%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU323-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:20 PM UTC 2026
% Result : Unsatisfiable 0.45s 0.84s
% Output : Refutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 68 unt; 1 def)
% Number of atoms : 68 ( 61 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-4 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,axiom,
! [X0,X1] : ifeq(element(X0,powerset(the_carrier(X1))),true,ifeq(closed_subset(X0,X1),true,ifeq(topological_space(X1),true,ifeq(top_str(X1),true,open_subset(subset_complement(the_carrier(X1),X0),X1),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_tops_1) ).
fof(f4,plain,
! [X0,X1] : true = ifeq(element(X0,powerset(the_carrier(X1))),true,ifeq(closed_subset(X0,X1),true,ifeq(topological_space(X1),true,ifeq(top_str(X1),true,open_subset(subset_complement(the_carrier(X1),X0),X1),true),true),true),true),
inference(reorient_equations,[],[f3]) ).
fof(f12,axiom,
one_sorted_str(sK6_existence_l1_struct_0_A) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(f13,plain,
true = one_sorted_str(sK6_existence_l1_struct_0_A),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X0,X1] : ifeq(element(X0,powerset(X1)),true,element(subset_complement(X1,X0),powerset(X1)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f15,plain,
! [X0,X1] : true = ifeq(element(X0,powerset(X1)),true,element(subset_complement(X1,X0),powerset(X1)),true),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X0,X1] : ifeq(element(X0,powerset(the_carrier(X1))),true,ifeq(top_str(X1),true,element(topstr_closure(X1,X0),powerset(the_carrier(X1))),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(f17,plain,
! [X0,X1] : true = ifeq(element(X0,powerset(the_carrier(X1))),true,ifeq(top_str(X1),true,element(topstr_closure(X1,X0),powerset(the_carrier(X1))),true),true),
inference(reorient_equations,[],[f16]) ).
fof(f18,axiom,
! [X0,X1] : ifeq(element(X0,powerset(the_carrier(X1))),true,ifeq(topological_space(X1),true,ifeq(top_str(X1),true,closed_subset(topstr_closure(X1,X0),X1),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_tops_1) ).
fof(f19,plain,
! [X0,X1] : true = ifeq(element(X0,powerset(the_carrier(X1))),true,ifeq(topological_space(X1),true,ifeq(top_str(X1),true,closed_subset(topstr_closure(X1,X0),X1),true),true),true),
inference(reorient_equations,[],[f18]) ).
fof(f38,axiom,
! [X0,X1] : ifeq2(element(X0,powerset(the_carrier(X1))),true,ifeq2(top_str(X1),true,subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X0))),interior(X1,X0)),interior(X1,X0)) = interior(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_1) ).
fof(f39,plain,
! [X0,X1] : interior(X1,X0) = ifeq2(element(X0,powerset(the_carrier(X1))),true,ifeq2(top_str(X1),true,subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X0))),interior(X1,X0)),interior(X1,X0)),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
top_str(sK2_t51_tops_1_A) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tops_1) ).
fof(f41,plain,
true = top_str(sK2_t51_tops_1_A),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
topological_space(sK2_t51_tops_1_A) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tops_1_1) ).
fof(f43,plain,
true = topological_space(sK2_t51_tops_1_A),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tops_1_2) ).
fof(f45,plain,
true = element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tops_1_3) ).
fof(f47,plain,
true != open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
~ sP0(open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f49,plain,
sP0(true),
inference(inequality_splitting,[],[f47,f48]) ).
fof(f50,plain,
sP0(element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A)))),
inference(backward_demodulation,[],[f49,f45]) ).
fof(f51,plain,
topological_space(sK2_t51_tops_1_A) = element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),
inference(backward_demodulation,[],[f45,f43]) ).
fof(f52,plain,
top_str(sK2_t51_tops_1_A) = topological_space(sK2_t51_tops_1_A),
inference(forward_demodulation,[],[f41,f43]) ).
fof(f53,plain,
! [X0,X1] : interior(X1,X0) = ifeq2(element(X0,powerset(the_carrier(X1))),topological_space(sK2_t51_tops_1_A),ifeq2(top_str(X1),topological_space(sK2_t51_tops_1_A),subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X0))),interior(X1,X0)),interior(X1,X0)),
inference(forward_demodulation,[],[f39,f43]) ).
fof(f63,plain,
! [X0,X1] : topological_space(sK2_t51_tops_1_A) = ifeq(element(X0,powerset(the_carrier(X1))),topological_space(sK2_t51_tops_1_A),ifeq(topological_space(X1),topological_space(sK2_t51_tops_1_A),ifeq(top_str(X1),topological_space(sK2_t51_tops_1_A),closed_subset(topstr_closure(X1,X0),X1),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),
inference(forward_demodulation,[],[f19,f43]) ).
