%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET097-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:13:34 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of clauses : 63 ( 22 unt; 18 nHn; 42 RR)
% Number of literals : 118 ( 32 equ; 52 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_number_of_elements_in_class_1,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_number_of_elements_in_class_1) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(intersection3,axiom,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(null_class_is_unique,axiom,
( member(not_subclass_element(X1,null_class),X1)
| X1 = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_unique) ).
cnf(existence_of_null_class,axiom,
~ member(X1,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
cnf(subclass_members,axiom,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(only_member_in_singleton,axiom,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
cnf(complement2,axiom,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(singleton_is_null_class,axiom,
( singleton(X1) = null_class
| member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
cnf(not_subclass_members2,axiom,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(not_subclass_members1,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(prove_number_of_elements_in_class_3,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_number_of_elements_in_class_3) ).
cnf(two_subsets_of_singleton,axiom,
( ~ subclass(X1,singleton(X2))
| singleton(X2) = X1
| X1 = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_subsets_of_singleton) ).
cnf(unordered_pair2,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(regularity1,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(prove_number_of_elements_in_class_2,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_number_of_elements_in_class_2) ).
cnf(c_0_17,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
inference(fof_simplification,[status(thm)],[prove_number_of_elements_in_class_1]) ).
cnf(c_0_18,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
c_0_17 ).
cnf(c_0_19,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_20,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_21,negated_conjecture,
~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19]) ).
cnf(c_0_22,axiom,
( member(not_subclass_element(X1,null_class),X1)
| X1 = null_class ),
null_class_is_unique ).
cnf(c_0_23,plain,
~ member(X1,null_class),
inference(fof_simplification,[status(thm)],[existence_of_null_class]) ).
cnf(c_0_24,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_25,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[only_member_in_singleton]) ).
cnf(c_0_26,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_20 ).
cnf(c_0_27,negated_conjecture,
intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
~ member(X1,null_class),
c_0_23 ).
cnf(c_0_29,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
cnf(c_0_30,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_24 ).
cnf(c_0_31,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_32,axiom,
( singleton(X1) = null_class
| member(X1,universal_class) ),
singleton_is_null_class ).
cnf(c_0_33,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
c_0_25 ).
cnf(c_0_34,negated_conjecture,
( ~ member(X1,x)
| ~ member(X1,complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_35,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_29 ).
cnf(c_0_36,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
( member(X1,universal_class)
| unordered_pair(X1,X1) = null_class ),
inference(rw,[status(thm)],[c_0_32,c_0_19]) ).
cnf(c_0_38,plain,
( ~ member(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(rw,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_39,negated_conjecture,
( ~ member(X1,x)
| member(X1,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( member(not_subclass_element(x,null_class),universal_class)
| intersection(complement(null_class),x) = null_class ),
inference(spm,[status(thm)],[c_0_27,c_0_37]) ).
cnf(c_0_41,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).
cnf(c_0_42,negated_conjecture,
( ~ member(X1,x)
| X1 = not_subclass_element(x,null_class) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
not_subclass_members1 ).
cnf(c_0_44,negated_conjecture,
( ~ member(X1,x)
| ~ member(X1,complement(null_class))
| member(not_subclass_element(x,null_class),universal_class) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_40]),c_0_28]) ).
cnf(c_0_45,negated_conjecture,
x != null_class,
inference(fof_simplification,[status(thm)],[prove_number_of_elements_in_class_3]) ).
cnf(c_0_46,plain,
( ~ subclass(X1,singleton(X2))
| singleton(X2) = X1
| X1 = null_class ),
inference(fof_simplification,[status(thm)],[two_subsets_of_singleton]) ).
cnf(c_0_47,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
c_0_41 ).
cnf(c_0_48,negated_conjecture,
( subclass(x,X1)
| not_subclass_element(x,X1) = not_subclass_element(x,null_class) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[unordered_pair2]) ).
cnf(c_0_50,negated_conjecture,
( ~ member(X1,x)
| member(not_subclass_element(x,null_class),universal_class) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_35]),c_0_28]),c_0_36]) ).
cnf(c_0_51,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_52,negated_conjecture,
x != null_class,
c_0_45 ).
cnf(c_0_53,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
inference(fof_simplification,[status(thm)],[prove_number_of_elements_in_class_2]) ).
cnf(c_0_54,plain,
( ~ subclass(X1,singleton(X2))
| singleton(X2) = X1
| X1 = null_class ),
c_0_46 ).
cnf(c_0_55,negated_conjecture,
( ~ member(not_subclass_element(x,null_class),X1)
| subclass(x,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_56,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
c_0_49 ).
cnf(c_0_57,negated_conjecture,
member(not_subclass_element(x,null_class),universal_class),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_58,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
c_0_53 ).
cnf(c_0_59,plain,
( ~ subclass(X1,unordered_pair(X2,X2))
| unordered_pair(X2,X2) = X1
| X1 = null_class ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_19]),c_0_19]) ).
