TSTP Solution File: SEU341+2 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SEU341+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n010.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:26:04 EDT 2023
% Result : Theorem 18.04s 2.87s
% Output : CNFRefutation 18.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 13 unt; 0 def)
% Number of atoms : 131 ( 11 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 151 ( 56 ~; 46 |; 22 &)
% ( 3 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn; 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t5_connsp_2,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( open_subset(X2,X1)
& in(X3,X2) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UI68M4fQLk/E---3.1_30177.p',t5_connsp_2) ).
fof(d1_connsp_2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(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/sandbox2/tmp/tmp.UI68M4fQLk/E---3.1_30177.p',d1_connsp_2) ).
fof(d1_tops_1,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UI68M4fQLk/E---3.1_30177.p',d1_tops_1) ).
fof(t30_tops_1,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( open_subset(X2,X1)
<=> closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UI68M4fQLk/E---3.1_30177.p',t30_tops_1) ).
fof(t52_pre_topc,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( ( closed_subset(X2,X1)
=> topstr_closure(X1,X2) = X2 )
& ( ( topological_space(X1)
& topstr_closure(X1,X2) = X2 )
=> closed_subset(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UI68M4fQLk/E---3.1_30177.p',t52_pre_topc) ).
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/tmp/tmp.UI68M4fQLk/E---3.1_30177.p',involutiveness_k3_subset_1) ).
fof(dt_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.UI68M4fQLk/E---3.1_30177.p',dt_k3_subset_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( open_subset(X2,X1)
& in(X3,X2) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t5_connsp_2])]) ).
fof(c_0_8,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(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]) ).
fof(c_0_9,negated_conjecture,
( ~ empty_carrier(esk416_0)
& topological_space(esk416_0)
& top_str(esk416_0)
& element(esk417_0,powerset(the_carrier(esk416_0)))
& element(esk418_0,the_carrier(esk416_0))
& open_subset(esk417_0,esk416_0)
& in(esk418_0,esk417_0)
& ~ point_neighbourhood(esk417_0,esk416_0,esk418_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X169,X170,X171] :
( ( ~ point_neighbourhood(X171,X169,X170)
| in(X170,interior(X169,X171))
| ~ element(X171,powerset(the_carrier(X169)))
| ~ element(X170,the_carrier(X169))
| empty_carrier(X169)
| ~ topological_space(X169)
| ~ top_str(X169) )
& ( ~ in(X170,interior(X169,X171))
| point_neighbourhood(X171,X169,X170)
| ~ element(X171,powerset(the_carrier(X169)))
| ~ element(X170,the_carrier(X169))
| empty_carrier(X169)
| ~ topological_space(X169)
| ~ top_str(X169) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_11,negated_conjecture,
~ point_neighbourhood(esk417_0,esk416_0,esk418_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( point_neighbourhood(X3,X2,X1)
| empty_carrier(X2)
| ~ in(X1,interior(X2,X3))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ element(X1,the_carrier(X2))
| ~ topological_space(X2)
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
topological_space(esk416_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
top_str(esk416_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
element(esk417_0,powerset(the_carrier(esk416_0))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
element(esk418_0,the_carrier(esk416_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
~ empty_carrier(esk416_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_18,plain,
! [X255,X256] :
( ~ top_str(X255)
| ~ element(X256,powerset(the_carrier(X255)))
| interior(X255,X256) = subset_complement(the_carrier(X255),topstr_closure(X255,subset_complement(the_carrier(X255),X256))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tops_1])])]) ).
fof(c_0_19,lemma,
! [X1645,X1646] :
( ( ~ open_subset(X1646,X1645)
| closed_subset(subset_complement(the_carrier(X1645),X1646),X1645)
| ~ element(X1646,powerset(the_carrier(X1645)))
| ~ top_str(X1645) )
& ( ~ closed_subset(subset_complement(the_carrier(X1645),X1646),X1645)
| open_subset(X1646,X1645)
| ~ element(X1646,powerset(the_carrier(X1645)))
| ~ top_str(X1645) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t30_tops_1])])])]) ).
cnf(c_0_20,negated_conjecture,
~ in(esk418_0,interior(esk416_0,esk417_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_11,c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16])]),c_0_17]) ).
