TSTP Solution File: SET126-6 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SET126-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n021.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 19:22:14 EDT 2023
% Result : Unsatisfiable 2.66s 0.82s
% Output : CNFRefutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of clauses : 72 ( 31 unt; 15 nHn; 38 RR)
% Number of literals : 122 ( 42 equ; 49 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 110 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',class_elements_are_sets) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',intersection1) ).
cnf(not_subclass_members1,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',not_subclass_members1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',complement1) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',regularity1) ).
cnf(not_subclass_members2,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',not_subclass_members2) ).
cnf(subclass_implies_equal,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',subclass_implies_equal) ).
cnf(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',regularity2) ).
cnf(domain1,axiom,
( restrict(X1,singleton(X2),universal_class) != null_class
| ~ member(X2,domain_of(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',domain1) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',singleton_set) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',restriction1) ).
cnf(definition_of_set_builder,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',definition_of_set_builder) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',complement2) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',intersection3) ).
cnf(prove_set_builder_and_singleton_1,negated_conjecture,
set_builder(x,null_class) != singleton(x),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',prove_set_builder_and_singleton_1) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p',union) ).
cnf(c_0_17,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_18,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_19,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_20,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_21,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_22,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_23,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_25,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X1)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_28,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_29,plain,
subclass(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_31,plain,
null_class = complement(universal_class),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,axiom,
( restrict(X1,singleton(X2),universal_class) != null_class
| ~ member(X2,domain_of(X1)) ),
domain1 ).
cnf(c_0_33,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_34,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_35,plain,
( intersection(X1,X2) = X1
| ~ subclass(X1,intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
( intersection(X1,regular(X1)) = complement(universal_class)
| X1 = complement(universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]) ).
cnf(c_0_37,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_32,c_0_33]),c_0_34]) ).
cnf(c_0_38,plain,
( complement(universal_class) = X1
| ~ subclass(X1,complement(universal_class)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
( intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)) != complement(universal_class)
| ~ member(X2,domain_of(X1)) ),
inference(rw,[status(thm)],[c_0_37,c_0_31]) ).
cnf(c_0_40,plain,
intersection(complement(universal_class),X1) = complement(universal_class),
inference(spm,[status(thm)],[c_0_38,c_0_29]) ).
cnf(c_0_41,plain,
~ member(X1,domain_of(complement(universal_class))),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,plain,
( X1 = complement(universal_class)
| member(regular(X1),X1) ),
inference(rw,[status(thm)],[c_0_22,c_0_31]) ).
cnf(c_0_43,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
definition_of_set_builder ).
cnf(c_0_44,plain,
domain_of(complement(universal_class)) = complement(universal_class),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_46,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_47,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_48,negated_conjecture,
set_builder(x,null_class) != singleton(x),
prove_set_builder_and_singleton_1 ).
cnf(c_0_49,plain,
union(unordered_pair(X1,X1),X2) = set_builder(X1,X2),
inference(rw,[status(thm)],[c_0_43,c_0_33]) ).
cnf(c_0_50,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_51,plain,
~ member(X1,complement(universal_class)),
inference(rw,[status(thm)],[c_0_41,c_0_44]) ).
cnf(c_0_52,plain,
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_45]),c_0_46]) ).
cnf(c_0_53,plain,
( subclass(X1,intersection(X2,X3))
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X3)
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_47]) ).
cnf(c_0_54,negated_conjecture,
complement(intersection(complement(unordered_pair(x,x)),complement(null_class))) != unordered_pair(x,x),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_33]),c_0_49]),c_0_50]) ).
cnf(c_0_55,plain,
( universal_class = X1
| ~ subclass(universal_class,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_18]) ).
cnf(c_0_56,plain,
subclass(X1,complement(complement(universal_class))),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,plain,
( subclass(X1,intersection(X2,universal_class))
| ~ member(not_subclass_element(X1,intersection(X2,universal_class)),X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_46]) ).
cnf(c_0_58,plain,
( subclass(X1,complement(complement(X2)))
| ~ member(not_subclass_element(X1,complement(complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_52]) ).
cnf(c_0_59,plain,
( subclass(complement(X1),X2)
| ~ member(not_subclass_element(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_60,negated_conjecture,
complement(intersection(complement(unordered_pair(x,x)),complement(complement(universal_class)))) != unordered_pair(x,x),
inference(spm,[status(thm)],[c_0_54,c_0_31]) ).
cnf(c_0_61,plain,
complement(complement(universal_class)) = universal_class,
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,plain,
subclass(X1,intersection(X1,universal_class)),
inference(spm,[status(thm)],[c_0_57,c_0_20]) ).
cnf(c_0_63,plain,
subclass(X1,complement(complement(X1))),
inference(spm,[status(thm)],[c_0_58,c_0_20]) ).
cnf(c_0_64,plain,
( member(not_subclass_element(complement(complement(X1)),X2),X1)
| subclass(complement(complement(X1)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_45]),c_0_46]) ).
cnf(c_0_65,negated_conjecture,
complement(intersection(complement(unordered_pair(x,x)),universal_class)) != unordered_pair(x,x),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,plain,
intersection(X1,universal_class) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_62]),c_0_29])]) ).
cnf(c_0_67,plain,
( complement(complement(X1)) = X1
| ~ subclass(complement(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_63]) ).
cnf(c_0_68,plain,
subclass(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_24,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
complement(complement(unordered_pair(x,x))) != unordered_pair(x,x),
inference(rw,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_71,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SET126-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.02/0.13 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n021.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 2400
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Oct 2 16:34:59 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.17/0.44 Running first-order model finding
% 0.17/0.45 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.ovxif0pNu3/E---3.1_31875.p
% 2.66/0.82 # Version: 3.1pre001
% 2.66/0.82 # Preprocessing class: FSLSSMSMSSSNFFN.
