TSTP Solution File: SET206-6 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SET206-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.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 19:18:53 EDT 2023
% Result : Unsatisfiable 41.32s 5.64s
% Output : CNFRefutation 41.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 40 ( 16 unt; 7 nHn; 24 RR)
% Number of literals : 67 ( 29 equ; 28 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 77 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/tmp/tmp.90aZUujGso/E---3.1_16757.p',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/tmp/tmp.90aZUujGso/E---3.1_16757.p',class_elements_are_sets) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.90aZUujGso/E---3.1_16757.p',intersection2) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.90aZUujGso/E---3.1_16757.p',regularity1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.90aZUujGso/E---3.1_16757.p',complement1) ).
cnf(domain1,axiom,
( restrict(X1,singleton(X2),universal_class) != null_class
| ~ member(X2,domain_of(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.90aZUujGso/E---3.1_16757.p',domain1) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox/tmp/tmp.90aZUujGso/E---3.1_16757.p',restriction1) ).
cnf(restriction2,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
file('/export/starexec/sandbox/tmp/tmp.90aZUujGso/E---3.1_16757.p',restriction2) ).
cnf(cartesian_product4,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.90aZUujGso/E---3.1_16757.p',cartesian_product4) ).
cnf(cartesian_product1,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox/tmp/tmp.90aZUujGso/E---3.1_16757.p',cartesian_product1) ).
cnf(prove_cross_product_with_null_class2_1,negated_conjecture,
cross_product(null_class,y) != null_class,
file('/export/starexec/sandbox/tmp/tmp.90aZUujGso/E---3.1_16757.p',prove_cross_product_with_null_class2_1) ).
cnf(c_0_11,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_12,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_13,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_14,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_15,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_16,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_19,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_20,axiom,
( restrict(X1,singleton(X2),universal_class) != null_class
| ~ member(X2,domain_of(X1)) ),
domain1 ).
cnf(c_0_21,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_22,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
restriction2 ).
cnf(c_0_23,plain,
( intersection(X1,complement(X2)) = null_class
| ~ member(regular(intersection(X1,complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_24,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( intersection(X1,cross_product(singleton(X2),universal_class)) != null_class
| ~ member(X2,domain_of(X1)) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
intersection(X1,cross_product(X2,X3)) = intersection(cross_product(X2,X3),X1),
inference(rw,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_27,plain,
intersection(X1,null_class) = null_class,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_19]),c_0_24]) ).
cnf(c_0_28,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
cartesian_product4 ).
cnf(c_0_29,plain,
( domain_of(X1) = null_class
| intersection(X1,cross_product(singleton(regular(domain_of(X1))),universal_class)) != null_class ),
inference(spm,[status(thm)],[c_0_25,c_0_14]) ).
cnf(c_0_30,plain,
intersection(null_class,cross_product(X1,X2)) = null_class,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product1 ).
cnf(c_0_32,plain,
( ordered_pair(first(regular(cross_product(X1,X2))),second(regular(cross_product(X1,X2)))) = regular(cross_product(X1,X2))
| cross_product(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_28,c_0_14]) ).
cnf(c_0_33,plain,
domain_of(null_class) = null_class,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( cross_product(X1,X2) = null_class
| member(first(regular(cross_product(X1,X2))),X3)
| ~ member(regular(cross_product(X1,X2)),cross_product(X3,X4)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
~ member(X1,null_class),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_33]),c_0_30])]) ).
cnf(c_0_36,plain,
( cross_product(X1,X2) = null_class
| member(first(regular(cross_product(X1,X2))),X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_14]) ).
cnf(c_0_37,negated_conjecture,
cross_product(null_class,y) != null_class,
prove_cross_product_with_null_class2_1 ).
cnf(c_0_38,plain,
cross_product(null_class,X1) = null_class,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET206-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 2400
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Oct 2 16:54:39 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.44 Running first-order theorem proving
% 0.16/0.44 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/tmp/tmp.90aZUujGso/E---3.1_16757.p
% 41.32/5.64 # Version: 3.1pre001
% 41.32/5.64 # Preprocessing class: FSLSSMSMSSSNFFN.
% 41.32/5.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 41.32/5.64 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 41.32/5.64 # Starting new_bool_3 with 300s (1) cores
% 41.32/5.64 # Starting new_bool_1 with 300s (1) cores
% 41.32/5.64 # Starting sh5l with 300s (1) cores
% 41.32/5.64 # sh5l with pid 16838 completed with status 0
% 41.32/5.64 # Result found by sh5l
% 41.32/5.64 # Preprocessing class: FSLSSMSMSSSNFFN.
% 41.32/5.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 41.32/5.64 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 41.32/5.64 # Starting new_bool_3 with 300s (1) cores
% 41.32/5.64 # Starting new_bool_1 with 300s (1) cores
% 41.32/5.64 # Starting sh5l with 300s (1) cores
% 41.32/5.64 # SinE strategy is gf500_gu_R04_F100_L20000
% 41.32/5.64 # Search class: FGHSM-FFMM31-MFFFFFNN
% 41.32/5.64 # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 41.32/5.64 # Starting G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with 23s (1) cores
% 41.32/5.64 # G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with pid 16841 completed with status 0
% 41.32/5.64 # Result found by G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S
% 41.32/5.64 # Preprocessing class: FSLSSMSMSSSNFFN.
