TSTP Solution File: SET122-7 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SET122-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n013.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 19:22:13 EDT 2023
% Result : Unsatisfiable 0.16s 0.51s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 39 ( 21 unt; 15 nHn; 15 RR)
% Number of literals : 57 ( 34 equ; 13 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox2/tmp/tmp.2zuEtS5lTg/E---3.1_21808.p',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/tmp/tmp.2zuEtS5lTg/E---3.1_21808.p',singleton_set) ).
cnf(singleton_is_null_class,axiom,
( member(X1,universal_class)
| singleton(X1) = null_class ),
file('/export/starexec/sandbox2/tmp/tmp.2zuEtS5lTg/E---3.1_21808.p',singleton_is_null_class) ).
cnf(unordered_pair_equals_singleton1,axiom,
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
file('/export/starexec/sandbox2/tmp/tmp.2zuEtS5lTg/E---3.1_21808.p',unordered_pair_equals_singleton1) ).
cnf(corollary_2_to_cartesian_product,axiom,
( member(X2,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.2zuEtS5lTg/E---3.1_21808.p',corollary_2_to_cartesian_product) ).
cnf(prove_corollary_2_to_OP_determines_components2_1,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox2/tmp/tmp.2zuEtS5lTg/E---3.1_21808.p',prove_corollary_2_to_OP_determines_components2_1) ).
cnf(prove_corollary_2_to_OP_determines_components2_2,negated_conjecture,
second(ordered_pair(x,y)) != ordered_pair(x,y),
file('/export/starexec/sandbox2/tmp/tmp.2zuEtS5lTg/E---3.1_21808.p',prove_corollary_2_to_OP_determines_components2_2) ).
cnf(existence_of_1st_and_2nd_3,axiom,
( member(ordered_pair(first(X1),second(X1)),cross_product(universal_class,universal_class))
| second(X1) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.2zuEtS5lTg/E---3.1_21808.p',existence_of_1st_and_2nd_3) ).
cnf(existence_of_1st_and_2nd_5,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| second(X1) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.2zuEtS5lTg/E---3.1_21808.p',existence_of_1st_and_2nd_5) ).
cnf(commutativity_of_unordered_pair,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/tmp/tmp.2zuEtS5lTg/E---3.1_21808.p',commutativity_of_unordered_pair) ).
cnf(c_0_10,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_11,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_12,axiom,
( member(X1,universal_class)
| singleton(X1) = null_class ),
singleton_is_null_class ).
cnf(c_0_13,axiom,
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
unordered_pair_equals_singleton1 ).
cnf(c_0_14,axiom,
( member(X2,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
corollary_2_to_cartesian_product ).
cnf(c_0_15,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
cnf(c_0_16,negated_conjecture,
~ member(y,universal_class),
prove_corollary_2_to_OP_determines_components2_1 ).
cnf(c_0_17,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
second(ordered_pair(x,y)) != ordered_pair(x,y),
prove_corollary_2_to_OP_determines_components2_2 ).
cnf(c_0_19,axiom,
( member(ordered_pair(first(X1),second(X1)),cross_product(universal_class,universal_class))
| second(X1) = X1 ),
existence_of_1st_and_2nd_3 ).
cnf(c_0_20,plain,
( unordered_pair(X1,X2) = unordered_pair(X1,X1)
| member(X2,universal_class) ),
inference(rw,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_21,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| second(X1) = X1 ),
existence_of_1st_and_2nd_5 ).
cnf(c_0_22,plain,
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,negated_conjecture,
unordered_pair(y,y) = null_class,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
second(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_15]),c_0_15]) ).
cnf(c_0_25,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
commutativity_of_unordered_pair ).
cnf(c_0_26,plain,
( second(X1) = X1
| member(unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))),cross_product(universal_class,universal_class)) ),
inference(rw,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_27,negated_conjecture,
unordered_pair(X1,y) = unordered_pair(X1,X1),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_28,plain,
( unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))) = X1
| second(X1) = X1 ),
inference(rw,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_29,negated_conjecture,
~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,null_class)),cross_product(X2,X3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_16]) ).
cnf(c_0_30,negated_conjecture,
second(unordered_pair(unordered_pair(null_class,x),unordered_pair(x,x))) != unordered_pair(unordered_pair(null_class,x),unordered_pair(x,x)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_23]),c_0_25]),c_0_25]),c_0_23]),c_0_25]),c_0_25]) ).
cnf(c_0_31,plain,
( second(X1) = X1
| member(unordered_pair(unordered_pair(y,first(X1)),unordered_pair(first(X1),unordered_pair(y,second(X1)))),cross_product(universal_class,universal_class)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_25]),c_0_27]),c_0_25]) ).
cnf(c_0_32,plain,
( unordered_pair(unordered_pair(y,first(X1)),unordered_pair(first(X1),unordered_pair(y,second(X1)))) = X1
| second(X1) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_27]),c_0_25]),c_0_27]),c_0_25]) ).
cnf(c_0_33,negated_conjecture,
~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(null_class,X1)),cross_product(X2,X3)),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_34,negated_conjecture,
unordered_pair(X1,X1) = unordered_pair(y,X1),
inference(spm,[status(thm)],[c_0_25,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
second(unordered_pair(unordered_pair(null_class,x),unordered_pair(y,x))) != unordered_pair(unordered_pair(null_class,x),unordered_pair(y,x)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_27]),c_0_25]),c_0_27]),c_0_25]) ).
