TSTP Solution File: NUM156-1 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : NUM156-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n003.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 18:58:24 EDT 2023
% Result : Unsatisfiable 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of clauses : 42 ( 28 unt; 3 nHn; 22 RR)
% Number of literals : 60 ( 16 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 52 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(inductive1,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',inductive1) ).
cnf(omega_is_inductive1,axiom,
inductive(omega),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',omega_is_inductive1) ).
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',class_elements_are_sets) ).
cnf(image,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',image) ).
cnf(range_of,axiom,
domain_of(inverse(X1)) = range_of(X1),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',range_of) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',restriction1) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',complement2) ).
cnf(kind_1_ordinals,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',kind_1_ordinals) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',singleton_set) ).
cnf(inverse,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',inverse) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',union) ).
cnf(prove_null_class_is_kind_1_1,negated_conjecture,
~ member(null_class,kind_1_ordinals),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',prove_null_class_is_kind_1_1) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',intersection1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',complement1) ).
cnf(unordered_pair2,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/tmp/tmp.tdFyhFii11/E---3.1_32265.p',unordered_pair2) ).
cnf(c_0_16,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
inductive1 ).
cnf(c_0_17,axiom,
inductive(omega),
omega_is_inductive1 ).
cnf(c_0_18,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_19,plain,
member(null_class,omega),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( member(null_class,X1)
| ~ subclass(omega,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_22,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
image ).
cnf(c_0_23,axiom,
domain_of(inverse(X1)) = range_of(X1),
range_of ).
cnf(c_0_24,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_25,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_26,plain,
member(null_class,universal_class),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
kind_1_ordinals ).
cnf(c_0_28,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_29,plain,
domain_of(inverse(intersection(X1,cross_product(X2,universal_class)))) = image(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_30,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inverse ).
cnf(c_0_31,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_32,plain,
( member(null_class,complement(X1))
| member(null_class,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
complement(intersection(complement(unordered_pair(null_class,null_class)),complement(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(ordinal_numbers,universal_class)),universal_class))))))) = kind_1_ordinals,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
~ member(null_class,kind_1_ordinals),
prove_null_class_is_kind_1_1 ).
cnf(c_0_35,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_36,plain,
member(null_class,intersection(complement(unordered_pair(null_class,null_class)),complement(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(ordinal_numbers,universal_class)),universal_class))))))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_37,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_38,plain,
member(null_class,complement(unordered_pair(null_class,null_class))),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
~ member(null_class,unordered_pair(null_class,null_class)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_41,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : NUM156-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 2400
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Oct 2 13:54:33 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.44 Running first-order model finding
% 0.17/0.44 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.tdFyhFii11/E---3.1_32265.p
% 0.17/0.49 # Version: 3.1pre001
% 0.17/0.49 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/0.49 # Starting new_bool_3 with 300s (1) cores
% 0.17/0.49 # Starting new_bool_1 with 300s (1) cores
% 0.17/0.49 # Starting sh5l with 300s (1) cores
% 0.17/0.49 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 32342 completed with status 0
% 0.17/0.49 # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.17/0.49 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/0.49 # No SInE strategy applied
% 0.17/0.49 # Search class: FGHSM-FFLM31-DFFFFFNN
% 0.17/0.49 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.49 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 0.17/0.49 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.17/0.49 # Starting new_bool_1 with 308s (1) cores
% 0.17/0.49 # Starting sh5l with 304s (1) cores
% 0.17/0.49 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.17/0.49 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 32349 completed with status 0
% 0.17/0.49 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.17/0.49 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/0.49 # No SInE strategy applied
% 0.17/0.49 # Search class: FGHSM-FFLM31-DFFFFFNN
% 0.17/0.49 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.49 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 0.17/0.49 # Preprocessing time : 0.002 s
% 0.17/0.49 # Presaturation interreduction done
% 0.17/0.49
% 0.17/0.49 # Proof found!
