%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU341+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 : Thu Sep 24 02:24:46 PM UTC 2026
% Result : Theorem 0.17s 0.59s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 13 unt; 0 def)
% Number of atoms : 150 ( 14 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 178 ( 66 ~; 54 |; 31 &)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 7 sgn 40 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X2)
& X1 != X2
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( empty(X2)
& element(X2,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(t5_connsp_2,conjecture,
! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( in(X3,X2)
& open_subset(X2,X1) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(t55_tops_1,axiom,
! [X1] :
( ( top_str(X1)
& topological_space(X1) )
=> ! [X2] :
( top_str(X2)
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ! [X4] :
( element(X4,powerset(the_carrier(X2)))
=> ( ( interior(X1,X3) = X3
=> open_subset(X3,X1) )
& ( open_subset(X4,X2)
=> interior(X2,X4) = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tops_1) ).
fof(d1_connsp_2,axiom,
! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( point_neighbourhood(X3,X1,X2)
<=> in(X2,interior(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X3))
& in(X1,X2) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(c_0_6,plain,
! [X1,X2] :
~ ( empty(X2)
& X1 != X2
& empty(X1) ),
inference(fof_simplification,[status(thm)],[t8_boole]) ).
fof(c_0_7,plain,
! [X45,X46] :
( ~ empty(X46)
| X45 = X46
| ~ empty(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X40] :
( empty(esk7_1(X40))
& element(esk7_1(X40),powerset(X40)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
cnf(c_0_9,plain,
( ~ empty(X2)
| ~ empty(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
empty(esk7_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( ~ empty(X1)
| X1 = esk7_1(X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( in(X3,X2)
& open_subset(X2,X1) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[t5_connsp_2]) ).
fof(c_0_13,plain,
! [X31,X32,X33,X34] :
( ( ~ top_str(X31)
| ~ topological_space(X31)
| ~ top_str(X32)
| ~ element(X33,powerset(the_carrier(X31)))
| ~ element(X34,powerset(the_carrier(X32)))
| open_subset(X33,X31)
| interior(X31,X33) != X33 )
& ( ~ top_str(X31)
| ~ topological_space(X31)
| ~ top_str(X32)
| ~ element(X33,powerset(the_carrier(X31)))
| ~ element(X34,powerset(the_carrier(X32)))
| interior(X32,X34) = X34
| ~ open_subset(X34,X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_tops_1])])])])]) ).
cnf(c_0_14,plain,
element(esk7_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
esk7_1(X1) = esk7_1(X2),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( in(X3,X2)
& open_subset(X2,X1) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( ~ top_str(X4)
| ~ topological_space(X4)
| ~ top_str(X2)
| ~ element(X3,powerset(the_carrier(X4)))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ open_subset(X1,X2)
| interior(X2,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
element(esk7_1(X1),powerset(X2)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_19,negated_conjecture,
( ~ point_neighbourhood(esk2_0,esk1_0,esk3_0)
& in(esk3_0,esk2_0)
& open_subset(esk2_0,esk1_0)
& element(esk3_0,the_carrier(esk1_0))
& element(esk2_0,powerset(the_carrier(esk1_0)))
& top_str(esk1_0)
& topological_space(esk1_0)
& ~ empty_carrier(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_20,plain,
! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( point_neighbourhood(X3,X1,X2)
<=> in(X2,interior(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_connsp_2]) ).
cnf(c_0_21,plain,
( ~ element(X2,powerset(the_carrier(X1)))
| ~ topological_space(X3)
| ~ top_str(X1)
| ~ top_str(X3)
| ~ open_subset(X2,X1)
| interior(X1,X2) = X2 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
open_subset(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
top_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
element(esk2_0,powerset(the_carrier(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_25,plain,
! [X23,X24,X25] :
( element(X23,X25)
| ~ element(X24,powerset(X25))
| ~ in(X23,X24) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])]) ).
fof(c_0_26,plain,
! [X8,X9,X10] :
( ( ~ top_str(X8)
| ~ topological_space(X8)
| empty_carrier(X8)
| ~ element(X9,the_carrier(X8))
| ~ element(X10,powerset(the_carrier(X8)))
| point_neighbourhood(X10,X8,X9)
| ~ in(X9,interior(X8,X10)) )
& ( ~ top_str(X8)
| ~ topological_space(X8)
| empty_carrier(X8)
| ~ element(X9,the_carrier(X8))
| ~ element(X10,powerset(the_carrier(X8)))
| in(X9,interior(X8,X10))
| ~ point_neighbourhood(X10,X8,X9) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])]) ).
cnf(c_0_27,negated_conjecture,
( ~ topological_space(X1)
| ~ top_str(X1)
| interior(esk1_0,esk2_0) = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]) ).
cnf(c_0_28,negated_conjecture,
topological_space(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( ~ element(X2,powerset(X3))
| ~ in(X1,X2)
| element(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
( ~ top_str(X2)
| ~ topological_space(X2)
| ~ element(X1,the_carrier(X2))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ in(X1,interior(X2,X3))
| empty_carrier(X2)
| point_neighbourhood(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
interior(esk1_0,esk2_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_23])]) ).
cnf(c_0_32,negated_conjecture,
~ empty_carrier(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_33,negated_conjecture,
( ~ in(X1,esk2_0)
| element(X1,the_carrier(esk1_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_34,negated_conjecture,
~ point_neighbourhood(esk2_0,esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_35,negated_conjecture,
( ~ in(X1,esk2_0)
| point_neighbourhood(esk2_0,esk1_0,X1) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_23]),c_0_28]),c_0_24])]),c_0_32]),c_0_33]) ).
