%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU388+2 : 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 : n001.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 02:24:56 PM UTC 2026
% Result : Theorem 5.16s 1.66s
% Output : CNFRefutation 5.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 124 ( 13 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 148 ( 53 ~; 53 |; 25 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 44 ( 0 sgn 25 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t3_yellow19,conjecture,
! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( in(X3,neighborhood_system(X1,X2))
<=> point_neighbourhood(X3,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_yellow19) ).
fof(d1_yellow19,axiom,
! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> neighborhood_system(X1,X2) = a_2_0_yellow19(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow19) ).
fof(fraenkel_a_2_0_yellow19,axiom,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X2))
& top_str(X2)
& topological_space(X2)
& ~ empty_carrier(X2) )
=> ( in(X1,a_2_0_yellow19(X2,X3))
<=> ? [X4] :
( X1 = X4
& point_neighbourhood(X4,X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_yellow19) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( in(X3,neighborhood_system(X1,X2))
<=> point_neighbourhood(X3,X1,X2) ) ) ),
inference(assume_negation,[status(cth)],[t3_yellow19]) ).
fof(c_0_4,plain,
! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> neighborhood_system(X1,X2) = a_2_0_yellow19(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[d1_yellow19]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( in(X3,neighborhood_system(X1,X2))
<=> point_neighbourhood(X3,X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X2))
& top_str(X2)
& topological_space(X2)
& ~ empty_carrier(X2) )
=> ( in(X1,a_2_0_yellow19(X2,X3))
<=> ? [X4] :
( X1 = X4
& point_neighbourhood(X4,X2,X3) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_yellow19]) ).
fof(c_0_7,plain,
! [X64,X65] :
( neighborhood_system(X64,X65) = a_2_0_yellow19(X64,X65)
| ~ element(X65,the_carrier(X64))
| ~ top_str(X64)
| ~ topological_space(X64)
| empty_carrier(X64) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_8,negated_conjecture,
( ( point_neighbourhood(esk3_0,esk1_0,esk2_0)
| in(esk3_0,neighborhood_system(esk1_0,esk2_0)) )
& ( ~ point_neighbourhood(esk3_0,esk1_0,esk2_0)
| ~ in(esk3_0,neighborhood_system(esk1_0,esk2_0)) )
& element(esk2_0,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_5])])])]) ).
fof(c_0_9,plain,
! [X165,X166,X167,X169] :
( ( ~ element(X167,the_carrier(X166))
| ~ top_str(X166)
| ~ topological_space(X166)
| empty_carrier(X166)
| in(X165,a_2_0_yellow19(X166,X167))
| X165 != X169
| ~ point_neighbourhood(X169,X166,X167) )
& ( ~ element(X167,the_carrier(X166))
| ~ top_str(X166)
| ~ topological_space(X166)
| empty_carrier(X166)
| ~ in(X165,a_2_0_yellow19(X166,X167))
| X165 = esk23_3(X165,X166,X167) )
& ( ~ element(X167,the_carrier(X166))
| ~ top_str(X166)
| ~ topological_space(X166)
| empty_carrier(X166)
| ~ in(X165,a_2_0_yellow19(X166,X167))
| point_neighbourhood(esk23_3(X165,X166,X167),X166,X167) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])]) ).
cnf(c_0_10,plain,
( ~ element(X2,the_carrier(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| neighborhood_system(X1,X2) = a_2_0_yellow19(X1,X2)
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
element(esk2_0,the_carrier(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
top_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
topological_space(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
~ empty_carrier(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( ~ element(X3,the_carrier(X2))
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ in(X1,a_2_0_yellow19(X2,X3))
| empty_carrier(X2)
| point_neighbourhood(esk23_3(X1,X2,X3),X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
a_2_0_yellow19(esk1_0,esk2_0) = neighborhood_system(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]),c_0_14]) ).
