%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET136-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 02:13:42 PM UTC 2026
% Result : Unsatisfiable 0.16s 5.52s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 16
% Syntax : Number of clauses : 66 ( 26 unt; 9 nHn; 45 RR)
% Number of literals : 115 ( 24 equ; 47 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 94 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(complement1,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(regularity1,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(complement2,axiom,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(not_subclass_members2,axiom,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(definition_of_set_builder,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_set_builder) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(subclass_implies_equal,axiom,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(not_subclass_members1,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(prove_corollary_4_to_member_of_triple_2,negated_conjecture,
set_builder(x,set_builder(y,set_builder(u,null_class))) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_4_to_member_of_triple_2) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
cnf(intersection2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(intersection1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(unordered_pair2,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(prove_corollary_4_to_member_of_triple_1,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_4_to_member_of_triple_1) ).
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,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_22,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_25,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
cnf(c_0_26,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_25 ).
cnf(c_0_28,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_26]),c_0_22]) ).
cnf(c_0_29,plain,
( member(regular(complement(complement(X1))),X1)
| complement(complement(X1)) = null_class ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_27]),c_0_24]) ).
cnf(c_0_30,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).
cnf(c_0_31,plain,
complement(complement(null_class)) = null_class,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
c_0_30 ).
cnf(c_0_33,plain,
( ~ member(X1,universal_class)
| member(X1,complement(null_class)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_31]),c_0_28]) ).
cnf(c_0_34,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
definition_of_set_builder ).
cnf(c_0_35,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_36,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[subclass_implies_equal]) ).
cnf(c_0_37,plain,
( ~ member(not_subclass_element(X1,complement(null_class)),universal_class)
| subclass(X1,complement(null_class)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
not_subclass_members1 ).
cnf(c_0_39,negated_conjecture,
set_builder(x,set_builder(y,set_builder(u,null_class))) = null_class,
prove_corollary_4_to_member_of_triple_2 ).
cnf(c_0_40,plain,
union(unordered_pair(X1,X1),X2) = set_builder(X1,X2),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_42,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
c_0_36 ).
cnf(c_0_43,plain,
subclass(universal_class,complement(null_class)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(u,u)),complement(null_class))))))))) = null_class,
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_39,c_0_40]),c_0_40]),c_0_40]),c_0_41]),c_0_41]),c_0_41]) ).
cnf(c_0_45,plain,
complement(null_class) = universal_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_19])]) ).
cnf(c_0_46,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
cnf(c_0_47,negated_conjecture,
complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(u,u)),universal_class)))))))) = null_class,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_46 ).
cnf(c_0_49,negated_conjecture,
( ~ member(X1,universal_class)
| member(X1,intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(u,u)),universal_class)))))))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_47]),c_0_28]) ).
cnf(c_0_50,negated_conjecture,
( ~ member(X1,universal_class)
| member(X1,complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(u,u)),universal_class))))))) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_51,negated_conjecture,
~ member(X1,complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(u,u)),universal_class)))))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_50]),c_0_22]) ).
cnf(c_0_52,negated_conjecture,
complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(u,u)),universal_class))))) = null_class,
inference(spm,[status(thm)],[c_0_51,c_0_21]) ).
cnf(c_0_53,negated_conjecture,
( ~ member(X1,universal_class)
| member(X1,intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(u,u)),universal_class))))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_52]),c_0_28]) ).
cnf(c_0_54,negated_conjecture,
( ~ member(X1,universal_class)
| member(X1,complement(complement(intersection(complement(unordered_pair(u,u)),universal_class)))) ),
inference(spm,[status(thm)],[c_0_48,c_0_53]) ).
cnf(c_0_55,negated_conjecture,
~ member(X1,complement(intersection(complement(unordered_pair(u,u)),universal_class))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_54]),c_0_22]) ).
cnf(c_0_56,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(fof_simplification,[status(thm)],[intersection1]) ).
cnf(c_0_57,negated_conjecture,
complement(intersection(complement(unordered_pair(u,u)),universal_class)) = null_class,
inference(spm,[status(thm)],[c_0_55,c_0_21]) ).
cnf(c_0_58,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
c_0_56 ).
cnf(c_0_59,negated_conjecture,
( ~ member(X1,universal_class)
| member(X1,intersection(complement(unordered_pair(u,u)),universal_class)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_57]),c_0_28]) ).
cnf(c_0_60,negated_conjecture,
( ~ member(X1,universal_class)
| member(X1,complement(unordered_pair(u,u))) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_61,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[unordered_pair2]) ).
cnf(c_0_62,negated_conjecture,
~ member(X1,unordered_pair(u,u)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_60]),c_0_22]) ).
cnf(c_0_63,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
c_0_61 ).
cnf(c_0_64,negated_conjecture,
member(u,universal_class),
prove_corollary_4_to_member_of_triple_1 ).
