%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU341+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n031.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 : Fri Jul 25 03:45:14 PM UTC 2025
% Result : Theorem 6.66s 1.10s
% Output : CNFRefutation 6.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 24 unt; 0 def)
% Number of atoms : 102 ( 4 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 102 ( 38 ~; 32 |; 12 &)
% ( 1 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 1 sgn 19 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t5_connsp_2,plain,
! [A] :
( ( ~ empty_carrier(A)
& topological_space(A)
& top_str(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( open_subset(B,A)
& in(C,B) )
=> point_neighbourhood(B,A,C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(t5_connsp_2_negated,plain,
~ ! [A] :
( ( ~ empty_carrier(A)
& topological_space(A)
& top_str(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( open_subset(B,A)
& in(C,B) )
=> point_neighbourhood(B,A,C) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t5_connsp_2]) ).
cnf(80,plain,
in(sK10,sK9),
inference(cnf,[status(esa)],[t5_connsp_2_negated]) ).
cnf(l0,plain,
in(sK10,sK9),
inference(instantiation,[status(thm)],[80]) ).
fof(t55_tops_1,plain,
! [A] :
( ( topological_space(A)
& top_str(A) )
=> ! [B] :
( top_str(B)
=> ! [C] :
( element(C,powerset(the_carrier(A)))
=> ! [D] :
( element(D,powerset(the_carrier(B)))
=> ( ( open_subset(D,B)
=> interior(B,D) = D )
& ( interior(A,C) = C
=> open_subset(C,A) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tops_1) ).
cnf(72,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X3)))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ top_str(X3)
| ~ open_subset(X2,X3)
| interior(X3,X2) = X2 ),
inference(cnf,[status(esa)],[t55_tops_1]) ).
cnf(l9,plain,
( ~ element(sK4(powerset(the_carrier(sK8))),powerset(the_carrier(sK8)))
| ~ element(sK9,powerset(the_carrier(sK8)))
| ~ topological_space(sK8)
| ~ top_str(sK8)
| ~ top_str(sK8)
| ~ open_subset(sK9,sK8)
| interior(sK8,sK9) = sK9 ),
inference(instantiation,[status(thm)],[72]) ).
cnf(79,plain,
open_subset(sK9,sK8),
inference(cnf,[status(esa)],[t5_connsp_2_negated]) ).
cnf(l66,plain,
open_subset(sK9,sK8),
inference(instantiation,[status(thm)],[79]) ).
cnf(76,plain,
top_str(sK8),
inference(cnf,[status(esa)],[t5_connsp_2_negated]) ).
cnf(l67,plain,
top_str(sK8),
inference(instantiation,[status(thm)],[76]) ).
cnf(l65,plain,
top_str(sK8),
inference(instantiation,[status(thm)],[76]) ).
fof(existence_m1_subset_1,plain,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
cnf(48,plain,
element(sK4(X0),X0),
inference(cnf,[status(esa)],[existence_m1_subset_1]) ).
cnf(l56,plain,
element(sK4(powerset(the_carrier(sK8))),powerset(the_carrier(sK8))),
inference(instantiation,[status(thm)],[48]) ).
fof(t4_subset,plain,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
cnf(71,plain,
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| element(X0,X2) ),
inference(cnf,[status(esa)],[t4_subset]) ).
cnf(l7,plain,
( ~ in(sK10,interior(sK8,sK9))
| ~ element(interior(sK8,sK9),powerset(the_carrier(sK8)))
| element(sK10,the_carrier(sK8)) ),
inference(instantiation,[status(thm)],[71]) ).
cnf(75,plain,
topological_space(sK8),
inference(cnf,[status(esa)],[t5_connsp_2_negated]) ).
cnf(l64,plain,
topological_space(sK8),
inference(instantiation,[status(thm)],[75]) ).
cnf(77,plain,
element(sK9,powerset(the_carrier(sK8))),
inference(cnf,[status(esa)],[t5_connsp_2_negated]) ).