cnf(c_0_17,plain,
( ~ element(X3,the_carrier(X2))
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ in(X1,a_2_0_yellow19(X2,X3))
| empty_carrier(X2)
| X1 = esk23_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
( ~ in(X1,neighborhood_system(esk1_0,esk2_0))
| point_neighbourhood(esk23_3(X1,esk1_0,esk2_0),esk1_0,esk2_0) ),
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_15,c_0_11]),c_0_12]),c_0_13]),c_0_16])]),c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( point_neighbourhood(esk3_0,esk1_0,esk2_0)
| in(esk3_0,neighborhood_system(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
( ~ in(X1,neighborhood_system(esk1_0,esk2_0))
| esk23_3(X1,esk1_0,esk2_0) = X1 ),
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_17,c_0_11]),c_0_12]),c_0_13]),c_0_16])]),c_0_14]) ).
cnf(c_0_21,plain,
( ~ element(X3,the_carrier(X2))
| ~ top_str(X2)
| ~ topological_space(X2)
| X4 != X1
| ~ point_neighbourhood(X1,X2,X3)
| empty_carrier(X2)
| in(X4,a_2_0_yellow19(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,negated_conjecture,
( point_neighbourhood(esk3_0,esk1_0,esk2_0)
| point_neighbourhood(esk23_3(esk3_0,esk1_0,esk2_0),esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( point_neighbourhood(esk3_0,esk1_0,esk2_0)
| esk23_3(esk3_0,esk1_0,esk2_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_24,plain,
( ~ element(X3,the_carrier(X1))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ point_neighbourhood(X2,X1,X3)
| in(X2,a_2_0_yellow19(X1,X3))
| empty_carrier(X1) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
point_neighbourhood(esk3_0,esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
( ~ point_neighbourhood(esk3_0,esk1_0,esk2_0)
| ~ in(esk3_0,neighborhood_system(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
in(esk3_0,neighborhood_system(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_16]),c_0_12]),c_0_13]),c_0_11])]),c_0_14]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_25])]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU388+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.54 % Computer : n001.cluster.edu
% 0.16/0.54 % Model : x86_64 x86_64
% 0.16/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.54 % Memory : 8046.5625MB
% 0.16/0.54 % OS : Linux 6.8.0-71-generic
% 0.16/0.54 % CPULimit : 300
% 0.16/0.54 % WCLimit : 300
% 0.16/0.54 % DateTime : Mon Sep 21 06:24:14 UTC 2026
% 0.16/0.54 % CPUTime :
% 0.16/0.54 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.61 Running first-order theorem proving
% 0.24/0.61 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
% 5.16/1.66 % Version: 3.5.1
% 5.16/1.66 % Preprocessing class: FSLMSMSSSSSNFFN.
% 5.16/1.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.16/1.66 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 5.16/1.66 % Starting new_bool_3 with 600s (2) cores
% 5.16/1.66 % Starting new_bool_1 with 600s (2) cores
% 5.16/1.66 % Starting sh5l with 300s (1) cores
% 5.16/1.66 % new_bool_3 with pid 2379270 completed with status 0
% 5.16/1.66 % Result found by new_bool_3
% 5.16/1.66 % Preprocessing class: FSLMSMSSSSSNFFN.
% 5.16/1.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.16/1.66 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 5.16/1.66 % Starting new_bool_3 with 600s (2) cores
% 5.16/1.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 5.16/1.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 5.16/1.66 % Search class: FGHSM-FSLM32-MFFFFFNN
% 5.16/1.66 % Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 5.16/1.66 % Starting SubtermCWHack with 55s (1) cores
% 5.16/1.66 % Starting new_bool_3 with 61s (1) cores
% 5.16/1.66 % new_bool_3 with pid 2379276 completed with status 0
% 5.16/1.66 % Result found by new_bool_3
% 5.16/1.66 % Preprocessing class: FSLMSMSSSSSNFFN.
% 5.16/1.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.16/1.66 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 5.16/1.66 % Starting new_bool_3 with 600s (2) cores
% 5.16/1.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 5.16/1.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 5.16/1.66 % Search class: FGHSM-FSLM32-MFFFFFNN
% 5.16/1.66 % Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 5.16/1.66 % Starting SubtermCWHack with 55s (1) cores
% 5.16/1.66 % Starting new_bool_3 with 61s (1) cores
% 5.16/1.66 % Preprocessing time : 0.023 s
% 5.16/1.66 % Presaturation interreduction done
% 5.16/1.66
% 5.16/1.66 % Proof found!