cnf(c_0_36,negated_conjecture,
in(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU341+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.52 % Computer : n007.cluster.edu
% 0.11/0.52 % Model : x86_64 x86_64
% 0.11/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.52 % Memory : 8046.5625MB
% 0.11/0.52 % OS : Linux 6.8.0-71-generic
% 0.11/0.52 % CPULimit : 300
% 0.11/0.52 % WCLimit : 300
% 0.11/0.52 % DateTime : Mon Sep 21 06:11:51 UTC 2026
% 0.11/0.52 % CPUTime :
% 0.11/0.52 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.56 Running first-order theorem proving
% 0.11/0.56 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.59 % Version: 3.5.1
% 0.17/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.59 % Starting sh5l with 300s (1) cores
% 0.17/0.59 % new_bool_3 with pid 352654 completed with status 0
% 0.17/0.59 % Result found by new_bool_3
% 0.17/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.59 % Search class: FGHSS-FFMM21-SFFFFFNN
% 0.17/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.59 % SubtermCWHack with pid 352657 completed with status 0
% 0.17/0.59 % Result found by SubtermCWHack
% 0.17/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.59 % Search class: FGHSS-FFMM21-SFFFFFNN
% 0.17/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.59 % Preprocessing time : 0.001 s
% 0.17/0.59
% 0.17/0.59 % Proof found!
% 0.17/0.59 % SZS status Theorem
% 0.17/0.59 % SZS output start CNFRefutation
% See solution above
% 0.17/0.59 % Parsed axioms : 45
% 0.17/0.59 % Removed by relevancy pruning/SinE : 27
% 0.17/0.59 % Initial clauses : 29
% 0.17/0.59 % Removed in clause preprocessing : 0
% 0.17/0.59 % Initial clauses in saturation : 29
% 0.17/0.59 % Processed clauses : 172
% 0.17/0.59 % ...of these trivial : 0
% 0.17/0.59 % ...subsumed : 75
% 0.17/0.59 % ...remaining for further processing : 97
% 0.17/0.59 % Other redundant clauses eliminated : 0
% 0.17/0.59 % Clauses deleted for lack of memory : 0
% 0.17/0.59 % Backward-subsumed : 6
% 0.17/0.59 % Backward-rewritten : 2
% 0.17/0.59 % Generated clauses : 260
% 0.17/0.59 % ...of the previous two non-redundant : 235
% 0.17/0.59 % ...aggressively subsumed : 0
% 0.17/0.59 % Contextual simplify-reflections : 6
% 0.17/0.59 % Paramodulations : 260
% 0.17/0.59 % Factorizations : 0
% 0.17/0.59 % NegExts : 0
% 0.17/0.59 % Equation resolutions : 0
% 0.17/0.59 % Disequality decompositions : 0
% 0.17/0.59 % Total rewrite steps : 42
% 0.17/0.59 % ...of those cached : 30
% 0.17/0.59 % Propositional unsat checks : 0
% 0.17/0.59 % Propositional check models : 0
% 0.17/0.59 % Propositional check unsatisfiable : 0
% 0.17/0.59 % Propositional clauses : 0
% 0.17/0.59 % Propositional clauses after purity: 0
% 0.17/0.59 % Propositional unsat core size : 0
% 0.17/0.59 % Propositional preprocessing time : 0.000
% 0.17/0.59 % Propositional encoding time : 0.000
% 0.17/0.59 % Propositional solver time : 0.000
% 0.17/0.59 % Success case prop preproc time : 0.000
% 0.17/0.59 % Success case prop encoding time : 0.000
% 0.17/0.59 % Success case prop solver time : 0.000
% 0.17/0.59 % Current number of processed clauses : 89
% 0.17/0.59 % Positive orientable unit clauses : 12
% 0.17/0.59 % Positive unorientable unit clauses: 1
% 0.17/0.59 % Negative unit clauses : 7
% 0.17/0.59 % Non-unit-clauses : 69
% 0.17/0.59 % Current number of unprocessed clauses: 83
% 0.17/0.59 % ...number of literals in the above : 391
% 0.17/0.59 % Current number of archived formulas : 0
% 0.17/0.59 % Current number of archived clauses : 8
% 0.17/0.59 % Clause-clause subsumption calls (NU) : 1635
% 0.17/0.59 % Rec. Clause-clause subsumption calls : 681
% 0.17/0.59 % Non-unit clause-clause subsumptions : 79
% 0.17/0.59 % Unit Clause-clause subsumption calls : 36
% 0.17/0.59 % Rewrite failures with RHS unbound : 20
% 0.17/0.59 % BW rewrite match attempts : 6
% 0.17/0.59 % BW rewrite match successes : 6
% 0.17/0.59 % Condensation attempts : 0
% 0.17/0.59 % Condensation successes : 0
% 0.17/0.59 % Termbank termtop insertions : 6203
% 0.17/0.59 % Search garbage collected termcells : 626
% 0.17/0.59
% 0.17/0.59 % -------------------------------------------------
% 0.17/0.59 % User time : 0.009 s
% 0.17/0.59 % System time : 0.003 s
% 0.17/0.59 % Total time : 0.012 s
% 0.17/0.59 % Maximum resident set size: 3680 pages
% 0.17/0.59
% 0.17/0.59 % -------------------------------------------------
% 0.17/0.59 % User time : 0.010 s
% 0.17/0.59 % System time : 0.008 s
% 0.17/0.59 % Total time : 0.018 s
% 0.17/0.59 % Maximum resident set size: 4864 pages
% 0.17/0.59 % E exiting
%------------------------------------------------------------------------------