%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM217-1 : 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 : 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 01:44:30 PM UTC 2026
% Result : Unsatisfiable 181.95s 26.82s
% Output : CNFRefutation 181.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of clauses : 56 ( 23 unt; 7 nHn; 35 RR)
% Number of literals : 93 ( 35 equ; 43 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 2 con; 0-3 aty)
% Number of variables : 103 ( 23 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(regularity1,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(domain1,axiom,
( ~ member(X2,domain_of(X1))
| restrict(X1,singleton(X2),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain1) ).
cnf(intersection2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(cartesian_product4,axiom,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(rest_of1,axiom,
subclass(rest_of(X1),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',rest_of1) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(restriction2,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction2) ).
cnf(rest_of2,axiom,
( ~ member(ordered_pair(X1,X2),rest_of(X3))
| member(X1,domain_of(X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',rest_of2) ).
cnf(prove_corollary_2_to_rest_defn_1,negated_conjecture,
rest_of(null_class) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_rest_defn_1) ).
cnf(c_0_14,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_15,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_16,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_14 ).
cnf(c_0_17,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_18,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_15 ).
cnf(c_0_19,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( ~ member(X2,domain_of(X1))
| restrict(X1,singleton(X2),universal_class) != null_class ),
inference(fof_simplification,[status(thm)],[domain1]) ).
cnf(c_0_22,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_24,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
cnf(c_0_25,plain,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[cartesian_product4]) ).
cnf(c_0_26,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_27,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_28,axiom,
subclass(rest_of(X1),cross_product(universal_class,universal_class)),
rest_of1 ).
cnf(c_0_29,plain,
( ~ member(X2,domain_of(X1))
| restrict(X1,singleton(X2),universal_class) != null_class ),
c_0_21 ).
cnf(c_0_30,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_31,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
restriction2 ).
cnf(c_0_32,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_33,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_24 ).
cnf(c_0_34,plain,
( ~ member(ordered_pair(X1,X2),rest_of(X3))
| member(X1,domain_of(X3)) ),
inference(fof_simplification,[status(thm)],[rest_of2]) ).
cnf(c_0_35,plain,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
c_0_25 ).
cnf(c_0_36,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_26,c_0_27]),c_0_27]) ).
cnf(c_0_37,plain,
( ~ member(X1,rest_of(X2))
| member(X1,cross_product(universal_class,universal_class)) ),
inference(spm,[status(thm)],[c_0_16,c_0_28]) ).
cnf(c_0_38,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_29,c_0_27]),c_0_30]) ).
cnf(c_0_39,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(rw,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_40,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_32]),c_0_20]) ).
cnf(c_0_41,plain,
( member(regular(intersection(X1,X2)),X2)
| intersection(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_42,plain,
( ~ member(ordered_pair(X1,X2),rest_of(X3))
| member(X1,domain_of(X3)) ),
c_0_34 ).
cnf(c_0_43,plain,
( ~ member(X1,cross_product(X2,X3))
| unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))) = X1 ),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,plain,
( member(regular(rest_of(X1)),cross_product(universal_class,universal_class))
| rest_of(X1) = null_class ),
inference(spm,[status(thm)],[c_0_37,c_0_19]) ).
cnf(c_0_45,plain,
( ~ member(X1,domain_of(X2))
| intersection(cross_product(unordered_pair(X1,X1),universal_class),X2) != null_class ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
intersection(X1,null_class) = null_class,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),rest_of(X3))
| member(X1,domain_of(X3)) ),
inference(rw,[status(thm)],[c_0_42,c_0_36]) ).
cnf(c_0_48,plain,
( rest_of(X1) = null_class
| unordered_pair(unordered_pair(first(regular(rest_of(X1))),first(regular(rest_of(X1)))),unordered_pair(first(regular(rest_of(X1))),unordered_pair(second(regular(rest_of(X1))),second(regular(rest_of(X1)))))) = regular(rest_of(X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
~ member(X1,domain_of(null_class)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,plain,
( ~ member(regular(rest_of(X1)),rest_of(X2))
| member(first(regular(rest_of(X1))),domain_of(X2))
| rest_of(X1) = null_class ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,plain,
domain_of(null_class) = null_class,
inference(spm,[status(thm)],[c_0_49,c_0_19]) ).
cnf(c_0_52,negated_conjecture,
rest_of(null_class) != null_class,
inference(fof_simplification,[status(thm)],[prove_corollary_2_to_rest_defn_1]) ).
cnf(c_0_53,plain,
( ~ member(regular(rest_of(X1)),rest_of(null_class))
| rest_of(X1) = null_class ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_40]) ).
cnf(c_0_54,negated_conjecture,
rest_of(null_class) != null_class,
c_0_52 ).
cnf(c_0_55,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_19]),c_0_54]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM217-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n003.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 02:15:00 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 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
% 181.95/26.82 % Version: 3.5.1
% 181.95/26.82 % Preprocessing class: FSLSSMSMSSSNFFN.
% 181.95/26.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 181.95/26.82 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 181.95/26.82 % Starting new_bool_3 with 300s (1) cores
% 181.95/26.82 % Starting new_bool_1 with 300s (1) cores
% 181.95/26.82 % Starting sh5l with 300s (1) cores
% 181.95/26.82 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 3188526 completed with status 0
% 181.95/26.82 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 181.95/26.82 % Preprocessing class: FSLSSMSMSSSNFFN.
