%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET099-7 : 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 : n011.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 02:13:35 PM UTC 2026
% Result : Unsatisfiable 0.64s 0.50s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 15 unt; 2 nHn; 26 RR)
% Number of literals : 50 ( 12 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_corollary_2_to_number_of_elements_in_class_2,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_2) ).
cnf(prove_corollary_2_to_number_of_elements_in_class_3,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_3) ).
cnf(intersection1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(number_of_elements_in_class,axiom,
( X1 = null_class
| singleton(not_subclass_element(X1,null_class)) = X1
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(singleton(not_subclass_element(X1,null_class))),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',number_of_elements_in_class) ).
cnf(prove_corollary_2_to_number_of_elements_in_class_1,negated_conjecture,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_1) ).
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(complement1,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(set_in_its_singleton,axiom,
( ~ member(X1,universal_class)
| member(X1,singleton(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_in_its_singleton) ).
cnf(c_0_9,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
inference(fof_simplification,[status(thm)],[prove_corollary_2_to_number_of_elements_in_class_2]) ).
cnf(c_0_10,negated_conjecture,
x != null_class,
inference(fof_simplification,[status(thm)],[prove_corollary_2_to_number_of_elements_in_class_3]) ).
cnf(c_0_11,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(fof_simplification,[status(thm)],[intersection1]) ).
cnf(c_0_12,axiom,
( X1 = null_class
| singleton(not_subclass_element(X1,null_class)) = X1
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(singleton(not_subclass_element(X1,null_class))),X1)) ),
number_of_elements_in_class ).
cnf(c_0_13,negated_conjecture,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
prove_corollary_2_to_number_of_elements_in_class_1 ).
cnf(c_0_14,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
c_0_9 ).
cnf(c_0_15,negated_conjecture,
x != null_class,
c_0_10 ).
cnf(c_0_16,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_17,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_18,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
c_0_11 ).
cnf(c_0_19,negated_conjecture,
member(not_subclass_element(x,null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]) ).
cnf(c_0_20,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_16 ).
cnf(c_0_21,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_22,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_17 ).
cnf(c_0_23,negated_conjecture,
member(not_subclass_element(x,null_class),complement(singleton(not_subclass_element(x,null_class)))),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( ~ member(X1,universal_class)
| member(X1,singleton(X1)) ),
inference(fof_simplification,[status(thm)],[set_in_its_singleton]) ).
cnf(c_0_25,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
~ member(not_subclass_element(x,null_class),singleton(not_subclass_element(x,null_class))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( ~ member(X1,universal_class)
| member(X1,singleton(X1)) ),
c_0_24 ).
cnf(c_0_28,negated_conjecture,
member(not_subclass_element(x,null_class),universal_class),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET099-7 : 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 : n011.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 04:52:40 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.41 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
% 0.64/0.50 % Version: 3.5.1
% 0.64/0.50 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.64/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.64/0.50 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.64/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.64/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.64/0.50 % Starting sh5l with 300s (1) cores
% 0.64/0.50 % new_bool_1 with pid 1010295 completed with status 0
% 0.64/0.50 % Result found by new_bool_1
% 0.64/0.50 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.64/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.64/0.50 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.64/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.64/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.64/0.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.64/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.64/0.50 % Search class: FGHSM-FFMS21-MFFFFFNN
% 0.64/0.50 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.64/0.50 % Starting SubtermCWHack with 31s (1) cores
% 0.64/0.50 % SubtermCWHack with pid 1010299 completed with status 0
% 0.64/0.50 % Result found by SubtermCWHack
% 0.64/0.50 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.64/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.64/0.50 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.64/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.64/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.64/0.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.64/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.64/0.50 % Search class: FGHSM-FFMS21-MFFFFFNN
% 0.64/0.50 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.64/0.50 % Starting SubtermCWHack with 31s (1) cores
% 0.64/0.50 % Preprocessing time : 0.002 s
% 0.64/0.50
% 0.64/0.50 % Proof found!
