%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET519-6 : 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 : n009.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 02:14:19 PM UTC 2026
% Result : Unsatisfiable 5.33s 1.50s
% Output : CNFRefutation 5.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of clauses : 68 ( 27 unt; 13 nHn; 34 RR)
% Number of literals : 120 ( 46 equ; 45 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 : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 115 ( 25 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(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(complement1,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(regularity1,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(prove_corollary_1_no_cycles_length_2_1,negated_conjecture,
ordered_pair(x,y) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_no_cycles_length_2_1) ).
cnf(domain1,axiom,
( ~ member(X2,domain_of(X1))
| restrict(X1,singleton(X2),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain1) ).
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(unordered_pairs_in_universal,axiom,
member(unordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(intersection3,axiom,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(unordered_pair_member,axiom,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(unordered_pair3,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(regularity2,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
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(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_16 ).
cnf(c_0_18,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_19,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_22,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_23,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_24,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_19 ).
cnf(c_0_25,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
ordered_pair(x,y) = x,
prove_corollary_1_no_cycles_length_2_1 ).
cnf(c_0_27,plain,
unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]) ).
cnf(c_0_28,plain,
( ~ member(X2,domain_of(X1))
| restrict(X1,singleton(X2),universal_class) != null_class ),
inference(fof_simplification,[status(thm)],[domain1]) ).
cnf(c_0_29,plain,
( ~ member(regular(X1),complement(universal_class))
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(fof_simplification,[status(thm)],[intersection1]) ).
cnf(c_0_31,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[unordered_pair2]) ).
cnf(c_0_32,axiom,
member(unordered_pair(X1,X2),universal_class),
unordered_pairs_in_universal ).
cnf(c_0_33,negated_conjecture,
unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))) = x,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
( ~ member(X2,domain_of(X1))
| restrict(X1,singleton(X2),universal_class) != null_class ),
c_0_28 ).
cnf(c_0_35,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_36,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_37,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
c_0_30 ).
cnf(c_0_38,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_39,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
c_0_31 ).
cnf(c_0_40,negated_conjecture,
member(x,universal_class),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_42,plain,
( ~ member(X2,domain_of(X1))
| intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)) != null_class ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_23]),c_0_35]) ).
cnf(c_0_43,plain,
( ~ member(regular(X1),null_class)
| X1 = null_class ),
inference(rw,[status(thm)],[c_0_29,c_0_36]) ).
cnf(c_0_44,plain,
( member(regular(intersection(X1,X2)),X1)
| intersection(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_37,c_0_21]) ).
cnf(c_0_45,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_38 ).
cnf(c_0_46,negated_conjecture,
member(x,unordered_pair(x,X1)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_41 ).
cnf(c_0_48,plain,
( intersection(X1,cross_product(unordered_pair(regular(domain_of(X1)),regular(domain_of(X1))),universal_class)) != null_class
| domain_of(X1) = null_class ),
inference(spm,[status(thm)],[c_0_42,c_0_21]) ).
cnf(c_0_49,plain,
intersection(null_class,X1) = null_class,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
member(unordered_pair(X1,X2),unordered_pair(unordered_pair(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_51,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
inference(fof_simplification,[status(thm)],[unordered_pair3]) ).
cnf(c_0_52,negated_conjecture,
( ~ member(x,X1)
| member(x,intersection(X1,unordered_pair(x,X2))) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
regularity2 ).
cnf(c_0_54,plain,
( unordered_pair(X1,X2) = null_class
| regular(unordered_pair(X1,X2)) = X2
| regular(unordered_pair(X1,X2)) = X1 ),
inference(spm,[status(thm)],[c_0_47,c_0_21]) ).
cnf(c_0_55,plain,
domain_of(null_class) = null_class,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,negated_conjecture,
member(unordered_pair(x,x),x),
inference(spm,[status(thm)],[c_0_50,c_0_33]) ).
cnf(c_0_57,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
c_0_51 ).
cnf(c_0_58,negated_conjecture,
member(x,intersection(unordered_pair(x,X1),unordered_pair(x,X2))),
inference(spm,[status(thm)],[c_0_52,c_0_46]) ).