cnf(c_0_60,negated_conjecture,
subclass(x,unordered_pair(not_subclass_element(x,null_class),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_61,negated_conjecture,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(rw,[status(thm)],[c_0_58,c_0_19]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET097-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 04:54:43 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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/benchmark/theBenchmark.p
% 0.14/0.45 % Version: 3.5.1
% 0.14/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.45 % Starting sh5l with 300s (1) cores
% 0.14/0.45 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1004343 completed with status 0
% 0.14/0.45 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.14/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.45 % No SInE strategy applied
% 0.14/0.45 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.14/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.14/0.45 % Starting new_bool_3 with 311s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 308s (1) cores
% 0.14/0.45 % Starting sh5l with 304s (1) cores
% 0.14/0.45 % sh5l with pid 1004353 completed with status 0
% 0.14/0.45 % Result found by sh5l
% 0.14/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.45 % No SInE strategy applied
% 0.14/0.45 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.14/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.14/0.45 % Starting new_bool_3 with 311s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 308s (1) cores
% 0.14/0.45 % Starting sh5l with 304s (1) cores
% 0.14/0.45 % Preprocessing time : 0.002 s
% 0.14/0.45 % Presaturation interreduction done
% 0.14/0.45
% 0.14/0.45 % Proof found!
% 0.14/0.45 % SZS status Unsatisfiable
% 0.14/0.45 % SZS output start CNFRefutation
% See solution above
% 0.14/0.45 % Parsed axioms : 143
% 0.14/0.45 % Removed by relevancy pruning/SinE : 0
% 0.14/0.45 % Initial clauses : 143
% 0.14/0.45 % Removed in clause preprocessing : 15
% 0.14/0.45 % Initial clauses in saturation : 128
% 0.14/0.45 % Processed clauses : 551
% 0.14/0.45 % ...of these trivial : 5
% 0.14/0.45 % ...subsumed : 241
% 0.14/0.45 % ...remaining for further processing : 305
% 0.14/0.45 % Other redundant clauses eliminated : 37
% 0.14/0.45 % Clauses deleted for lack of memory : 0
% 0.14/0.45 % Backward-subsumed : 7
% 0.14/0.45 % Backward-rewritten : 5
% 0.14/0.45 % Generated clauses : 1374
% 0.14/0.45 % ...of the previous two non-redundant : 1038
% 0.14/0.45 % ...aggressively subsumed : 0
% 0.14/0.45 % Contextual simplify-reflections : 2
% 0.14/0.45 % Paramodulations : 1331
% 0.14/0.45 % Factorizations : 3
% 0.14/0.45 % NegExts : 0
% 0.14/0.45 % Equation resolutions : 40
% 0.14/0.45 % Disequality decompositions : 0
% 0.14/0.45 % Total rewrite steps : 342
% 0.14/0.45 % ...of those cached : 299
% 0.14/0.45 % Propositional unsat checks : 0
% 0.14/0.45 % Propositional check models : 0
% 0.14/0.45 % Propositional check unsatisfiable : 0
% 0.14/0.45 % Propositional clauses : 0
% 0.14/0.45 % Propositional clauses after purity: 0
% 0.14/0.45 % Propositional unsat core size : 0
% 0.14/0.45 % Propositional preprocessing time : 0.000
% 0.14/0.45 % Propositional encoding time : 0.000
% 0.14/0.45 % Propositional solver time : 0.000
% 0.14/0.45 % Success case prop preproc time : 0.000
% 0.14/0.45 % Success case prop encoding time : 0.000
% 0.14/0.45 % Success case prop solver time : 0.000
% 0.14/0.45 % Current number of processed clauses : 169
% 0.14/0.45 % Positive orientable unit clauses : 34
% 0.14/0.45 % Positive unorientable unit clauses: 2
% 0.14/0.45 % Negative unit clauses : 12
% 0.14/0.45 % Non-unit-clauses : 121
% 0.14/0.45 % Current number of unprocessed clauses: 726
% 0.14/0.45 % ...number of literals in the above : 2017
% 0.14/0.45 % Current number of archived formulas : 0
% 0.14/0.45 % Current number of archived clauses : 148
% 0.14/0.45 % Clause-clause subsumption calls (NU) : 6206
% 0.14/0.45 % Rec. Clause-clause subsumption calls : 3226
% 0.14/0.45 % Non-unit clause-clause subsumptions : 159
% 0.14/0.45 % Unit Clause-clause subsumption calls : 188
% 0.14/0.45 % Rewrite failures with RHS unbound : 0
% 0.14/0.45 % BW rewrite match attempts : 53
% 0.14/0.45 % BW rewrite match successes : 50
% 0.14/0.45 % Condensation attempts : 551
% 0.14/0.45 % Condensation successes : 2
% 0.14/0.45 % Termbank termtop insertions : 20371
% 0.14/0.45 % Search garbage collected termcells : 230
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.022 s
% 0.14/0.45 % System time : 0.005 s
% 0.14/0.45 % Total time : 0.027 s
% 0.14/0.45 % Maximum resident set size: 4004 pages
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.115 s
% 0.14/0.45 % System time : 0.020 s
% 0.14/0.45 % Total time : 0.135 s
% 0.14/0.45 % Maximum resident set size: 4608 pages
% 0.14/0.45 % E exiting
%------------------------------------------------------------------------------