_t51_tops_1_A) = element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),
inference(transitivity,[status(thm)],[133,117,112,110]) ).
tff(135,plain,
ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)) = ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),
inference(monotonicity,[status(thm)],[134,108]) ).
tff(136,plain,
^ [B: $i,A: $i] :
refl(
( ( ifeq2(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq2(top_str(A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) )
<=> ( ifeq2(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq2(top_str(A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ) )),
inference(bind,[status(th)],]) ).
tff(137,plain,
( ! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq2(top_str(A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) )
<=> ! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq2(top_str(A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,plain,
^ [B: $i,A: $i] :
rewrite(
( ( ifeq2(element(B,powerset(the_carrier(A))),top_str(sK5_existence_l1_pre_topc_A),ifeq2(top_str(A),top_str(sK5_existence_l1_pre_topc_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) )
<=> ( ifeq2(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq2(top_str(A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ) )),
inference(bind,[status(th)],]) ).
tff(139,plain,
( ! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),top_str(sK5_existence_l1_pre_topc_A),ifeq2(top_str(A),top_str(sK5_existence_l1_pre_topc_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) )
<=> ! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq2(top_str(A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,plain,
^ [B: $i,A: $i] :
rewrite(
( ( ifeq2(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq2(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) )
<=> ( ifeq2(element(B,powerset(the_carrier(A))),top_str(sK5_existence_l1_pre_topc_A),ifeq2(top_str(A),top_str(sK5_existence_l1_pre_topc_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ) )),
inference(bind,[status(th)],]) ).
tff(141,plain,
( ! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq2(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) )
<=> ! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),top_str(sK5_existence_l1_pre_topc_A),ifeq2(top_str(A),top_str(sK5_existence_l1_pre_topc_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,plain,
^ [B: $i,A: $i] :
rewrite(
( ( ifeq2(element(B,powerset(the_carrier(A))),true,ifeq2(top_str(A),true,subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) )
<=> ( ifeq2(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq2(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ) )),
inference(bind,[status(th)],]) ).
tff(143,plain,
( ! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),true,ifeq2(top_str(A),true,subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) )
<=> ! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq2(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,plain,
( ! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),true,ifeq2(top_str(A),true,subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) )
<=> ! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),true,ifeq2(top_str(A),true,subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(145,axiom,
! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),true,ifeq2(top_str(A),true,subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
tff(146,plain,
! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),true,ifeq2(top_str(A),true,subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq2(top_str(A),one_sorted_str(sK6_existence_l1_struct_0_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ),
inference(modus_ponens,[status(thm)],[146,143]) ).
tff(148,plain,
! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),top_str(sK5_existence_l1_pre_topc_A),ifeq2(top_str(A),top_str(sK5_existence_l1_pre_topc_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ),
inference(modus_ponens,[status(thm)],[147,141]) ).
tff(149,plain,
! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq2(top_str(A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ),
inference(modus_ponens,[status(thm)],[148,139]) ).
tff(150,plain,
! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq2(top_str(A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ),
inference(skolemize,[status(sab)],[149]) ).
tff(151,plain,
! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq2(top_str(A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) ),
inference(modus_ponens,[status(thm)],[150,137]) ).
tff(152,plain,
( ~ ! [B: $i,A: $i] : ( ifeq2(element(B,powerset(the_carrier(A))),topological_space(sK2_t51_tops_1_A),ifeq2(top_str(A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))),interior(A,B)),interior(A,B)) = interior(A,B) )
| ( ifeq2(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),ifeq2(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
ifeq2(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),ifeq2(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),
inference(unit_resolution,[status(thm)],[152,151]) ).
tff(154,plain,
ifeq2(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq2(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = ifeq2(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),topological_space(sK2_t51_tops_1_A),ifeq2(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),
inference(monotonicity,[status(thm)],[68,32]) ).
tff(155,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ifeq2(A,A,B,C) = B )
<=> ( ifeq2(A,A,B,C) = B ) )),
inference(bind,[status(th)],]) ).
tff(156,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(159,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[159]) ).
tff(161,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq2(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = ifeq2(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(163,plain,
ifeq2(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq2(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = ifeq2(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),
inference(unit_resolution,[status(thm)],[162,161]) ).
tff(164,plain,
ifeq2(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = ifeq2(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq2(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
ifeq2(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = ifeq2(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),
inference(monotonicity,[status(thm)],[99,32]) ).
tff(166,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(167,plain,
ifeq2(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),
inference(unit_resolution,[status(thm)],[166,161]) ).
tff(168,plain,
subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))) = ifeq2(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))) = interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),
inference(transitivity,[status(thm)],[168,165,164,154,153]) ).
tff(170,plain,
open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A) = open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) = open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),one_sorted_str(sK6_existence_l1_struct_0_A)) = ifeq(top_str(sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A),open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),sK2_t51_tops_1_A),topological_space(sK2_t51_tops_1_A)),
inference(monotonicity,[status(thm)],[99,32,171,32]) ).
tff(173,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),one_sorted_str(sK6_existence_l1_struct_0_A)) = open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),one_sorted_str(sK6_existence_l1_struct_0_A)) = open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),
inference(unit_resolution,[status(thm)],[173,22]) ).
tff(175,plain,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) = ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) = topological_space(sK2_t51_tops_1_A),
inference(transitivity,[status(thm)],[175,172,107,33,135,15]) ).
tff(177,plain,
( ( open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != top_str(sK5_existence_l1_pre_topc_A) )
<=> ( open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != topological_space(sK2_t51_tops_1_A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(178,plain,
( ( open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != one_sorted_str(sK6_existence_l1_struct_0_A) )
<=> ( open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != top_str(sK5_existence_l1_pre_topc_A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(179,plain,
( ( open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != true )
<=> ( open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != one_sorted_str(sK6_existence_l1_struct_0_A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(180,plain,
( ( open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != true )
<=> ( open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != true ) ),
inference(rewrite,[status(thm)],]) ).
tff(181,axiom,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1_3) ).
tff(182,plain,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != true,
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != one_sorted_str(sK6_existence_l1_struct_0_A),
inference(modus_ponens,[status(thm)],[182,179]) ).
tff(184,plain,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != top_str(sK5_existence_l1_pre_topc_A),
inference(modus_ponens,[status(thm)],[183,178]) ).
tff(185,plain,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != topological_space(sK2_t51_tops_1_A),
inference(modus_ponens,[status(thm)],[184,177]) ).
tff(186,plain,
$false,
inference(unit_resolution,[status(thm)],[185,176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU323-10 : TPTP v8.1.0. Released v7.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 12:14:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------