% 0.17/0.49 # SZS status Unsatisfiable
% 0.17/0.49 # SZS output start CNFRefutation
% See solution above
% 0.17/0.49 # Parsed axioms : 159
% 0.17/0.49 # Removed by relevancy pruning/SinE : 0
% 0.17/0.49 # Initial clauses : 159
% 0.17/0.49 # Removed in clause preprocessing : 19
% 0.17/0.49 # Initial clauses in saturation : 140
% 0.17/0.49 # Processed clauses : 587
% 0.17/0.49 # ...of these trivial : 2
% 0.17/0.49 # ...subsumed : 91
% 0.17/0.49 # ...remaining for further processing : 494
% 0.17/0.49 # Other redundant clauses eliminated : 6
% 0.17/0.49 # Clauses deleted for lack of memory : 0
% 0.17/0.49 # Backward-subsumed : 27
% 0.17/0.49 # Backward-rewritten : 12
% 0.17/0.49 # Generated clauses : 836
% 0.17/0.49 # ...of the previous two non-redundant : 743
% 0.17/0.49 # ...aggressively subsumed : 0
% 0.17/0.49 # Contextual simplify-reflections : 6
% 0.17/0.49 # Paramodulations : 826
% 0.17/0.49 # Factorizations : 4
% 0.17/0.49 # NegExts : 0
% 0.17/0.49 # Equation resolutions : 6
% 0.17/0.49 # Total rewrite steps : 90
% 0.17/0.49 # Propositional unsat checks : 0
% 0.17/0.49 # Propositional check models : 0
% 0.17/0.49 # Propositional check unsatisfiable : 0
% 0.17/0.49 # Propositional clauses : 0
% 0.17/0.49 # Propositional clauses after purity: 0
% 0.17/0.49 # Propositional unsat core size : 0
% 0.17/0.49 # Propositional preprocessing time : 0.000
% 0.17/0.49 # Propositional encoding time : 0.000
% 0.17/0.49 # Propositional solver time : 0.000
% 0.17/0.49 # Success case prop preproc time : 0.000
% 0.17/0.49 # Success case prop encoding time : 0.000
% 0.17/0.49 # Success case prop solver time : 0.000
% 0.17/0.49 # Current number of processed clauses : 310
% 0.17/0.49 # Positive orientable unit clauses : 44
% 0.17/0.49 # Positive unorientable unit clauses: 3
% 0.17/0.49 # Negative unit clauses : 4
% 0.17/0.49 # Non-unit-clauses : 259
% 0.17/0.49 # Current number of unprocessed clauses: 340
% 0.17/0.49 # ...number of literals in the above : 984
% 0.17/0.49 # Current number of archived formulas : 0
% 0.17/0.49 # Current number of archived clauses : 197
% 0.17/0.49 # Clause-clause subsumption calls (NU) : 16909
% 0.17/0.49 # Rec. Clause-clause subsumption calls : 7747
% 0.17/0.49 # Non-unit clause-clause subsumptions : 103
% 0.17/0.49 # Unit Clause-clause subsumption calls : 488
% 0.17/0.49 # Rewrite failures with RHS unbound : 0
% 0.17/0.49 # BW rewrite match attempts : 25
% 0.17/0.49 # BW rewrite match successes : 15
% 0.17/0.49 # Condensation attempts : 0
% 0.17/0.49 # Condensation successes : 0
% 0.17/0.49 # Termbank termtop insertions : 23830
% 0.17/0.49
% 0.17/0.49 # -------------------------------------------------
% 0.17/0.49 # User time : 0.035 s
% 0.17/0.49 # System time : 0.006 s
% 0.17/0.49 # Total time : 0.041 s
% 0.17/0.49 # Maximum resident set size: 2228 pages
% 0.17/0.49
% 0.17/0.49 # -------------------------------------------------
% 0.17/0.49 # User time : 0.179 s
% 0.17/0.49 # System time : 0.013 s
% 0.17/0.49 # Total time : 0.192 s
% 0.17/0.49 # Maximum resident set size: 1812 pages
% 0.17/0.49 % E---3.1 exiting
%------------------------------------------------------------------------------