cnf(c_0_21,plain,
( interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2)))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_22,lemma,
! [X1773,X1774] :
( ( ~ closed_subset(X1774,X1773)
| topstr_closure(X1773,X1774) = X1774
| ~ element(X1774,powerset(the_carrier(X1773)))
| ~ top_str(X1773) )
& ( ~ topological_space(X1773)
| topstr_closure(X1773,X1774) != X1774
| closed_subset(X1774,X1773)
| ~ element(X1774,powerset(the_carrier(X1773)))
| ~ top_str(X1773) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t52_pre_topc])])])]) ).
cnf(c_0_23,lemma,
( closed_subset(subset_complement(the_carrier(X2),X1),X2)
| ~ open_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
open_subset(esk417_0,esk416_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,negated_conjecture,
~ in(esk418_0,subset_complement(the_carrier(esk416_0),topstr_closure(esk416_0,subset_complement(the_carrier(esk416_0),esk417_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14]),c_0_15])]) ).
cnf(c_0_26,lemma,
( topstr_closure(X2,X1) = X1
| ~ closed_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
closed_subset(subset_complement(the_carrier(esk416_0),esk417_0),esk416_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_14]),c_0_15])]) ).
fof(c_0_28,plain,
! [X754,X755] :
( ~ element(X755,powerset(X754))
| subset_complement(X754,subset_complement(X754,X755)) = X755 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).
cnf(c_0_29,lemma,
( ~ element(subset_complement(the_carrier(esk416_0),esk417_0),powerset(the_carrier(esk416_0)))
| ~ in(esk418_0,subset_complement(the_carrier(esk416_0),subset_complement(the_carrier(esk416_0),esk417_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_14])]) ).
cnf(c_0_30,plain,
( subset_complement(X2,subset_complement(X2,X1)) = X1
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,negated_conjecture,
in(esk418_0,esk417_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_32,plain,
! [X589,X590] :
( ~ element(X590,powerset(X589))
| element(subset_complement(X589,X590),powerset(X589)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).
cnf(c_0_33,lemma,
~ element(subset_complement(the_carrier(esk416_0),esk417_0),powerset(the_carrier(esk416_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_15])]) ).
cnf(c_0_34,plain,
( element(subset_complement(X2,X1),powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_35,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : SEU341+2 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.16 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 2400
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Oct 2 08:54:35 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.20/0.51 Running first-order theorem proving
% 0.20/0.51 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.UI68M4fQLk/E---3.1_30177.p
% 18.04/2.87 # Version: 3.1pre001
% 18.04/2.87 # Preprocessing class: FSLMSMSSSSSNFFN.
% 18.04/2.87 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.04/2.87 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 18.04/2.87 # Starting new_bool_3 with 600s (2) cores
% 18.04/2.87 # Starting new_bool_1 with 600s (2) cores
% 18.04/2.87 # Starting sh5l with 300s (1) cores
% 18.04/2.87 # G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 30255 completed with status 0
% 18.04/2.87 # Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 18.04/2.87 # Preprocessing class: FSLMSMSSSSSNFFN.
% 18.04/2.87 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.04/2.87 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 18.04/2.87 # No SInE strategy applied
% 18.04/2.87 # Search class: FGHSM-SMLM32-MFFFFFNN
% 18.04/2.87 # Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 18.04/2.87 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 68s (1) cores
% 18.04/2.87 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 18.04/2.87 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 68s (1) cores
% 18.04/2.87 # G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 30265 completed with status 0
% 18.04/2.87 # Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 18.04/2.87 # Preprocessing class: FSLMSMSSSSSNFFN.
% 18.04/2.87 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.04/2.87 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 18.04/2.87 # No SInE strategy applied
% 18.04/2.87 # Search class: FGHSM-SMLM32-MFFFFFNN
% 18.04/2.87 # Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 18.04/2.87 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 68s (1) cores
% 18.04/2.87 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 18.04/2.87 # Preprocessing time : 0.042 s
% 18.04/2.87 # Presaturation interreduction done
% 18.04/2.87
% 18.04/2.87 # Proof found!
