%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM159-1 : 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 : 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 01:51:23 PM UTC 2026
% Result : Unsatisfiable 25.01s 3.70s
% Output : CNFRefutation 25.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of clauses : 55 ( 27 unt; 9 nHn; 27 RR)
% Number of literals : 92 ( 21 equ; 35 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 91 ( 7 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(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(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(complement2,axiom,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
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(intersection2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(subclass_implies_equal,axiom,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
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(prove_corollary_to_kind_1_ordinal_1,negated_conjecture,
~ subclass(image(successor_relation,ordinal_numbers),kind_1_ordinals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_kind_1_ordinal_1) ).
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(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(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,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_17 ).
cnf(c_0_21,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
not_subclass_members1 ).
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(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).
cnf(c_0_25,plain,
( ~ member(not_subclass_element(complement(X1),X2),X1)
| subclass(complement(X1),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_22 ).
cnf(c_0_27,plain,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),universal_class) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_28,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
c_0_24 ).
cnf(c_0_29,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
cnf(c_0_30,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[subclass_implies_equal]) ).
cnf(c_0_31,plain,
( subclass(complement(complement(X1)),X2)
| member(not_subclass_element(complement(complement(X1)),X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_32,plain,
( subclass(X1,complement(X2))
| member(not_subclass_element(X1,complement(X2)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_26]),c_0_27]) ).
cnf(c_0_33,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_29 ).
cnf(c_0_34,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
image ).
cnf(c_0_35,axiom,
domain_of(inverse(X1)) = range_of(X1),
range_of ).
cnf(c_0_36,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_37,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
c_0_30 ).
cnf(c_0_38,plain,
subclass(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_39,plain,
( ~ member(not_subclass_element(X1,complement(complement(X2))),X2)
| subclass(X1,complement(complement(X2))) ),
inference(spm,[status(thm)],[c_0_20,c_0_32]) ).
cnf(c_0_40,negated_conjecture,
~ subclass(image(successor_relation,ordinal_numbers),kind_1_ordinals),
inference(fof_simplification,[status(thm)],[prove_corollary_to_kind_1_ordinal_1]) ).
cnf(c_0_41,plain,
( subclass(X1,complement(intersection(X2,X3)))
| member(not_subclass_element(X1,complement(intersection(X2,X3))),X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_42,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
kind_1_ordinals ).
cnf(c_0_43,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_44,plain,
domain_of(inverse(intersection(X1,cross_product(X2,universal_class)))) = image(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_45,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inverse ).
cnf(c_0_46,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_47,plain,
( ~ subclass(X1,complement(complement(X1)))
| complement(complement(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_48,plain,
subclass(X1,complement(complement(X1))),
inference(spm,[status(thm)],[c_0_39,c_0_21]) ).
cnf(c_0_49,negated_conjecture,
~ subclass(image(successor_relation,ordinal_numbers),kind_1_ordinals),
c_0_40 ).
cnf(c_0_50,plain,
subclass(complement(X1),complement(intersection(X2,X1))),
inference(spm,[status(thm)],[c_0_25,c_0_41]) ).
cnf(c_0_51,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_42,c_0_43]),c_0_44]),c_0_45]),c_0_46]) ).
cnf(c_0_52,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_53,negated_conjecture,
~ subclass(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)],[c_0_49,c_0_44]),c_0_45]) ).
cnf(c_0_54,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM159-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.44 % Computer : n018.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Mon Sep 21 02:10:59 UTC 2026
% 0.20/0.44 % CPUTime :
% 0.20/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.51 Running first-order theorem proving
% 0.25/0.51 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
% 25.01/3.70 % Version: 3.5.1
% 25.01/3.70 % Preprocessing class: FSLSSMSMSSSNFFN.
% 25.01/3.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.01/3.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 25.01/3.70 % Starting new_bool_3 with 300s (1) cores
% 25.01/3.70 % Starting new_bool_1 with 300s (1) cores
% 25.01/3.70 % Starting sh5l with 300s (1) cores
% 25.01/3.70 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 746626 completed with status 0
% 25.01/3.70 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 25.01/3.70 % Preprocessing class: FSLSSMSMSSSNFFN.
% 25.01/3.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.01/3.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 25.01/3.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 25.01/3.70 % No SInE strategy applied
% 25.01/3.70 % Search class: FGHSM-FFLM31-DFFFFFNN
% 25.01/3.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 25.01/3.70 % Starting SubtermCWHack with 136s (1) cores
% 25.01/3.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 25.01/3.70 % Starting new_bool_3 with 311s (1) cores
% 25.01/3.70 % Starting new_bool_1 with 308s (1) cores
% 25.01/3.70 % Starting sh5l with 304s (1) cores
% 25.01/3.70 % SubtermCWHack with pid 746633 completed with status 0
% 25.01/3.70 % Result found by SubtermCWHack
% 25.01/3.70 % Preprocessing class: FSLSSMSMSSSNFFN.
