%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU323-10 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 : Sat Jun 21 05:27:36 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 42
% Syntax : Number of formulae : 129 ( 98 unt; 0 typ; 0 def)
% Number of atoms : 174 ( 166 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 55 ( 17 ~; 13 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-4 aty)
% Number of variables : 178 ( 162 !; 0 ?; 178 :)
% Comments :
%------------------------------------------------------------------------------
tff(true_type,type,
true: $i ).
tff(open_subset_type,type,
open_subset: ( $i * $i ) > $i ).
tff(sK2_t51_tops_1_A_type,type,
sK2_t51_tops_1_A: $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(topological_space_type,type,
topological_space: $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(ifeq2_type,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( 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))),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(bind,[status(th)],[]) ).
tff(2,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(quant_intro,[status(thm)],[1]) ).
tff(3,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(4,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(5,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)],[4,3]) ).
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 ),
inference(skolemize,[status(sab)],[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 ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,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 )
| ( 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))),true,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),true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,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))),true,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),true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),true),true) = true,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true) = ifeq(top_str(sK2_t51_tops_1_A),true,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),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true) = ifeq(top_str(sK2_t51_tops_1_A),true,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),true),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ( topological_space(sK2_t51_tops_1_A) = true )
<=> ( topological_space(sK2_t51_tops_1_A) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
topological_space(sK2_t51_tops_1_A) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1_1) ).
tff(21,plain,
topological_space(sK2_t51_tops_1_A) = true,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
true = topological_space(sK2_t51_tops_1_A),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true) = ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true) = ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true) = ifeq(top_str(sK2_t51_tops_1_A),true,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),true),
inference(transitivity,[status(thm)],[24,18]) ).
tff(26,plain,
^ [B: $i,A: $i] :
refl(( ( 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))),true,ifeq(topological_space(A),true,ifeq(top_str(A),true,closed_subset(topstr_closure(A,B),A),true),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(27,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(quant_intro,[status(thm)],[26]) ).
tff(28,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(29,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(30,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)],[29,28]) ).
tff(31,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(skolemize,[status(sab)],[30]) ).
tff(32,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)],[31,27]) ).
tff(33,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 )
| ( ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,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))),true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),true) = true,
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true) = ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),
inference(monotonicity,[status(thm)],[22]) ).
tff(36,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true) = ifeq(top_str(sK2_t51_tops_1_A),true,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),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true) = ifeq(top_str(sK2_t51_tops_1_A),true,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),true),
inference(unit_resolution,[status(thm)],[36,16]) ).
tff(38,plain,
ifeq(top_str(sK2_t51_tops_1_A),true,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),true) = ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
ifeq(top_str(sK2_t51_tops_1_A),true,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),true) = ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),
inference(transitivity,[status(thm)],[38,35]) ).
tff(40,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true) = 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(41,plain,
ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true) = 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)],[40,16]) ).
tff(42,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(43,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(44,plain,
element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = true,
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
true = element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true) = ifeq(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
ifeq(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true) = ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
^ [B: $i,A: $i] :
refl(( ( ifeq(element(B,powerset(A)),true,element(subset_complement(A,B),powerset(A)),true) = true )
<=> ( ifeq(element(B,powerset(A)),true,element(subset_complement(A,B),powerset(A)),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(49,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(quant_intro,[status(thm)],[48]) ).
tff(50,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(51,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(52,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)],[51,50]) ).
tff(53,plain,
! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),true,element(subset_complement(A,B),powerset(A)),true) = true ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,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)],[53,49]) ).
tff(55,plain,
( ~ ! [B: $i,A: $i] : ( ifeq(element(B,powerset(A)),true,element(subset_complement(A,B),powerset(A)),true) = true )
| ( ifeq(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
ifeq(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true) = true,
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
true = ifeq(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true),
inference(symmetry,[status(thm)],[56]) ).
tff(58,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)],[21,57,47,41]) ).
tff(59,plain,
ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true) = ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),true),
inference(monotonicity,[status(thm)],[58,39]) ).
tff(60,plain,
( ( top_str(sK2_t51_tops_1_A) = true )
<=> ( top_str(sK2_t51_tops_1_A) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
top_str(sK2_t51_tops_1_A) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
tff(62,plain,
top_str(sK2_t51_tops_1_A) = true,
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
true = top_str(sK2_t51_tops_1_A),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
ifeq(true,true,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),true) = ifeq(top_str(sK2_t51_tops_1_A),true,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),true),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,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),true) = 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(66,plain,
ifeq(true,true,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),true) = 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)],[65,16]) ).
tff(67,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(true,true,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),true),
inference(symmetry,[status(thm)],[66]) ).
tff(68,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)],[67,64,38,35,59,34,22]) ).
tff(69,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),true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),true) = ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),
inference(monotonicity,[status(thm)],[68,25]) ).