fof(f64,plain,
! [X0,X1] : topological_space(sK2_t51_tops_1_A) = ifeq(element(X0,powerset(the_carrier(X1))),topological_space(sK2_t51_tops_1_A),ifeq(top_str(X1),topological_space(sK2_t51_tops_1_A),element(topstr_closure(X1,X0),powerset(the_carrier(X1))),topological_space(sK2_t51_tops_1_A)),topological_space(sK2_t51_tops_1_A)),
inference(forward_demodulation,[],[f17,f43]) ).
fof(f65,plain,
! [X0,X1] : topological_space(sK2_t51_tops_1_A) = ifeq(element(X0,powerset(X1)),topological_space(sK2_t51_tops_1_A),element(subset_complement(X1,X0),powerset(X1)),topological_space(sK2_t51_tops_1_A)),
inference(forward_demodulation,[],[f15,f43]) ).
fof(f66,plain,
one_sorted_str(sK6_existence_l1_struct_0_A) = topological_space(sK2_t51_tops_1_A),
inference(backward_demodulation,[],[f43,f13]) ).
fof(f71,plain,
! [X0,X1] : one_sorted_str(sK6_existence_l1_struct_0_A) = ifeq(element(X0,powerset(the_carrier(X1))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(closed_subset(X0,X1),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(X1),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(X1),one_sorted_str(sK6_existence_l1_struct_0_A),open_subset(subset_complement(the_carrier(X1),X0),X1),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(forward_demodulation,[],[f4,f13]) ).
fof(f72,plain,
sP0(topological_space(sK2_t51_tops_1_A)),
inference(backward_demodulation,[],[f50,f51]) ).
fof(f73,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(backward_demodulation,[],[f51,f66]) ).
fof(f74,plain,
one_sorted_str(sK6_existence_l1_struct_0_A) = top_str(sK2_t51_tops_1_A),
inference(backward_demodulation,[],[f52,f66]) ).
fof(f75,plain,
! [X0,X1] : interior(X1,X0) = ifeq2(element(X0,powerset(the_carrier(X1))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq2(top_str(X1),one_sorted_str(sK6_existence_l1_struct_0_A),subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X0))),interior(X1,X0)),interior(X1,X0)),
inference(backward_demodulation,[],[f53,f66]) ).
fof(f85,plain,
! [X0,X1] : one_sorted_str(sK6_existence_l1_struct_0_A) = ifeq(element(X0,powerset(the_carrier(X1))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(X1),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(X1),one_sorted_str(sK6_existence_l1_struct_0_A),closed_subset(topstr_closure(X1,X0),X1),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(backward_demodulation,[],[f63,f66]) ).
fof(f86,plain,
! [X0,X1] : one_sorted_str(sK6_existence_l1_struct_0_A) = ifeq(element(X0,powerset(the_carrier(X1))),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(X1),one_sorted_str(sK6_existence_l1_struct_0_A),element(topstr_closure(X1,X0),powerset(the_carrier(X1))),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(backward_demodulation,[],[f64,f66]) ).
fof(f87,plain,
! [X0,X1] : one_sorted_str(sK6_existence_l1_struct_0_A) = ifeq(element(X0,powerset(X1)),one_sorted_str(sK6_existence_l1_struct_0_A),element(subset_complement(X1,X0),powerset(X1)),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(backward_demodulation,[],[f65,f66]) ).
fof(f88,plain,
sP0(one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(forward_demodulation,[],[f72,f66]) ).
fof(f110,plain,
one_sorted_str(sK6_existence_l1_struct_0_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(superposition,[],[f87,f73]) ).
fof(f111,plain,
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(forward_demodulation,[],[f110,f2]) ).
fof(f204,plain,
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),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)),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),
inference(superposition,[],[f75,f73]) ).
fof(f209,plain,
interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B) = ifeq2(top_str(sK2_t51_tops_1_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(forward_demodulation,[],[f204,f1]) ).
fof(f213,plain,
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),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(forward_demodulation,[],[f209,f74]) ).
fof(f216,plain,
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(forward_demodulation,[],[f213,f1]) ).
fof(f586,plain,
one_sorted_str(sK6_existence_l1_struct_0_A) = ifeq(one_sorted_str(sK6_existence_l1_struct_0_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(sK2_t51_tops_1_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(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),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(superposition,[],[f85,f111]) ).
fof(f588,plain,
one_sorted_str(sK6_existence_l1_struct_0_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),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)),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(superposition,[],[f86,f111]) ).
fof(f598,plain,
one_sorted_str(sK6_existence_l1_struct_0_A) = ifeq(top_str(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))),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(forward_demodulation,[],[f588,f2]) ).
fof(f600,plain,
one_sorted_str(sK6_existence_l1_struct_0_A) = ifeq(topological_space(sK2_t51_tops_1_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(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),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(forward_demodulation,[],[f586,f2]) ).
fof(f607,plain,
one_sorted_str(sK6_existence_l1_struct_0_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(forward_demodulation,[],[f598,f74]) ).
fof(f609,plain,
one_sorted_str(sK6_existence_l1_struct_0_A) = ifeq(topological_space(sK2_t51_tops_1_A),one_sorted_str(sK6_existence_l1_struct_0_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)),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(forward_demodulation,[],[f600,f74]) ).