% 25.01/3.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.01/3.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 25.01/3.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 25.01/3.70 % No SInE strategy applied
% 25.01/3.70 % Search class: FGHSM-FFLM31-DFFFFFNN
% 25.01/3.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 25.01/3.70 % Starting SubtermCWHack with 136s (1) cores
% 25.01/3.70 % Preprocessing time : 0.003 s
% 25.01/3.70
% 25.01/3.70 % Proof found!
% 25.01/3.70 % SZS status Unsatisfiable
% 25.01/3.70 % SZS output start CNFRefutation
% See solution above
% 25.01/3.70 % Parsed axioms : 159
% 25.01/3.70 % Removed by relevancy pruning/SinE : 0
% 25.01/3.70 % Initial clauses : 159
% 25.01/3.70 % Removed in clause preprocessing : 19
% 25.01/3.70 % Initial clauses in saturation : 140
% 25.01/3.70 % Processed clauses : 14150
% 25.01/3.70 % ...of these trivial : 24
% 25.01/3.70 % ...subsumed : 11593
% 25.01/3.70 % ...remaining for further processing : 2533
% 25.01/3.70 % Other redundant clauses eliminated : 22
% 25.01/3.70 % Clauses deleted for lack of memory : 0
% 25.01/3.70 % Backward-subsumed : 183
% 25.01/3.70 % Backward-rewritten : 171
% 25.01/3.70 % Generated clauses : 131320
% 25.01/3.70 % ...of the previous two non-redundant : 111431
% 25.01/3.70 % ...aggressively subsumed : 0
% 25.01/3.70 % Contextual simplify-reflections : 27
% 25.01/3.70 % Paramodulations : 131282
% 25.01/3.70 % Factorizations : 16
% 25.01/3.70 % NegExts : 0
% 25.01/3.70 % Equation resolutions : 22
% 25.01/3.70 % Disequality decompositions : 0
% 25.01/3.70 % Total rewrite steps : 84445
% 25.01/3.70 % ...of those cached : 82905
% 25.01/3.70 % Propositional unsat checks : 0
% 25.01/3.70 % Propositional check models : 0
% 25.01/3.70 % Propositional check unsatisfiable : 0
% 25.01/3.70 % Propositional clauses : 0
% 25.01/3.70 % Propositional clauses after purity: 0
% 25.01/3.70 % Propositional unsat core size : 0
% 25.01/3.70 % Propositional preprocessing time : 0.000
% 25.01/3.70 % Propositional encoding time : 0.000
% 25.01/3.70 % Propositional solver time : 0.000
% 25.01/3.70 % Success case prop preproc time : 0.000
% 25.01/3.70 % Success case prop encoding time : 0.000
% 25.01/3.70 % Success case prop solver time : 0.000
% 25.01/3.70 % Current number of processed clauses : 2173
% 25.01/3.70 % Positive orientable unit clauses : 237
% 25.01/3.70 % Positive unorientable unit clauses: 3
% 25.01/3.70 % Negative unit clauses : 10
% 25.01/3.70 % Non-unit-clauses : 1923
% 25.01/3.70 % Current number of unprocessed clauses: 96827
% 25.01/3.70 % ...number of literals in the above : 430210
% 25.01/3.70 % Current number of archived formulas : 0
% 25.01/3.70 % Current number of archived clauses : 373
% 25.01/3.70 % Clause-clause subsumption calls (NU) : 499626
% 25.01/3.70 % Rec. Clause-clause subsumption calls : 234900
% 25.01/3.70 % Non-unit clause-clause subsumptions : 5636
% 25.01/3.70 % Unit Clause-clause subsumption calls : 9915
% 25.01/3.70 % Rewrite failures with RHS unbound : 16
% 25.01/3.70 % BW rewrite match attempts : 438
% 25.01/3.70 % BW rewrite match successes : 78
% 25.01/3.70 % Condensation attempts : 0
% 25.01/3.70 % Condensation successes : 0
% 25.01/3.70 % Termbank termtop insertions : 7350845
% 25.01/3.70 % Search garbage collected termcells : 287
% 25.01/3.70
% 25.01/3.70 % -------------------------------------------------
% 25.01/3.70 % User time : 3.012 s
% 25.01/3.70 % System time : 0.084 s
% 25.01/3.70 % Total time : 3.096 s
% 25.01/3.70 % Maximum resident set size: 3984 pages
% 25.01/3.70
% 25.01/3.70 % -------------------------------------------------
% 25.01/3.70 % User time : 15.137 s
% 25.01/3.70 % System time : 0.409 s
% 25.01/3.70 % Total time : 15.545 s
% 25.01/3.70 % Maximum resident set size: 4864 pages
% 25.01/3.70 % E exiting
%------------------------------------------------------------------------------