tff(70,plain,
ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true) = 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),true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),true),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
ifeq(top_str(sK2_t51_tops_1_A),true,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),true) = ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),
inference(symmetry,[status(thm)],[18]) ).
tff(72,plain,
ifeq(top_str(sK2_t51_tops_1_A),true,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),true) = 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),true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),true),
inference(transitivity,[status(thm)],[71,23,70]) ).
tff(73,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,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))),true) = 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(74,plain,
ifeq(true,true,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))),true) = 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)],[73,16]) ).
tff(75,plain,
ifeq(true,true,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))),true) = ifeq(top_str(sK2_t51_tops_1_A),true,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))),true),
inference(monotonicity,[status(thm)],[63]) ).
tff(76,plain,
ifeq(top_str(sK2_t51_tops_1_A),true,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))),true) = ifeq(true,true,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))),true),
inference(symmetry,[status(thm)],[75]) ).
tff(77,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(true,true,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))),true),
inference(symmetry,[status(thm)],[74]) ).
tff(78,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),true,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))),true),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,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)],[62,57,47,41]) ).
tff(80,plain,
ifeq(top_str(sK2_t51_tops_1_A),true,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))),true) = ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(top_str(sK2_t51_tops_1_A),true,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))),true),true),
inference(monotonicity,[status(thm)],[79,78]) ).
tff(81,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))),true,ifeq(top_str(sK2_t51_tops_1_A),true,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))),true),true) = ifeq(top_str(sK2_t51_tops_1_A),true,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))),true),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
^ [B: $i,A: $i] :
refl(( ( 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))),true,ifeq(top_str(A),true,element(topstr_closure(A,B),powerset(the_carrier(A))),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(83,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(quant_intro,[status(thm)],[82]) ).
tff(84,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(85,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(86,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)],[85,84]) ).
tff(87,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(skolemize,[status(sab)],[86]) ).
tff(88,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)],[87,83]) ).
tff(89,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 )
| ( ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(top_str(sK2_t51_tops_1_A),true,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))),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,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))),true,ifeq(top_str(sK2_t51_tops_1_A),true,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))),true),true) = true,
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
true = ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(top_str(sK2_t51_tops_1_A),true,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))),true),true),
inference(symmetry,[status(thm)],[90]) ).
tff(92,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)],[21,91,81,76,74]) ).
tff(93,plain,
ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true) = 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))),true,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),true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,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),true),true),true),true),
inference(monotonicity,[status(thm)],[92,72]) ).
tff(94,plain,
^ [B: $i,A: $i] :
refl(( ( 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))),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(bind,[status(th)],[]) ).
tff(95,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(quant_intro,[status(thm)],[94]) ).
tff(96,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(97,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(98,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)],[97,96]) ).
tff(99,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(skolemize,[status(sab)],[98]) ).
tff(100,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)],[99,95]) ).
tff(101,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) )
| ( ifeq2(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq2(top_str(sK2_t51_tops_1_A),true,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(102,plain,
ifeq2(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq2(top_str(sK2_t51_tops_1_A),true,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)],[101,100]) ).
tff(103,plain,
ifeq2(true,true,ifeq2(top_str(sK2_t51_tops_1_A),true,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))),true,ifeq2(top_str(sK2_t51_tops_1_A),true,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)],[45]) ).
tff(104,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(105,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)],[104]) ).
tff(106,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(107,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(108,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,ifeq2(top_str(sK2_t51_tops_1_A),true,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),true,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(112,plain,
ifeq2(true,true,ifeq2(top_str(sK2_t51_tops_1_A),true,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),true,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)],[111,110]) ).
tff(113,plain,
ifeq2(top_str(sK2_t51_tops_1_A),true,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(true,true,ifeq2(top_str(sK2_t51_tops_1_A),true,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)],[112]) ).
tff(114,plain,
ifeq2(true,true,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),true,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)],[63]) ).
tff(115,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,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(116,plain,
ifeq2(true,true,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)],[115,110]) ).
tff(117,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(true,true,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)],[116]) ).
tff(118,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)],[117,114,113,103,102]) ).
tff(119,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)],[118]) ).
tff(120,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)],[119]) ).
tff(121,plain,
ifeq(true,true,open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true) = ifeq(top_str(sK2_t51_tops_1_A),true,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),true),
inference(monotonicity,[status(thm)],[63,120]) ).
tff(122,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,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) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
ifeq(true,true,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),
inference(unit_resolution,[status(thm)],[122,16]) ).
tff(124,plain,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) = ifeq(true,true,open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) = true,
inference(transitivity,[status(thm)],[124,121,71,23,93,9]) ).
tff(126,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(127,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(128,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)],[127,126]) ).
tff(129,plain,
$false,
inference(unit_resolution,[status(thm)],[128,125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU323-10 : TPTP v9.0.0. Released v7.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:44:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------