TSTP Solution File: SET505-6 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SET505-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 19:19:17 EDT 2023
% Result : Unsatisfiable 0.82s 0.61s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of clauses : 68 ( 26 unt; 19 nHn; 35 RR)
% Number of literals : 125 ( 45 equ; 47 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 125 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',subclass_members) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',regularity1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',complement1) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',class_elements_are_sets) ).
cnf(domain1,axiom,
( restrict(X1,singleton(X2),universal_class) != null_class
| ~ member(X2,domain_of(X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',domain1) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',singleton_set) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',restriction1) ).
cnf(restriction2,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',restriction2) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',intersection2) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',intersection3) ).
cnf(not_subclass_members1,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',not_subclass_members1) ).
cnf(unordered_pair_member,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',unordered_pair_member) ).
cnf(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',regularity2) ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',ordered_pair) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',intersection1) ).
cnf(cartesian_product1,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',cartesian_product1) ).
cnf(prove_corollary_2_to_universal_class_not_set_1,negated_conjecture,
member(ordered_pair(universal_class,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',prove_corollary_2_to_universal_class_not_set_1) ).
cnf(unordered_pair2,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/tmp/tmp.zt2LwC1aIs/E---3.1_10305.p',unordered_pair2) ).
cnf(c_0_18,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_19,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_20,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_21,plain,
( X1 = null_class
| member(regular(X1),X2)
| ~ subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_23,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_24,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,axiom,
( restrict(X1,singleton(X2),universal_class) != null_class
| ~ member(X2,domain_of(X1)) ),
domain1 ).
cnf(c_0_26,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_27,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_28,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
restriction2 ).
cnf(c_0_29,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_31,plain,
( intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)) != null_class
| ~ member(X2,domain_of(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_32,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(rw,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_33,plain,
( ~ member(X1,null_class)
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_29]) ).
cnf(c_0_34,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_35,plain,
( intersection(cross_product(unordered_pair(X1,X1),universal_class),X2) != null_class
| ~ member(X1,domain_of(X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
intersection(X1,null_class) = null_class,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_24]) ).
cnf(c_0_37,plain,
~ member(X1,domain_of(null_class)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
domain_of(null_class) = null_class,
inference(spm,[status(thm)],[c_0_37,c_0_19]) ).
cnf(c_0_39,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_40,plain,
~ member(X1,null_class),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_42,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_43,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ member(X1,X4)
| ~ subclass(intersection(X4,X3),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_39]) ).
cnf(c_0_44,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_45,plain,
subclass(null_class,X1),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
( regular(unordered_pair(X1,X2)) = X1
| regular(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_42,c_0_19]) ).
cnf(c_0_47,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_48,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_49,plain,
( X1 = null_class
| member(X2,X3)
| ~ member(X2,regular(X1))
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_50,plain,
( regular(unordered_pair(X1,X1)) = X1
| unordered_pair(X1,X1) = null_class ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_46])]) ).
cnf(c_0_51,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product1 ).
cnf(c_0_52,plain,
unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_26]),c_0_26]) ).
cnf(c_0_53,negated_conjecture,
member(ordered_pair(universal_class,y),cross_product(universal_class,universal_class)),
prove_corollary_2_to_universal_class_not_set_1 ).
cnf(c_0_54,plain,
( intersection(X1,complement(X2)) = null_class
| ~ member(regular(intersection(X1,complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_34]) ).
cnf(c_0_55,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_19]) ).
cnf(c_0_56,plain,
( unordered_pair(X1,X1) = null_class
| member(X2,X3)
| ~ member(X2,unordered_pair(X1,X1))
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_58,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_24,c_0_50]) ).
cnf(c_0_59,plain,
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_60,negated_conjecture,
member(unordered_pair(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,unordered_pair(y,y))),cross_product(universal_class,universal_class)),
inference(rw,[status(thm)],[c_0_53,c_0_52]) ).
cnf(c_0_61,plain,
intersection(X1,complement(X1)) = null_class,
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,X2)
| ~ member(X1,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_63,negated_conjecture,
member(universal_class,universal_class),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,plain,
~ member(X1,domain_of(complement(cross_product(unordered_pair(X1,X1),universal_class)))),
inference(spm,[status(thm)],[c_0_35,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
( unordered_pair(universal_class,universal_class) = null_class
| member(universal_class,X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,negated_conjecture,
unordered_pair(universal_class,universal_class) = null_class,
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_66]),c_0_63])]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET505-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 2400
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Oct 2 16:17:19 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 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.zt2LwC1aIs/E---3.1_10305.p
% 0.82/0.61 # Version: 3.1pre001
% 0.82/0.61 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.82/0.61 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.61 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.82/0.61 # Starting new_bool_3 with 300s (1) cores
% 0.82/0.61 # Starting new_bool_1 with 300s (1) cores
% 0.82/0.61 # Starting sh5l with 300s (1) cores
% 0.82/0.61 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 10383 completed with status 0
% 0.82/0.61 # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.82/0.61 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.82/0.61 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.61 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.82/0.61 # No SInE strategy applied
% 0.82/0.61 # Search class: FGHSM-FFLM31-DFFFFFNN
% 0.82/0.61 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.82/0.61 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 0.82/0.61 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.82/0.61 # Starting new_bool_1 with 308s (1) cores
% 0.82/0.61 # Starting sh5l with 304s (1) cores
% 0.82/0.61 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.82/0.61 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 10390 completed with status 0
% 0.82/0.61 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.82/0.61 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.82/0.61 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.61 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.82/0.61 # No SInE strategy applied
% 0.82/0.61 # Search class: FGHSM-FFLM31-DFFFFFNN
% 0.82/0.61 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.82/0.61 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 0.82/0.61 # Preprocessing time : 0.004 s
% 0.82/0.61 # Presaturation interreduction done
% 0.82/0.61
% 0.82/0.61 # Proof found!