cnf(c_0_59,plain,
( unordered_pair(X1,X2) = null_class
| regular(unordered_pair(X1,X2)) = X1
| intersection(unordered_pair(X1,X2),X2) = null_class ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,plain,
~ member(X1,null_class),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_55]),c_0_49])]) ).
cnf(c_0_61,negated_conjecture,
( ~ member(unordered_pair(x,x),X1)
| member(unordered_pair(x,x),intersection(X1,x)) ),
inference(spm,[status(thm)],[c_0_45,c_0_56]) ).
cnf(c_0_62,plain,
member(unordered_pair(X1,X2),unordered_pair(X3,unordered_pair(X1,X2))),
inference(spm,[status(thm)],[c_0_57,c_0_32]) ).
cnf(c_0_63,negated_conjecture,
( unordered_pair(x,unordered_pair(x,X1)) = null_class
| regular(unordered_pair(x,unordered_pair(x,X1))) = x ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
cnf(c_0_64,negated_conjecture,
member(unordered_pair(x,x),intersection(unordered_pair(X1,unordered_pair(x,x)),x)),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_65,negated_conjecture,
( unordered_pair(x,unordered_pair(x,X1)) = null_class
| intersection(unordered_pair(x,unordered_pair(x,X1)),x) = null_class ),
inference(spm,[status(thm)],[c_0_53,c_0_63]) ).
cnf(c_0_66,negated_conjecture,
unordered_pair(x,unordered_pair(x,x)) = null_class,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_60]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_66]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET519-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.51 % Computer : n009.cluster.edu
% 0.19/0.51 % Model : x86_64 x86_64
% 0.19/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.51 % Memory : 8046.5625MB
% 0.19/0.51 % OS : Linux 6.8.0-71-generic
% 0.19/0.51 % CPULimit : 300
% 0.19/0.51 % WCLimit : 300
% 0.19/0.51 % DateTime : Mon Sep 21 05:23:13 UTC 2026
% 0.20/0.52 % CPUTime :
% 0.20/0.52 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.60 Running first-order theorem proving
% 0.20/0.60 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
% 5.33/1.50 % Version: 3.5.1
% 5.33/1.50 % Preprocessing class: FSLSSMSMSSSNFFN.
% 5.33/1.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.33/1.50 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 5.33/1.50 % Starting new_bool_3 with 300s (1) cores
% 5.33/1.50 % Starting new_bool_1 with 300s (1) cores
% 5.33/1.50 % Starting sh5l with 300s (1) cores
% 5.33/1.50 % new_bool_3 with pid 927408 completed with status 9
% 5.33/1.50 % new_bool_1 with pid 927409 completed with status 9
% 5.33/1.50 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 927407 completed with status 0
% 5.33/1.50 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 5.33/1.50 % Preprocessing class: FSLSSMSMSSSNFFN.
% 5.33/1.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.33/1.50 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 5.33/1.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.33/1.50 % No SInE strategy applied
% 5.33/1.50 % Search class: FGHSM-FFLM31-DFFFFFNN
% 5.33/1.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.33/1.50 % Starting SubtermCWHack with 136s (1) cores
% 5.33/1.50 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 5.33/1.50 % Starting new_bool_3 with 311s (1) cores
% 5.33/1.50 % Starting new_bool_1 with 308s (1) cores
% 5.33/1.50 % Starting sh5l with 304s (1) cores
% 5.33/1.50 % new_bool_3 with pid 927416 completed with status 0
% 5.33/1.50 % Result found by new_bool_3
% 5.33/1.50 % Preprocessing class: FSLSSMSMSSSNFFN.
% 5.33/1.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.33/1.50 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 5.33/1.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.33/1.50 % No SInE strategy applied
% 5.33/1.50 % Search class: FGHSM-FFLM31-DFFFFFNN
% 5.33/1.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.33/1.50 % Starting SubtermCWHack with 136s (1) cores
% 5.33/1.50 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 5.33/1.50 % Starting new_bool_3 with 311s (1) cores
% 5.33/1.50 % Preprocessing time : 0.004 s
% 5.33/1.50 % Presaturation interreduction done
% 5.33/1.50
% 5.33/1.50 % Proof found!