cnf(c_0_36,plain,
( second(X1) = X1
| member(X1,cross_product(universal_class,universal_class)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
~ member(unordered_pair(unordered_pair(null_class,X1),unordered_pair(y,X1)),cross_product(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_25]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SET122-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.10/0.14 % Command : run_E %s %d THM
% 0.11/0.34 % Computer : n013.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 2400
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Mon Oct 2 16:24:59 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.16/0.46 Running first-order model finding
% 0.16/0.46 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.2zuEtS5lTg/E---3.1_21808.p
% 0.16/0.51 # Version: 3.1pre001
% 0.16/0.51 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.51 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/0.51 # Starting new_bool_3 with 300s (1) cores
% 0.16/0.51 # Starting new_bool_1 with 300s (1) cores
% 0.16/0.51 # Starting sh5l with 300s (1) cores
% 0.16/0.51 # new_bool_1 with pid 21903 completed with status 0
% 0.16/0.51 # Result found by new_bool_1
% 0.16/0.51 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.51 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/0.51 # Starting new_bool_3 with 300s (1) cores
% 0.16/0.51 # Starting new_bool_1 with 300s (1) cores
% 0.16/0.51 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.51 # Search class: FGHSM-FFMF21-MFFFFFNN
% 0.16/0.51 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.51 # Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with 181s (1) cores
% 0.16/0.51 # G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with pid 21906 completed with status 0
% 0.16/0.51 # Result found by G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN
% 0.16/0.51 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.51 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/0.51 # Starting new_bool_3 with 300s (1) cores
% 0.16/0.51 # Starting new_bool_1 with 300s (1) cores
% 0.16/0.51 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.51 # Search class: FGHSM-FFMF21-MFFFFFNN
% 0.16/0.51 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.51 # Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with 181s (1) cores
% 0.16/0.51 # Preprocessing time : 0.004 s
% 0.16/0.51 # Presaturation interreduction done
% 0.16/0.51
% 0.16/0.51 # Proof found!
% 0.16/0.51 # SZS status Unsatisfiable
% 0.16/0.51 # SZS output start CNFRefutation
% See solution above
% 0.16/0.51 # Parsed axioms : 169
% 0.16/0.51 # Removed by relevancy pruning/SinE : 95
% 0.16/0.51 # Initial clauses : 74
% 0.16/0.51 # Removed in clause preprocessing : 0
% 0.16/0.51 # Initial clauses in saturation : 74
% 0.16/0.51 # Processed clauses : 619
% 0.16/0.51 # ...of these trivial : 15
% 0.16/0.51 # ...subsumed : 364
% 0.16/0.51 # ...remaining for further processing : 239
% 0.16/0.51 # Other redundant clauses eliminated : 14
% 0.16/0.51 # Clauses deleted for lack of memory : 0
% 0.16/0.51 # Backward-subsumed : 11
% 0.16/0.51 # Backward-rewritten : 34
% 0.16/0.51 # Generated clauses : 2282
% 0.16/0.51 # ...of the previous two non-redundant : 1741
% 0.16/0.51 # ...aggressively subsumed : 0
% 0.16/0.51 # Contextual simplify-reflections : 0
% 0.16/0.51 # Paramodulations : 2244
% 0.16/0.51 # Factorizations : 24
% 0.16/0.51 # NegExts : 0
% 0.16/0.51 # Equation resolutions : 14
% 0.16/0.51 # Total rewrite steps : 2659
% 0.16/0.51 # Propositional unsat checks : 0
% 0.16/0.51 # Propositional check models : 0
% 0.16/0.51 # Propositional check unsatisfiable : 0
% 0.16/0.51 # Propositional clauses : 0
% 0.16/0.51 # Propositional clauses after purity: 0
% 0.16/0.51 # Propositional unsat core size : 0
% 0.16/0.51 # Propositional preprocessing time : 0.000
% 0.16/0.51 # Propositional encoding time : 0.000
% 0.16/0.51 # Propositional solver time : 0.000
% 0.16/0.51 # Success case prop preproc time : 0.000
% 0.16/0.51 # Success case prop encoding time : 0.000
% 0.16/0.51 # Success case prop solver time : 0.000
% 0.16/0.51 # Current number of processed clauses : 129
% 0.16/0.51 # Positive orientable unit clauses : 22
% 0.16/0.51 # Positive unorientable unit clauses: 3
% 0.16/0.51 # Negative unit clauses : 20
% 0.16/0.51 # Non-unit-clauses : 84
% 0.16/0.51 # Current number of unprocessed clauses: 1238
% 0.16/0.51 # ...number of literals in the above : 3111
% 0.16/0.51 # Current number of archived formulas : 0
% 0.16/0.51 # Current number of archived clauses : 108
% 0.16/0.51 # Clause-clause subsumption calls (NU) : 1156
% 0.16/0.51 # Rec. Clause-clause subsumption calls : 1023
% 0.16/0.51 # Non-unit clause-clause subsumptions : 182
% 0.16/0.51 # Unit Clause-clause subsumption calls : 289
% 0.16/0.51 # Rewrite failures with RHS unbound : 0
% 0.16/0.51 # BW rewrite match attempts : 92
% 0.16/0.51 # BW rewrite match successes : 49
% 0.16/0.51 # Condensation attempts : 0
% 0.16/0.51 # Condensation successes : 0
% 0.16/0.51 # Termbank termtop insertions : 33431
% 0.16/0.51
% 0.16/0.51 # -------------------------------------------------
% 0.16/0.51 # User time : 0.035 s
% 0.16/0.51 # System time : 0.007 s
% 0.16/0.51 # Total time : 0.042 s
% 0.16/0.51 # Maximum resident set size: 1972 pages
% 0.16/0.51
% 0.16/0.51 # -------------------------------------------------
% 0.16/0.51 # User time : 0.039 s
% 0.16/0.51 # System time : 0.007 s
% 0.16/0.51 # Total time : 0.046 s
% 0.16/0.51 # Maximum resident set size: 1804 pages
% 0.16/0.51 % E---3.1 exiting
%------------------------------------------------------------------------------