% 181.95/26.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 181.95/26.82 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 181.95/26.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 181.95/26.82 % No SInE strategy applied
% 181.95/26.82 % Search class: FGHSM-FFLM31-DFFFFFNN
% 181.95/26.82 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 181.95/26.82 % Starting SubtermCWHack with 136s (1) cores
% 181.95/26.82 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 181.95/26.82 % Starting new_bool_3 with 311s (1) cores
% 181.95/26.82 % Starting new_bool_1 with 308s (1) cores
% 181.95/26.82 % Starting sh5l with 304s (1) cores
% 181.95/26.82 % sh5l with pid 3188537 completed with status 0
% 181.95/26.82 % Result found by sh5l
% 181.95/26.82 % Preprocessing class: FSLSSMSMSSSNFFN.
% 181.95/26.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 181.95/26.82 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 181.95/26.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 181.95/26.82 % No SInE strategy applied
% 181.95/26.82 % Search class: FGHSM-FFLM31-DFFFFFNN
% 181.95/26.82 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 181.95/26.82 % Starting SubtermCWHack with 136s (1) cores
% 181.95/26.82 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 181.95/26.82 % Starting new_bool_3 with 311s (1) cores
% 181.95/26.82 % Starting new_bool_1 with 308s (1) cores
% 181.95/26.82 % Starting sh5l with 304s (1) cores
% 181.95/26.82 % Preprocessing time : 0.006 s
% 181.95/26.82 % Presaturation interreduction done
% 181.95/26.82
% 181.95/26.82 % Proof found!
% 181.95/26.82 % SZS status Unsatisfiable
% 181.95/26.82 % SZS output start CNFRefutation
% See solution above
% 181.95/26.82 % Parsed axioms : 159
% 181.95/26.82 % Removed by relevancy pruning/SinE : 0
% 181.95/26.82 % Initial clauses : 159
% 181.95/26.82 % Removed in clause preprocessing : 19
% 181.95/26.82 % Initial clauses in saturation : 140
% 181.95/26.82 % Processed clauses : 71997
% 181.95/26.82 % ...of these trivial : 107
% 181.95/26.82 % ...subsumed : 65335
% 181.95/26.82 % ...remaining for further processing : 6555
% 181.95/26.82 % Other redundant clauses eliminated : 32
% 181.95/26.82 % Clauses deleted for lack of memory : 0
% 181.95/26.82 % Backward-subsumed : 634
% 181.95/26.82 % Backward-rewritten : 263
% 181.95/26.82 % Generated clauses : 644884
% 181.95/26.82 % ...of the previous two non-redundant : 524032
% 181.95/26.82 % ...aggressively subsumed : 0
% 181.95/26.82 % Contextual simplify-reflections : 193
% 181.95/26.82 % Paramodulations : 644819
% 181.95/26.82 % Factorizations : 32
% 181.95/26.82 % NegExts : 0
% 181.95/26.82 % Equation resolutions : 33
% 181.95/26.82 % Disequality decompositions : 0
% 181.95/26.82 % Total rewrite steps : 587670
% 181.95/26.82 % ...of those cached : 579325
% 181.95/26.82 % Propositional unsat checks : 0
% 181.95/26.82 % Propositional check models : 0
% 181.95/26.82 % Propositional check unsatisfiable : 0
% 181.95/26.82 % Propositional clauses : 0
% 181.95/26.82 % Propositional clauses after purity: 0
% 181.95/26.82 % Propositional unsat core size : 0
% 181.95/26.82 % Propositional preprocessing time : 0.000
% 181.95/26.82 % Propositional encoding time : 0.000
% 181.95/26.82 % Propositional solver time : 0.000
% 181.95/26.82 % Success case prop preproc time : 0.000
% 181.95/26.82 % Success case prop encoding time : 0.000
% 181.95/26.82 % Success case prop solver time : 0.000
% 181.95/26.82 % Current number of processed clauses : 5513
% 181.95/26.82 % Positive orientable unit clauses : 244
% 181.95/26.82 % Positive unorientable unit clauses: 4
% 181.95/26.82 % Negative unit clauses : 79
% 181.95/26.82 % Non-unit-clauses : 5186
% 181.95/26.82 % Current number of unprocessed clauses: 449800
% 181.95/26.82 % ...number of literals in the above : 1935150
% 181.95/26.82 % Current number of archived formulas : 0
% 181.95/26.82 % Current number of archived clauses : 1055
% 181.95/26.82 % Clause-clause subsumption calls (NU) : 3598737
% 181.95/26.82 % Rec. Clause-clause subsumption calls : 1583616
% 181.95/26.82 % Non-unit clause-clause subsumptions : 41361
% 181.95/26.82 % Unit Clause-clause subsumption calls : 44680
% 181.95/26.82 % Rewrite failures with RHS unbound : 77
% 181.95/26.82 % BW rewrite match attempts : 2030
% 181.95/26.82 % BW rewrite match successes : 1280
% 181.95/26.82 % Condensation attempts : 71997
% 181.95/26.82 % Condensation successes : 5201
% 181.95/26.82 % Termbank termtop insertions : 27500404
% 181.95/26.82 % Search garbage collected termcells : 287
% 181.95/26.82
% 181.95/26.82 % -------------------------------------------------
% 181.95/26.82 % User time : 25.314 s
% 181.95/26.82 % System time : 0.477 s
% 181.95/26.82 % Total time : 25.792 s
% 181.95/26.82 % Maximum resident set size: 4036 pages
% 181.95/26.82
% 181.95/26.82 % -------------------------------------------------
% 181.95/26.82 % User time : 125.196 s
% 181.95/26.82 % System time : 4.109 s
% 181.95/26.82 % Total time : 129.305 s
% 181.95/26.82 % Maximum resident set size: 4864 pages
% 181.95/26.82 % E exiting
%------------------------------------------------------------------------------