% 2.66/0.82 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.66/0.82 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.66/0.82 # Starting new_bool_3 with 300s (1) cores
% 2.66/0.82 # Starting new_bool_1 with 300s (1) cores
% 2.66/0.82 # Starting sh5l with 300s (1) cores
% 2.66/0.82 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 31952 completed with status 0
% 2.66/0.82 # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 2.66/0.82 # Preprocessing class: FSLSSMSMSSSNFFN.
% 2.66/0.82 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.66/0.82 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.66/0.82 # No SInE strategy applied
% 2.66/0.82 # Search class: FGHSM-FFLM31-DFFFFFNN
% 2.66/0.82 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.66/0.82 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 2.66/0.82 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 2.66/0.82 # Starting new_bool_1 with 308s (1) cores
% 2.66/0.82 # Starting sh5l with 304s (1) cores
% 2.66/0.82 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.66/0.82 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 31960 completed with status 0
% 2.66/0.82 # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 2.66/0.82 # Preprocessing class: FSLSSMSMSSSNFFN.
% 2.66/0.82 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.66/0.82 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.66/0.82 # No SInE strategy applied
% 2.66/0.82 # Search class: FGHSM-FFLM31-DFFFFFNN
% 2.66/0.82 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.66/0.82 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 2.66/0.82 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 2.66/0.82 # Preprocessing time : 0.005 s
% 2.66/0.82 # Presaturation interreduction done
% 2.66/0.82
% 2.66/0.82 # Proof found!
% 2.66/0.82 # SZS status Unsatisfiable
% 2.66/0.82 # SZS output start CNFRefutation
% See solution above
% 2.66/0.82 # Parsed axioms : 93
% 2.66/0.82 # Removed by relevancy pruning/SinE : 0
% 2.66/0.82 # Initial clauses : 93
% 2.66/0.82 # Removed in clause preprocessing : 16
% 2.66/0.82 # Initial clauses in saturation : 77
% 2.66/0.82 # Processed clauses : 2475
% 2.66/0.82 # ...of these trivial : 76
% 2.66/0.82 # ...subsumed : 1616
% 2.66/0.82 # ...remaining for further processing : 783
% 2.66/0.82 # Other redundant clauses eliminated : 13
% 2.66/0.82 # Clauses deleted for lack of memory : 0
% 2.66/0.82 # Backward-subsumed : 23
% 2.66/0.82 # Backward-rewritten : 266
% 2.66/0.82 # Generated clauses : 9157
% 2.66/0.82 # ...of the previous two non-redundant : 7920
% 2.66/0.82 # ...aggressively subsumed : 0
% 2.66/0.82 # Contextual simplify-reflections : 11
% 2.66/0.82 # Paramodulations : 9134
% 2.66/0.82 # Factorizations : 10
% 2.66/0.82 # NegExts : 0
% 2.66/0.82 # Equation resolutions : 13
% 2.66/0.82 # Total rewrite steps : 6408
% 2.66/0.82 # Propositional unsat checks : 0
% 2.66/0.82 # Propositional check models : 0
% 2.66/0.82 # Propositional check unsatisfiable : 0
% 2.66/0.82 # Propositional clauses : 0
% 2.66/0.82 # Propositional clauses after purity: 0
% 2.66/0.82 # Propositional unsat core size : 0
% 2.66/0.82 # Propositional preprocessing time : 0.000
% 2.66/0.82 # Propositional encoding time : 0.000
% 2.66/0.82 # Propositional solver time : 0.000
% 2.66/0.82 # Success case prop preproc time : 0.000
% 2.66/0.82 # Success case prop encoding time : 0.000
% 2.66/0.82 # Success case prop solver time : 0.000
% 2.66/0.82 # Current number of processed clauses : 415
% 2.66/0.82 # Positive orientable unit clauses : 53
% 2.66/0.82 # Positive unorientable unit clauses: 1
% 2.66/0.82 # Negative unit clauses : 12
% 2.66/0.82 # Non-unit-clauses : 349
% 2.66/0.82 # Current number of unprocessed clauses: 5391
% 2.66/0.82 # ...number of literals in the above : 19815
% 2.66/0.82 # Current number of archived formulas : 0
% 2.66/0.82 # Current number of archived clauses : 381
% 2.66/0.82 # Clause-clause subsumption calls (NU) : 59439
% 2.66/0.82 # Rec. Clause-clause subsumption calls : 32628
% 2.66/0.82 # Non-unit clause-clause subsumptions : 1158
% 2.66/0.82 # Unit Clause-clause subsumption calls : 2577
% 2.66/0.82 # Rewrite failures with RHS unbound : 0
% 2.66/0.82 # BW rewrite match attempts : 171
% 2.66/0.82 # BW rewrite match successes : 81
% 2.66/0.82 # Condensation attempts : 0
% 2.66/0.82 # Condensation successes : 0
% 2.66/0.82 # Termbank termtop insertions : 529152
% 2.66/0.82
% 2.66/0.82 # -------------------------------------------------
% 2.66/0.82 # User time : 0.341 s
% 2.66/0.82 # System time : 0.013 s
% 2.66/0.82 # Total time : 0.354 s
% 2.66/0.82 # Maximum resident set size: 1980 pages
% 2.66/0.82
% 2.66/0.82 # -------------------------------------------------
% 2.66/0.82 # User time : 1.708 s
% 2.66/0.82 # System time : 0.047 s
% 2.66/0.82 # Total time : 1.755 s
% 2.66/0.82 # Maximum resident set size: 1756 pages
% 2.66/0.82 % E---3.1 exiting
%------------------------------------------------------------------------------