cnf(c_0_65,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET136-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.38 % Computer : n003.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Mon Sep 21 04:57:21 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.16/5.52 % Version: 3.5.1
% 0.16/5.52 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/5.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/5.52 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.52 % Starting new_bool_1 with 300s (1) cores
% 0.16/5.52 % Starting sh5l with 300s (1) cores
% 0.16/5.52 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 3456381 completed with status 0
% 0.16/5.52 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.16/5.52 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/5.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/5.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.52 % No SInE strategy applied
% 0.16/5.52 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.16/5.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.52 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.16/5.52 % Starting new_bool_3 with 311s (1) cores
% 0.16/5.52 % Starting new_bool_1 with 308s (1) cores
% 0.16/5.52 % Starting sh5l with 304s (1) cores
% 0.16/5.52 % sh5l with pid 3456392 completed with status 0
% 0.16/5.52 % Result found by sh5l
% 0.16/5.52 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/5.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/5.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.52 % No SInE strategy applied
% 0.16/5.52 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.16/5.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.52 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.16/5.52 % Starting new_bool_3 with 311s (1) cores
% 0.16/5.52 % Starting new_bool_1 with 308s (1) cores
% 0.16/5.52 % Starting sh5l with 304s (1) cores
% 0.16/5.52 % Preprocessing time : 0.003 s
% 0.16/5.52 % Presaturation interreduction done
% 0.16/5.52
% 0.16/5.52 % Proof found!
% 0.16/5.52 % SZS status Unsatisfiable
% 0.16/5.52 % SZS output start CNFRefutation
% See solution above
% 0.16/5.52 % Parsed axioms : 94
% 0.16/5.52 % Removed by relevancy pruning/SinE : 0
% 0.16/5.52 % Initial clauses : 94
% 0.16/5.52 % Removed in clause preprocessing : 16
% 0.16/5.52 % Initial clauses in saturation : 78
% 0.16/5.52 % Processed clauses : 554
% 0.16/5.52 % ...of these trivial : 15
% 0.16/5.52 % ...subsumed : 174
% 0.16/5.52 % ...remaining for further processing : 365
% 0.16/5.52 % Other redundant clauses eliminated : 5
% 0.16/5.52 % Clauses deleted for lack of memory : 0
% 0.16/5.52 % Backward-subsumed : 23
% 0.16/5.52 % Backward-rewritten : 15
% 0.16/5.52 % Generated clauses : 1271
% 0.16/5.52 % ...of the previous two non-redundant : 1033
% 0.16/5.52 % ...aggressively subsumed : 0
% 0.16/5.52 % Contextual simplify-reflections : 13
% 0.16/5.52 % Paramodulations : 1264
% 0.16/5.52 % Factorizations : 2
% 0.16/5.52 % NegExts : 0
% 0.16/5.52 % Equation resolutions : 5
% 0.16/5.52 % Disequality decompositions : 0
% 0.16/5.52 % Total rewrite steps : 1389
% 0.16/5.52 % ...of those cached : 1328
% 0.16/5.52 % Propositional unsat checks : 0
% 0.16/5.52 % Propositional check models : 0
% 0.16/5.52 % Propositional check unsatisfiable : 0
% 0.16/5.52 % Propositional clauses : 0
% 0.16/5.52 % Propositional clauses after purity: 0
% 0.16/5.52 % Propositional unsat core size : 0
% 0.16/5.52 % Propositional preprocessing time : 0.000
% 0.16/5.52 % Propositional encoding time : 0.000
% 0.16/5.52 % Propositional solver time : 0.000
% 0.16/5.52 % Success case prop preproc time : 0.000
% 0.16/5.52 % Success case prop encoding time : 0.000
% 0.16/5.52 % Success case prop solver time : 0.000
% 0.16/5.52 % Current number of processed clauses : 247
% 0.16/5.52 % Positive orientable unit clauses : 43
% 0.16/5.52 % Positive unorientable unit clauses: 1
% 0.16/5.52 % Negative unit clauses : 16
% 0.16/5.52 % Non-unit-clauses : 187
% 0.16/5.52 % Current number of unprocessed clauses: 578
% 0.16/5.52 % ...number of literals in the above : 1591
% 0.16/5.52 % Current number of archived formulas : 0
% 0.16/5.52 % Current number of archived clauses : 131
% 0.16/5.52 % Clause-clause subsumption calls (NU) : 5993
% 0.16/5.52 % Rec. Clause-clause subsumption calls : 4164
% 0.16/5.52 % Non-unit clause-clause subsumptions : 125
% 0.16/5.52 % Unit Clause-clause subsumption calls : 979
% 0.16/5.52 % Rewrite failures with RHS unbound : 0
% 0.16/5.52 % BW rewrite match attempts : 39
% 0.16/5.52 % BW rewrite match successes : 12
% 0.16/5.52 % Condensation attempts : 554
% 0.16/5.52 % Condensation successes : 7
% 0.16/5.52 % Termbank termtop insertions : 43504
% 0.16/5.52 % Search garbage collected termcells : 154
% 0.16/5.52
% 0.16/5.52 % -------------------------------------------------
% 0.16/5.52 % User time : 0.060 s
% 0.16/5.52 % System time : 0.006 s
% 0.16/5.52 % Total time : 0.066 s
% 0.16/5.52 % Maximum resident set size: 3720 pages
% 0.16/5.52
% 0.16/5.52 % -------------------------------------------------
% 0.16/5.52 % User time : 0.291 s
% 0.16/5.52 % System time : 0.035 s
% 0.16/5.52 % Total time : 0.326 s
% 0.16/5.52 % Maximum resident set size: 4608 pages
% 0.16/5.52 % E exiting
%------------------------------------------------------------------------------