% 41.32/5.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 41.32/5.64 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 41.32/5.64 # Starting new_bool_3 with 300s (1) cores
% 41.32/5.64 # Starting new_bool_1 with 300s (1) cores
% 41.32/5.64 # Starting sh5l with 300s (1) cores
% 41.32/5.64 # SinE strategy is gf500_gu_R04_F100_L20000
% 41.32/5.64 # Search class: FGHSM-FFMM31-MFFFFFNN
% 41.32/5.64 # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 41.32/5.64 # Starting G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with 23s (1) cores
% 41.32/5.64 # Preprocessing time : 0.003 s
% 41.32/5.64 # Presaturation interreduction done
% 41.32/5.64
% 41.32/5.64 # Proof found!
% 41.32/5.64 # SZS status Unsatisfiable
% 41.32/5.64 # SZS output start CNFRefutation
% See solution above
% 41.32/5.64 # Parsed axioms : 113
% 41.32/5.64 # Removed by relevancy pruning/SinE : 14
% 41.32/5.64 # Initial clauses : 99
% 41.32/5.64 # Removed in clause preprocessing : 0
% 41.32/5.64 # Initial clauses in saturation : 99
% 41.32/5.64 # Processed clauses : 12471
% 41.32/5.64 # ...of these trivial : 710
% 41.32/5.64 # ...subsumed : 7360
% 41.32/5.64 # ...remaining for further processing : 4401
% 41.32/5.64 # Other redundant clauses eliminated : 16
% 41.32/5.64 # Clauses deleted for lack of memory : 0
% 41.32/5.64 # Backward-subsumed : 168
% 41.32/5.64 # Backward-rewritten : 688
% 41.32/5.64 # Generated clauses : 397883
% 41.32/5.64 # ...of the previous two non-redundant : 325469
% 41.32/5.64 # ...aggressively subsumed : 0
% 41.32/5.64 # Contextual simplify-reflections : 7
% 41.32/5.64 # Paramodulations : 397836
% 41.32/5.64 # Factorizations : 22
% 41.32/5.64 # NegExts : 0
% 41.32/5.64 # Equation resolutions : 25
% 41.32/5.64 # Total rewrite steps : 159650
% 41.32/5.64 # Propositional unsat checks : 0
% 41.32/5.64 # Propositional check models : 0
% 41.32/5.64 # Propositional check unsatisfiable : 0
% 41.32/5.64 # Propositional clauses : 0
% 41.32/5.64 # Propositional clauses after purity: 0
% 41.32/5.64 # Propositional unsat core size : 0
% 41.32/5.64 # Propositional preprocessing time : 0.000
% 41.32/5.64 # Propositional encoding time : 0.000
% 41.32/5.64 # Propositional solver time : 0.000
% 41.32/5.64 # Success case prop preproc time : 0.000
% 41.32/5.64 # Success case prop encoding time : 0.000
% 41.32/5.64 # Success case prop solver time : 0.000
% 41.32/5.64 # Current number of processed clauses : 3445
% 41.32/5.64 # Positive orientable unit clauses : 1453
% 41.32/5.64 # Positive unorientable unit clauses: 10
% 41.32/5.64 # Negative unit clauses : 13
% 41.32/5.64 # Non-unit-clauses : 1969
% 41.32/5.64 # Current number of unprocessed clauses: 311653
% 41.32/5.64 # ...number of literals in the above : 613110
% 41.32/5.64 # Current number of archived formulas : 0
% 41.32/5.64 # Current number of archived clauses : 954
% 41.32/5.64 # Clause-clause subsumption calls (NU) : 676012
% 41.32/5.64 # Rec. Clause-clause subsumption calls : 458571
% 41.32/5.64 # Non-unit clause-clause subsumptions : 5401
% 41.32/5.64 # Unit Clause-clause subsumption calls : 185261
% 41.32/5.64 # Rewrite failures with RHS unbound : 86
% 41.32/5.64 # BW rewrite match attempts : 6481
% 41.32/5.64 # BW rewrite match successes : 182
% 41.32/5.64 # Condensation attempts : 0
% 41.32/5.64 # Condensation successes : 0
% 41.32/5.64 # Termbank termtop insertions : 6685116
% 41.32/5.64
% 41.32/5.64 # -------------------------------------------------
% 41.32/5.64 # User time : 4.949 s
% 41.32/5.64 # System time : 0.200 s
% 41.32/5.64 # Total time : 5.149 s
% 41.32/5.64 # Maximum resident set size: 1968 pages
% 41.32/5.64
% 41.32/5.64 # -------------------------------------------------
% 41.32/5.64 # User time : 4.952 s
% 41.32/5.64 # System time : 0.201 s
% 41.32/5.64 # Total time : 5.154 s
% 41.32/5.64 # Maximum resident set size: 1768 pages
% 41.32/5.64 % E---3.1 exiting
% 41.32/5.64 % E---3.1 exiting
%------------------------------------------------------------------------------