% 0.82/0.61 # SZS status Unsatisfiable
% 0.82/0.61 # SZS output start CNFRefutation
% See solution above
% 0.82/0.61 # Parsed axioms : 113
% 0.82/0.61 # Removed by relevancy pruning/SinE : 0
% 0.82/0.61 # Initial clauses : 113
% 0.82/0.61 # Removed in clause preprocessing : 17
% 0.82/0.61 # Initial clauses in saturation : 96
% 0.82/0.61 # Processed clauses : 706
% 0.82/0.61 # ...of these trivial : 4
% 0.82/0.61 # ...subsumed : 209
% 0.82/0.61 # ...remaining for further processing : 493
% 0.82/0.61 # Other redundant clauses eliminated : 8
% 0.82/0.61 # Clauses deleted for lack of memory : 0
% 0.82/0.61 # Backward-subsumed : 19
% 0.82/0.61 # Backward-rewritten : 29
% 0.82/0.61 # Generated clauses : 1757
% 0.82/0.61 # ...of the previous two non-redundant : 1344
% 0.82/0.61 # ...aggressively subsumed : 0
% 0.82/0.61 # Contextual simplify-reflections : 4
% 0.82/0.61 # Paramodulations : 1745
% 0.82/0.61 # Factorizations : 4
% 0.82/0.61 # NegExts : 0
% 0.82/0.61 # Equation resolutions : 8
% 0.82/0.61 # Total rewrite steps : 486
% 0.82/0.61 # Propositional unsat checks : 0
% 0.82/0.61 # Propositional check models : 0
% 0.82/0.61 # Propositional check unsatisfiable : 0
% 0.82/0.61 # Propositional clauses : 0
% 0.82/0.61 # Propositional clauses after purity: 0
% 0.82/0.61 # Propositional unsat core size : 0
% 0.82/0.61 # Propositional preprocessing time : 0.000
% 0.82/0.61 # Propositional encoding time : 0.000
% 0.82/0.61 # Propositional solver time : 0.000
% 0.82/0.61 # Success case prop preproc time : 0.000
% 0.82/0.61 # Success case prop encoding time : 0.000
% 0.82/0.61 # Success case prop solver time : 0.000
% 0.82/0.61 # Current number of processed clauses : 346
% 0.82/0.61 # Positive orientable unit clauses : 54
% 0.82/0.61 # Positive unorientable unit clauses: 1
% 0.82/0.61 # Negative unit clauses : 2
% 0.82/0.61 # Non-unit-clauses : 289
% 0.82/0.61 # Current number of unprocessed clauses: 810
% 0.82/0.61 # ...number of literals in the above : 2448
% 0.82/0.61 # Current number of archived formulas : 0
% 0.82/0.61 # Current number of archived clauses : 160
% 0.82/0.61 # Clause-clause subsumption calls (NU) : 20323
% 0.82/0.61 # Rec. Clause-clause subsumption calls : 9953
% 0.82/0.61 # Non-unit clause-clause subsumptions : 200
% 0.82/0.61 # Unit Clause-clause subsumption calls : 846
% 0.82/0.61 # Rewrite failures with RHS unbound : 0
% 0.82/0.61 # BW rewrite match attempts : 41
% 0.82/0.61 # BW rewrite match successes : 12
% 0.82/0.61 # Condensation attempts : 0
% 0.82/0.61 # Condensation successes : 0
% 0.82/0.61 # Termbank termtop insertions : 57394
% 0.82/0.61
% 0.82/0.61 # -------------------------------------------------
% 0.82/0.61 # User time : 0.084 s
% 0.82/0.61 # System time : 0.009 s
% 0.82/0.61 # Total time : 0.093 s
% 0.82/0.61 # Maximum resident set size: 2004 pages
% 0.82/0.61
% 0.82/0.61 # -------------------------------------------------
% 0.82/0.61 # User time : 0.371 s
% 0.82/0.61 # System time : 0.028 s
% 0.82/0.61 # Total time : 0.399 s
% 0.82/0.61 # Maximum resident set size: 1772 pages
% 0.82/0.61 % E---3.1 exiting
% 1.00/0.61 % E---3.1 exiting
%------------------------------------------------------------------------------