% 0.64/0.50 % SZS status Unsatisfiable
% 0.64/0.50 % SZS output start CNFRefutation
% See solution above
% 0.64/0.50 % Parsed axioms : 144
% 0.64/0.50 % Removed by relevancy pruning/SinE : 79
% 0.64/0.50 % Initial clauses : 65
% 0.64/0.50 % Removed in clause preprocessing : 0
% 0.64/0.50 % Initial clauses in saturation : 65
% 0.64/0.50 % Processed clauses : 978
% 0.64/0.50 % ...of these trivial : 42
% 0.64/0.50 % ...subsumed : 642
% 0.64/0.50 % ...remaining for further processing : 294
% 0.64/0.50 % Other redundant clauses eliminated : 6
% 0.64/0.50 % Clauses deleted for lack of memory : 0
% 0.64/0.50 % Backward-subsumed : 12
% 0.64/0.50 % Backward-rewritten : 11
% 0.64/0.50 % Generated clauses : 4864
% 0.64/0.50 % ...of the previous two non-redundant : 3457
% 0.64/0.50 % ...aggressively subsumed : 0
% 0.64/0.50 % Contextual simplify-reflections : 3
% 0.64/0.50 % Paramodulations : 4845
% 0.64/0.50 % Factorizations : 12
% 0.64/0.50 % NegExts : 0
% 0.64/0.50 % Equation resolutions : 7
% 0.64/0.50 % Disequality decompositions : 0
% 0.64/0.50 % Total rewrite steps : 1983
% 0.64/0.50 % ...of those cached : 1717
% 0.64/0.50 % Propositional unsat checks : 0
% 0.64/0.50 % Propositional check models : 0
% 0.64/0.50 % Propositional check unsatisfiable : 0
% 0.64/0.50 % Propositional clauses : 0
% 0.64/0.50 % Propositional clauses after purity: 0
% 0.64/0.50 % Propositional unsat core size : 0
% 0.64/0.50 % Propositional preprocessing time : 0.000
% 0.64/0.50 % Propositional encoding time : 0.000
% 0.64/0.50 % Propositional solver time : 0.000
% 0.64/0.50 % Success case prop preproc time : 0.000
% 0.64/0.50 % Success case prop encoding time : 0.000
% 0.64/0.50 % Success case prop solver time : 0.000
% 0.64/0.50 % Current number of processed clauses : 269
% 0.64/0.50 % Positive orientable unit clauses : 67
% 0.64/0.50 % Positive unorientable unit clauses: 1
% 0.64/0.50 % Negative unit clauses : 7
% 0.64/0.50 % Non-unit-clauses : 194
% 0.64/0.50 % Current number of unprocessed clauses: 2510
% 0.64/0.50 % ...number of literals in the above : 7130
% 0.64/0.50 % Current number of archived formulas : 0
% 0.64/0.50 % Current number of archived clauses : 23
% 0.64/0.50 % Clause-clause subsumption calls (NU) : 5533
% 0.64/0.50 % Rec. Clause-clause subsumption calls : 4590
% 0.64/0.50 % Non-unit clause-clause subsumptions : 553
% 0.64/0.50 % Unit Clause-clause subsumption calls : 1407
% 0.64/0.50 % Rewrite failures with RHS unbound : 0
% 0.64/0.50 % BW rewrite match attempts : 63
% 0.64/0.50 % BW rewrite match successes : 17
% 0.64/0.50 % Condensation attempts : 0
% 0.64/0.50 % Condensation successes : 0
% 0.64/0.50 % Termbank termtop insertions : 49745
% 0.64/0.50 % Search garbage collected termcells : 474
% 0.64/0.50
% 0.64/0.50 % -------------------------------------------------
% 0.64/0.50 % User time : 0.066 s
% 0.64/0.50 % System time : 0.005 s
% 0.64/0.50 % Total time : 0.071 s
% 0.64/0.50 % Maximum resident set size: 3748 pages
% 0.64/0.50
% 0.64/0.50 % -------------------------------------------------
% 0.64/0.50 % User time : 0.069 s
% 0.64/0.50 % System time : 0.010 s
% 0.64/0.50 % Total time : 0.079 s
% 0.64/0.50 % Maximum resident set size: 4608 pages
% 0.64/0.50 % E exiting
%------------------------------------------------------------------------------