% 5.16/1.66 % SZS status Theorem
% 5.16/1.66 % SZS output start CNFRefutation
% See solution above
% 5.16/1.66 % Parsed axioms : 885
% 5.16/1.66 % Removed by relevancy pruning/SinE : 690
% 5.16/1.66 % Initial clauses : 861
% 5.16/1.66 % Removed in clause preprocessing : 29
% 5.16/1.66 % Initial clauses in saturation : 832
% 5.16/1.66 % Processed clauses : 4398
% 5.16/1.66 % ...of these trivial : 98
% 5.16/1.66 % ...subsumed : 2100
% 5.16/1.66 % ...remaining for further processing : 2199
% 5.16/1.66 % Other redundant clauses eliminated : 389
% 5.16/1.66 % Clauses deleted for lack of memory : 0
% 5.16/1.66 % Backward-subsumed : 10
% 5.16/1.66 % Backward-rewritten : 109
% 5.16/1.66 % Generated clauses : 13174
% 5.16/1.66 % ...of the previous two non-redundant : 12013
% 5.16/1.66 % ...aggressively subsumed : 0
% 5.16/1.66 % Contextual simplify-reflections : 48
% 5.16/1.66 % Paramodulations : 12855
% 5.16/1.66 % Factorizations : 8
% 5.16/1.66 % NegExts : 0
% 5.16/1.66 % Equation resolutions : 389
% 5.16/1.66 % Disequality decompositions : 0
% 5.16/1.66 % Total rewrite steps : 2569
% 5.16/1.66 % ...of those cached : 2082
% 5.16/1.66 % Propositional unsat checks : 0
% 5.16/1.66 % Propositional check models : 0
% 5.16/1.66 % Propositional check unsatisfiable : 0
% 5.16/1.66 % Propositional clauses : 0
% 5.16/1.66 % Propositional clauses after purity: 0
% 5.16/1.66 % Propositional unsat core size : 0
% 5.16/1.66 % Propositional preprocessing time : 0.000
% 5.16/1.66 % Propositional encoding time : 0.000
% 5.16/1.66 % Propositional solver time : 0.000
% 5.16/1.66 % Success case prop preproc time : 0.000
% 5.16/1.66 % Success case prop encoding time : 0.000
% 5.16/1.66 % Success case prop solver time : 0.000
% 5.16/1.66 % Current number of processed clauses : 1135
% 5.16/1.66 % Positive orientable unit clauses : 302
% 5.16/1.66 % Positive unorientable unit clauses: 1
% 5.16/1.66 % Negative unit clauses : 163
% 5.16/1.66 % Non-unit-clauses : 669
% 5.16/1.66 % Current number of unprocessed clauses: 9174
% 5.16/1.66 % ...number of literals in the above : 30417
% 5.16/1.66 % Current number of archived formulas : 0
% 5.16/1.66 % Current number of archived clauses : 869
% 5.16/1.66 % Clause-clause subsumption calls (NU) : 400606
% 5.16/1.66 % Rec. Clause-clause subsumption calls : 84721
% 5.16/1.66 % Non-unit clause-clause subsumptions : 892
% 5.16/1.66 % Unit Clause-clause subsumption calls : 8304
% 5.16/1.66 % Rewrite failures with RHS unbound : 0
% 5.16/1.66 % BW rewrite match attempts : 68
% 5.16/1.66 % BW rewrite match successes : 30
% 5.16/1.66 % Condensation attempts : 0
% 5.16/1.66 % Condensation successes : 0
% 5.16/1.66 % Termbank termtop insertions : 244073
% 5.16/1.66 % Search garbage collected termcells : 15812
% 5.16/1.66
% 5.16/1.66 % -------------------------------------------------
% 5.16/1.66 % User time : 0.904 s
% 5.16/1.66 % System time : 0.038 s
% 5.16/1.66 % Total time : 0.943 s
% 5.16/1.66 % Maximum resident set size: 6672 pages
% 5.16/1.66
% 5.16/1.66 % -------------------------------------------------
% 5.16/1.66 % User time : 1.813 s
% 5.16/1.66 % System time : 0.075 s
% 5.16/1.66 % Total time : 1.887 s
% 5.16/1.66 % Maximum resident set size: 6144 pages
% 5.16/1.66 % E exiting
%------------------------------------------------------------------------------