%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM156-1 : 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 01:44:26 PM UTC 2026
% Result : Unsatisfiable 0.35s 15.55s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of clauses : 49 ( 29 unt; 4 nHn; 26 RR)
% Number of literals : 75 ( 16 equ; 29 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 : 68 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
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(inductive1,axiom,
( ~ inductive(X1)
| member(null_class,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive1) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(omega_is_inductive1,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
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(image,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',image) ).
cnf(range_of,axiom,
domain_of(inverse(X1)) = range_of(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',range_of) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(unordered_pair3,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(kind_1_ordinals,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',kind_1_ordinals) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(inverse,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inverse) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
cnf(prove_null_class_is_kind_1_1,negated_conjecture,
~ member(null_class,kind_1_ordinals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_class_is_kind_1_1) ).
cnf(complement1,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(intersection1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
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,
( ~ inductive(X1)
| member(null_class,X1) ),
inference(fof_simplification,[status(thm)],[inductive1]) ).
cnf(c_0_18,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_16 ).
cnf(c_0_19,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_20,plain,
( ~ inductive(X1)
| member(null_class,X1) ),
c_0_17 ).
cnf(c_0_21,axiom,
inductive(omega),
omega_is_inductive1 ).
cnf(c_0_22,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
cnf(c_0_23,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
member(null_class,omega),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
image ).
cnf(c_0_26,axiom,
domain_of(inverse(X1)) = range_of(X1),
range_of ).
cnf(c_0_27,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_28,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
inference(fof_simplification,[status(thm)],[unordered_pair3]) ).
cnf(c_0_29,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_22 ).
cnf(c_0_30,plain,
member(null_class,universal_class),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
kind_1_ordinals ).
cnf(c_0_32,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_33,plain,
domain_of(inverse(intersection(X1,cross_product(X2,universal_class)))) = image(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_34,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inverse ).
cnf(c_0_35,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_36,negated_conjecture,
~ member(null_class,kind_1_ordinals),
inference(fof_simplification,[status(thm)],[prove_null_class_is_kind_1_1]) ).
cnf(c_0_37,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_38,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
c_0_28 ).
cnf(c_0_39,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(fof_simplification,[status(thm)],[intersection1]) ).
cnf(c_0_40,plain,
( member(null_class,X1)
| member(null_class,complement(X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_41,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_31,c_0_32]),c_0_33]),c_0_34]),c_0_35]) ).
cnf(c_0_42,negated_conjecture,
~ member(null_class,kind_1_ordinals),
c_0_36 ).
cnf(c_0_43,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_37 ).
cnf(c_0_44,plain,
member(null_class,unordered_pair(X1,null_class)),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_45,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
c_0_39 ).
cnf(c_0_46,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_40,c_0_41]),c_0_42]) ).
cnf(c_0_47,plain,
~ member(null_class,complement(unordered_pair(X1,null_class))),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM156-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.43 % CPULimit : 300
% 0.09/15.43 % WCLimit : 300
% 0.09/15.43 % DateTime : Mon Sep 21 02:08:37 UTC 2026
% 0.09/15.43 % CPUTime :
% 0.09/15.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/15.48 Running first-order theorem proving
% 0.09/15.48 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
% 0.35/15.55 % Version: 3.5.1
% 0.35/15.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.35/15.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/15.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.35/15.55 % Starting new_bool_3 with 300s (1) cores
% 0.35/15.55 % Starting new_bool_1 with 300s (1) cores
% 0.35/15.55 % Starting sh5l with 300s (1) cores
% 0.35/15.55 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 3925961 completed with status 0
% 0.35/15.55 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.35/15.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.35/15.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/15.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.35/15.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.35/15.55 % No SInE strategy applied
% 0.35/15.55 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.35/15.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.35/15.55 % Starting SubtermCWHack with 136s (1) cores
% 0.35/15.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.35/15.55 % Starting new_bool_3 with 311s (1) cores
% 0.35/15.55 % Starting new_bool_1 with 308s (1) cores
% 0.35/15.55 % Starting sh5l with 304s (1) cores
% 0.35/15.55 % new_bool_3 with pid 3925970 completed with status 0
% 0.35/15.55 % Result found by new_bool_3
% 0.35/15.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.35/15.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/15.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.35/15.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.35/15.55 % No SInE strategy applied
% 0.35/15.55 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.35/15.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.35/15.55 % Starting SubtermCWHack with 136s (1) cores
% 0.35/15.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.35/15.55 % Starting new_bool_3 with 311s (1) cores
% 0.35/15.55 % Preprocessing time : 0.004 s
% 0.35/15.55 % Presaturation interreduction done
% 0.35/15.55
% 0.35/15.55 % Proof found!