% 18.04/2.87 # SZS status Theorem
% 18.04/2.87 # SZS output start CNFRefutation
% See solution above
% 18.04/2.87 # Parsed axioms : 573
% 18.04/2.87 # Removed by relevancy pruning/SinE : 0
% 18.04/2.87 # Initial clauses : 2561
% 18.04/2.87 # Removed in clause preprocessing : 40
% 18.04/2.87 # Initial clauses in saturation : 2521
% 18.04/2.87 # Processed clauses : 10014
% 18.04/2.87 # ...of these trivial : 104
% 18.04/2.87 # ...subsumed : 4219
% 18.04/2.87 # ...remaining for further processing : 5691
% 18.04/2.87 # Other redundant clauses eliminated : 928
% 18.04/2.87 # Clauses deleted for lack of memory : 0
% 18.04/2.87 # Backward-subsumed : 32
% 18.04/2.87 # Backward-rewritten : 61
% 18.04/2.87 # Generated clauses : 27938
% 18.04/2.87 # ...of the previous two non-redundant : 25212
% 18.04/2.87 # ...aggressively subsumed : 0
% 18.04/2.87 # Contextual simplify-reflections : 290
% 18.04/2.87 # Paramodulations : 27236
% 18.04/2.87 # Factorizations : 2
% 18.04/2.87 # NegExts : 0
% 18.04/2.87 # Equation resolutions : 933
% 18.04/2.87 # Total rewrite steps : 5844
% 18.04/2.87 # Propositional unsat checks : 1
% 18.04/2.87 # Propositional check models : 1
% 18.04/2.87 # Propositional check unsatisfiable : 0
% 18.04/2.87 # Propositional clauses : 0
% 18.04/2.87 # Propositional clauses after purity: 0
% 18.04/2.87 # Propositional unsat core size : 0
% 18.04/2.87 # Propositional preprocessing time : 0.000
% 18.04/2.87 # Propositional encoding time : 0.023
% 18.04/2.87 # Propositional solver time : 0.021
% 18.04/2.87 # Success case prop preproc time : 0.000
% 18.04/2.87 # Success case prop encoding time : 0.000
% 18.04/2.87 # Success case prop solver time : 0.000
% 18.04/2.87 # Current number of processed clauses : 2621
% 18.04/2.87 # Positive orientable unit clauses : 238
% 18.04/2.87 # Positive unorientable unit clauses: 4
% 18.04/2.87 # Negative unit clauses : 583
% 18.04/2.87 # Non-unit-clauses : 1796
% 18.04/2.87 # Current number of unprocessed clauses: 19924
% 18.04/2.87 # ...number of literals in the above : 69157
% 18.04/2.87 # Current number of archived formulas : 0
% 18.04/2.87 # Current number of archived clauses : 2444
% 18.04/2.87 # Clause-clause subsumption calls (NU) : 3965187
% 18.04/2.87 # Rec. Clause-clause subsumption calls : 517921
% 18.04/2.87 # Non-unit clause-clause subsumptions : 1702
% 18.04/2.87 # Unit Clause-clause subsumption calls : 132158
% 18.04/2.87 # Rewrite failures with RHS unbound : 3
% 18.04/2.87 # BW rewrite match attempts : 128
% 18.04/2.87 # BW rewrite match successes : 84
% 18.04/2.87 # Condensation attempts : 0
% 18.04/2.87 # Condensation successes : 0
% 18.04/2.87 # Termbank termtop insertions : 573070
% 18.04/2.87
% 18.04/2.87 # -------------------------------------------------
% 18.04/2.87 # User time : 2.257 s
% 18.04/2.87 # System time : 0.042 s
% 18.04/2.87 # Total time : 2.299 s
% 18.04/2.87 # Maximum resident set size: 8652 pages
% 18.04/2.87
% 18.04/2.87 # -------------------------------------------------
% 18.04/2.87 # User time : 6.553 s
% 18.04/2.87 # System time : 0.114 s
% 18.04/2.87 # Total time : 6.667 s
% 18.04/2.87 # Maximum resident set size: 2464 pages
% 18.04/2.87 % E---3.1 exiting
% 18.04/2.87 % E---3.1 exiting
%------------------------------------------------------------------------------