% 5.33/1.50 % SZS status Unsatisfiable
% 5.33/1.50 % SZS output start CNFRefutation
% See solution above
% 5.33/1.50 % Parsed axioms : 113
% 5.33/1.50 % Removed by relevancy pruning/SinE : 0
% 5.33/1.50 % Initial clauses : 113
% 5.33/1.50 % Removed in clause preprocessing : 17
% 5.33/1.50 % Initial clauses in saturation : 96
% 5.33/1.50 % Processed clauses : 4105
% 5.33/1.50 % ...of these trivial : 106
% 5.33/1.50 % ...subsumed : 1922
% 5.33/1.50 % ...remaining for further processing : 2077
% 5.33/1.50 % Other redundant clauses eliminated : 12
% 5.33/1.50 % Clauses deleted for lack of memory : 0
% 5.33/1.50 % Backward-subsumed : 76
% 5.33/1.50 % Backward-rewritten : 81
% 5.33/1.50 % Generated clauses : 39744
% 5.33/1.50 % ...of the previous two non-redundant : 33894
% 5.33/1.50 % ...aggressively subsumed : 0
% 5.33/1.50 % Contextual simplify-reflections : 5
% 5.33/1.50 % Paramodulations : 39718
% 5.33/1.50 % Factorizations : 12
% 5.33/1.50 % NegExts : 0
% 5.33/1.50 % Equation resolutions : 14
% 5.33/1.50 % Disequality decompositions : 0
% 5.33/1.50 % Total rewrite steps : 9906
% 5.33/1.50 % ...of those cached : 9091
% 5.33/1.50 % Propositional unsat checks : 0
% 5.33/1.50 % Propositional check models : 0
% 5.33/1.50 % Propositional check unsatisfiable : 0
% 5.33/1.50 % Propositional clauses : 0
% 5.33/1.50 % Propositional clauses after purity: 0
% 5.33/1.50 % Propositional unsat core size : 0
% 5.33/1.50 % Propositional preprocessing time : 0.000
% 5.33/1.50 % Propositional encoding time : 0.000
% 5.33/1.50 % Propositional solver time : 0.000
% 5.33/1.50 % Success case prop preproc time : 0.000
% 5.33/1.50 % Success case prop encoding time : 0.000
% 5.33/1.50 % Success case prop solver time : 0.000
% 5.33/1.50 % Current number of processed clauses : 1821
% 5.33/1.50 % Positive orientable unit clauses : 421
% 5.33/1.50 % Positive unorientable unit clauses: 1
% 5.33/1.50 % Negative unit clauses : 232
% 5.33/1.50 % Non-unit-clauses : 1167
% 5.33/1.50 % Current number of unprocessed clauses: 29747
% 5.33/1.50 % ...number of literals in the above : 59177
% 5.33/1.50 % Current number of archived formulas : 0
% 5.33/1.50 % Current number of archived clauses : 269
% 5.33/1.50 % Clause-clause subsumption calls (NU) : 111130
% 5.33/1.50 % Rec. Clause-clause subsumption calls : 70176
% 5.33/1.50 % Non-unit clause-clause subsumptions : 1368
% 5.33/1.50 % Unit Clause-clause subsumption calls : 16820
% 5.33/1.50 % Rewrite failures with RHS unbound : 0
% 5.33/1.50 % BW rewrite match attempts : 834
% 5.33/1.50 % BW rewrite match successes : 36
% 5.33/1.50 % Condensation attempts : 0
% 5.33/1.50 % Condensation successes : 0
% 5.33/1.50 % Termbank termtop insertions : 1001611
% 5.33/1.50 % Search garbage collected termcells : 183
% 5.33/1.50
% 5.33/1.50 % -------------------------------------------------
% 5.33/1.50 % User time : 0.792 s
% 5.33/1.50 % System time : 0.037 s
% 5.33/1.50 % Total time : 0.830 s
% 5.33/1.50 % Maximum resident set size: 4000 pages
% 5.33/1.50
% 5.33/1.50 % -------------------------------------------------
% 5.33/1.50 % User time : 3.988 s
% 5.33/1.50 % System time : 0.202 s
% 5.33/1.50 % Total time : 4.190 s
% 5.33/1.50 % Maximum resident set size: 4608 pages
% 5.33/1.50 % E exiting
%------------------------------------------------------------------------------