% 0.35/15.55 % SZS status Unsatisfiable
% 0.35/15.55 % SZS output start CNFRefutation
% See solution above
% 0.35/15.55 % Parsed axioms : 159
% 0.35/15.55 % Removed by relevancy pruning/SinE : 0
% 0.35/15.55 % Initial clauses : 159
% 0.35/15.55 % Removed in clause preprocessing : 19
% 0.35/15.55 % Initial clauses in saturation : 140
% 0.35/15.55 % Processed clauses : 408
% 0.35/15.55 % ...of these trivial : 0
% 0.35/15.55 % ...subsumed : 18
% 0.35/15.55 % ...remaining for further processing : 390
% 0.35/15.55 % Other redundant clauses eliminated : 6
% 0.35/15.55 % Clauses deleted for lack of memory : 0
% 0.35/15.55 % Backward-subsumed : 2
% 0.35/15.55 % Backward-rewritten : 5
% 0.35/15.55 % Generated clauses : 831
% 0.35/15.55 % ...of the previous two non-redundant : 735
% 0.35/15.55 % ...aggressively subsumed : 0
% 0.35/15.55 % Contextual simplify-reflections : 0
% 0.35/15.55 % Paramodulations : 825
% 0.35/15.55 % Factorizations : 0
% 0.35/15.55 % NegExts : 0
% 0.35/15.55 % Equation resolutions : 6
% 0.35/15.55 % Disequality decompositions : 0
% 0.35/15.55 % Total rewrite steps : 84
% 0.35/15.55 % ...of those cached : 56
% 0.35/15.55 % Propositional unsat checks : 0
% 0.35/15.55 % Propositional check models : 0
% 0.35/15.55 % Propositional check unsatisfiable : 0
% 0.35/15.55 % Propositional clauses : 0
% 0.35/15.55 % Propositional clauses after purity: 0
% 0.35/15.55 % Propositional unsat core size : 0
% 0.35/15.55 % Propositional preprocessing time : 0.000
% 0.35/15.55 % Propositional encoding time : 0.000
% 0.35/15.55 % Propositional solver time : 0.000
% 0.35/15.55 % Success case prop preproc time : 0.000
% 0.35/15.55 % Success case prop encoding time : 0.000
% 0.35/15.55 % Success case prop solver time : 0.000
% 0.35/15.55 % Current number of processed clauses : 238
% 0.35/15.55 % Positive orientable unit clauses : 50
% 0.35/15.55 % Positive unorientable unit clauses: 3
% 0.35/15.55 % Negative unit clauses : 22
% 0.35/15.55 % Non-unit-clauses : 163
% 0.35/15.55 % Current number of unprocessed clauses: 602
% 0.35/15.55 % ...number of literals in the above : 1079
% 0.35/15.55 % Current number of archived formulas : 0
% 0.35/15.55 % Current number of archived clauses : 165
% 0.35/15.55 % Clause-clause subsumption calls (NU) : 4408
% 0.35/15.55 % Rec. Clause-clause subsumption calls : 3002
% 0.35/15.55 % Non-unit clause-clause subsumptions : 19
% 0.35/15.55 % Unit Clause-clause subsumption calls : 319
% 0.35/15.55 % Rewrite failures with RHS unbound : 10
% 0.35/15.55 % BW rewrite match attempts : 23
% 0.35/15.55 % BW rewrite match successes : 11
% 0.35/15.55 % Condensation attempts : 0
% 0.35/15.55 % Condensation successes : 0
% 0.35/15.55 % Termbank termtop insertions : 23645
% 0.35/15.55 % Search garbage collected termcells : 287
% 0.35/15.55
% 0.35/15.55 % -------------------------------------------------
% 0.35/15.55 % User time : 0.042 s
% 0.35/15.55 % System time : 0.012 s
% 0.35/15.55 % Total time : 0.054 s
% 0.35/15.55 % Maximum resident set size: 4036 pages
% 0.35/15.55
% 0.35/15.55 % -------------------------------------------------
% 0.35/15.55 % User time : 0.209 s
% 0.35/15.55 % System time : 0.039 s
% 0.35/15.55 % Total time : 0.248 s
% 0.35/15.55 % Maximum resident set size: 4864 pages
% 0.35/15.55 % E exiting
%------------------------------------------------------------------------------