fof(f613,plain,
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(forward_demodulation,[],[f607,f2]) ).
fof(f615,plain,
one_sorted_str(sK6_existence_l1_struct_0_A) = ifeq(topological_space(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),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(forward_demodulation,[],[f609,f2]) ).
fof(f620,plain,
one_sorted_str(sK6_existence_l1_struct_0_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(forward_demodulation,[],[f615,f66]) ).
fof(f623,plain,
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(forward_demodulation,[],[f620,f2]) ).
fof(f712,plain,
one_sorted_str(sK6_existence_l1_struct_0_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))),one_sorted_str(sK6_existence_l1_struct_0_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),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(sK2_t51_tops_1_A),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(top_str(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),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(superposition,[],[f71,f216]) ).
fof(f721,plain,
one_sorted_str(sK6_existence_l1_struct_0_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))),one_sorted_str(sK6_existence_l1_struct_0_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),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(sK2_t51_tops_1_A),one_sorted_str(sK6_existence_l1_struct_0_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)),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(forward_demodulation,[],[f712,f74]) ).
fof(f727,plain,
one_sorted_str(sK6_existence_l1_struct_0_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))),one_sorted_str(sK6_existence_l1_struct_0_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),one_sorted_str(sK6_existence_l1_struct_0_A),ifeq(topological_space(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),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(forward_demodulation,[],[f721,f2]) ).
fof(f736,plain,
one_sorted_str(sK6_existence_l1_struct_0_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))),one_sorted_str(sK6_existence_l1_struct_0_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),one_sorted_str(sK6_existence_l1_struct_0_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)),one_sorted_str(sK6_existence_l1_struct_0_A)),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(forward_demodulation,[],[f727,f66]) ).
fof(f741,plain,
one_sorted_str(sK6_existence_l1_struct_0_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))),one_sorted_str(sK6_existence_l1_struct_0_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),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)),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(forward_demodulation,[],[f736,f2]) ).
fof(f743,plain,
one_sorted_str(sK6_existence_l1_struct_0_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))),one_sorted_str(sK6_existence_l1_struct_0_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)),one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(forward_demodulation,[],[f741,f623]) ).
fof(f745,plain,
one_sorted_str(sK6_existence_l1_struct_0_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))),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(forward_demodulation,[],[f743,f2]) ).
fof(f746,plain,
one_sorted_str(sK6_existence_l1_struct_0_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(forward_demodulation,[],[f745,f613]) ).
fof(f747,plain,
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(forward_demodulation,[],[f746,f2]) ).
fof(f749,plain,
~ sP0(one_sorted_str(sK6_existence_l1_struct_0_A)),
inference(backward_demodulation,[],[f48,f747]) ).
fof(f750,plain,
$false,
inference(forward_subsumption_resolution,[],[f749,f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU323-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 28 04:42:19 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.84 % (3021059)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.45/0.84 % (3021070)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2261690823:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.45/0.84 % (3021067)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=153532407:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.45/0.84 % (3021069)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1951872661:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.45/0.84 % (3021066)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=755924929:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.45/0.84 % (3021068)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2514098346:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.45/0.84 % (3021064)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=668329048:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.45/0.84 % (3021065)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=309400402:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.45/0.84 % (3021067)First to succeed.
% 0.45/0.84 % (3021067)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3021059"
% 0.45/0.84 % (3021070)Also succeeded, but the first one will report.
% 0.45/0.84 % (3021069)Also succeeded, but the first one will report.
% 0.45/0.84 % (3021068)Instruction limit reached!
% 0.45/0.84 % (3021068)------------------------------
% 0.45/0.84 % (3021068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.45/0.84 % (3021068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.45/0.84 % (3021068)CaDiCaL version: 2.1.3
% 0.45/0.84 % (3021068)Termination reason: Instruction limit
% 0.45/0.84 % (3021068)Termination phase: Saturation
% 0.45/0.84 % (3021068)Time elapsed: 0.053 s
% 0.45/0.84 % (3021068)Peak memory usage: 89 MB
% 0.45/0.84 % (3021068)Instructions burned: 183 (million)
% 0.45/0.84 % (3021067)Refutation found. Thanks to Tanya!
% 0.45/0.84 % SZS status Unsatisfiable for theBenchmark
% 0.45/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 2.40/0.94 % (3021067)------------------------------
% 2.40/0.94 % (3021067)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.40/0.94 % (3021067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.94 % (3021067)CaDiCaL version: 2.1.3
% 2.40/0.94 % (3021067)Termination reason: Refutation
% 2.40/0.94 % (3021067)Time elapsed: 0.013 s
% 2.40/0.94 % (3021067)Peak memory usage: 88 MB
% 2.40/0.94 % (3021067)Instructions burned: 40 (million)
% 2.40/0.94 % (3021067)------------------------------
% 2.40/0.94 % (3021067)------------------------------
% 2.40/0.94 % (3021059)Success in time 0.31 s
% 2.40/0.94 % Vampire exiting
%------------------------------------------------------------------------------