cnf(l47,plain,
element(sK9,powerset(the_carrier(sK8))),
inference(instantiation,[status(thm)],[77]) ).
fof(dt_k1_tops_1,plain,
! [A,B] :
( ( top_str(A)
& element(B,powerset(the_carrier(A))) )
=> element(interior(A,B),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).
cnf(42,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| element(interior(X1,X0),powerset(the_carrier(X1))) ),
inference(cnf,[status(esa)],[dt_k1_tops_1]) ).
cnf(l14,plain,
( ~ element(sK9,powerset(the_carrier(sK8)))
| ~ top_str(sK8)
| element(interior(sK8,sK9),powerset(the_carrier(sK8))) ),
inference(instantiation,[status(thm)],[42]) ).
cnf(l28,plain,
top_str(sK8),
inference(instantiation,[status(thm)],[76]) ).
cnf(l24,plain,
element(sK9,powerset(the_carrier(sK8))),
inference(instantiation,[status(thm)],[77]) ).
fof(d1_connsp_2,plain,
! [A] :
( ( ~ empty_carrier(A)
& topological_space(A)
& top_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,powerset(the_carrier(A)))
=> ( point_neighbourhood(C,A,B)
<=> in(B,interior(A,C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_connsp_2) ).
cnf(41,plain,
( ~ in(X0,interior(X1,X2))
| ~ element(X0,the_carrier(X1))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1)
| empty_carrier(X1)
| point_neighbourhood(X2,X1,X0) ),
inference(cnf,[status(esa)],[d1_connsp_2]) ).
cnf(l132,plain,
( ~ in(sK10,interior(sK8,sK9))
| ~ element(sK10,the_carrier(sK8))
| ~ element(sK9,powerset(the_carrier(sK8)))
| ~ topological_space(sK8)
| ~ top_str(sK8)
| empty_carrier(sK8)
| point_neighbourhood(sK9,sK8,sK10) ),
inference(instantiation,[status(thm)],[41]) ).
cnf(l150,plain,
top_str(sK8),
inference(instantiation,[status(thm)],[76]) ).
cnf(74,plain,
~ empty_carrier(sK8),
inference(cnf,[status(esa)],[t5_connsp_2_negated]) ).
cnf(l149,plain,
~ empty_carrier(sK8),
inference(instantiation,[status(thm)],[74]) ).
cnf(81,plain,
~ point_neighbourhood(sK9,sK8,sK10),
inference(cnf,[status(esa)],[t5_connsp_2_negated]) ).
cnf(l337,plain,
~ point_neighbourhood(sK9,sK8,sK10),
inference(instantiation,[status(thm)],[81]) ).
cnf(l148,plain,
topological_space(sK8),
inference(instantiation,[status(thm)],[75]) ).
cnf(l147,plain,
element(sK9,powerset(the_carrier(sK8))),
inference(instantiation,[status(thm)],[77]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l9,l66,l67,l65,l56,l7,l64,l47,l14,l28,l24,l132,l150,l149,l337,l148,l147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU341+1 : TPTP v9.0.0. Released v3.3.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.26 % Computer : n031.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue Jul 22 00:58:03 EDT 2025
% 0.07/0.26 % CPUTime :
% 0.07/0.27 % launching worker at depth: 3
% 0.07/0.27 % launching worker at depth: 5
% 0.07/0.27 % launching worker at depth: 6
% 0.07/0.27 % launching worker at depth: 1
% 0.07/0.27 % launching worker at depth: 2
% 0.07/0.27 % launching worker at depth: 4
% 0.07/0.27 % launching worker at depth: 7
% 0.07/0.27 % launching worker at depth: 8
% 0.07/0.27 % launching worker at depth: 9
% 0.07/0.27 % launching worker at depth: 10
% 0.11/0.32 % launching worker at depth: 11
% 6.66/1.10 % SZS status Theorem for theBenchmark
% 6.66/1.10 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------