%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET146-6 : 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 : n002.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 02:16:41 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.53s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 44 ( 19 unt; 5 nHn; 27 RR)
% Number of literals : 72 ( 28 equ; 34 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 : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 77 ( 14 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(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(complement1,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(regularity1,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(intersection2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
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(intersection1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(prove_intersection_with_null_class_1,negated_conjecture,
intersection(null_class,x) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_with_null_class_1) ).
cnf(c_0_11,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_12,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_11 ).
cnf(c_0_13,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_14,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_15,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_17,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_14 ).
cnf(c_0_18,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( ~ member(regular(X1),complement(universal_class))
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
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,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_23,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_20 ).
cnf(c_0_24,plain,
( ~ member(X2,domain_of(X1))
| restrict(X1,singleton(X2),universal_class) != null_class ),
c_0_21 ).
cnf(c_0_25,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_26,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_27,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
restriction2 ).
cnf(c_0_28,plain,
( ~ member(regular(X1),null_class)
| X1 = null_class ),
inference(rw,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_29,plain,
( member(regular(intersection(X1,X2)),X2)
| intersection(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_30,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_24,c_0_25]),c_0_26]) ).
cnf(c_0_31,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(rw,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_32,plain,
intersection(X1,null_class) = null_class,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,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_30,c_0_16]) ).
cnf(c_0_34,plain,
intersection(null_class,cross_product(X1,X2)) = null_class,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(fof_simplification,[status(thm)],[intersection1]) ).
cnf(c_0_36,plain,
domain_of(null_class) = null_class,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
c_0_35 ).
cnf(c_0_38,negated_conjecture,
intersection(null_class,x) != null_class,
inference(fof_simplification,[status(thm)],[prove_intersection_with_null_class_1]) ).
cnf(c_0_39,plain,
~ member(X1,null_class),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_36]),c_0_34])]) ).
cnf(c_0_40,plain,
( member(regular(intersection(X1,X2)),X1)
| intersection(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_37,c_0_16]) ).
cnf(c_0_41,negated_conjecture,
intersection(null_class,x) != null_class,
c_0_38 ).
cnf(c_0_42,plain,
intersection(null_class,X1) = null_class,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET146-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n002.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 21 04:59:16 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 0.13/0.53 % Version: 3.5.1
% 0.13/0.53 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.13/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.53 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.13/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.53 % Starting sh5l with 300s (1) cores
% 0.13/0.53 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2480112 completed with status 0
% 0.13/0.53 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.13/0.53 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.13/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.53 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.13/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.53 % No SInE strategy applied
% 0.13/0.53 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.13/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.53 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.13/0.53 % Starting new_bool_3 with 311s (1) cores
% 0.13/0.53 % Starting new_bool_1 with 308s (1) cores
% 0.13/0.53 % Starting sh5l with 304s (1) cores
% 0.13/0.53 % new_bool_1 with pid 2480120 completed with status 0
% 0.13/0.53 % Result found by new_bool_1
% 0.13/0.53 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.13/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.53 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.13/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.53 % No SInE strategy applied
% 0.13/0.53 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.13/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.53 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.13/0.53 % Starting new_bool_3 with 311s (1) cores
% 0.13/0.53 % Starting new_bool_1 with 308s (1) cores
% 0.13/0.53 % Preprocessing time : 0.005 s
% 0.13/0.53 % Presaturation interreduction done
% 0.13/0.53
% 0.13/0.53 % Proof found!
% 0.13/0.53 % SZS status Unsatisfiable
% 0.13/0.53 % SZS output start CNFRefutation
% See solution above
% 0.13/0.53 % Parsed axioms : 113
% 0.13/0.53 % Removed by relevancy pruning/SinE : 0
% 0.13/0.53 % Initial clauses : 113
% 0.13/0.53 % Removed in clause preprocessing : 17
% 0.13/0.53 % Initial clauses in saturation : 96
% 0.13/0.53 % Processed clauses : 326
% 0.13/0.53 % ...of these trivial : 0
% 0.13/0.53 % ...subsumed : 6
% 0.13/0.53 % ...remaining for further processing : 320
% 0.13/0.53 % Other redundant clauses eliminated : 4
% 0.13/0.53 % Clauses deleted for lack of memory : 0
% 0.13/0.53 % Backward-subsumed : 13
% 0.13/0.53 % Backward-rewritten : 6
% 0.13/0.53 % Generated clauses : 849
% 0.13/0.53 % ...of the previous two non-redundant : 704
% 0.13/0.53 % ...aggressively subsumed : 0
% 0.13/0.53 % Contextual simplify-reflections : 0
% 0.13/0.53 % Paramodulations : 845
% 0.13/0.53 % Factorizations : 0
% 0.13/0.53 % NegExts : 0
% 0.13/0.53 % Equation resolutions : 4
% 0.13/0.53 % Disequality decompositions : 0
% 0.13/0.53 % Total rewrite steps : 156
% 0.13/0.53 % ...of those cached : 112
% 0.13/0.53 % Propositional unsat checks : 0
% 0.13/0.53 % Propositional check models : 0
% 0.13/0.53 % Propositional check unsatisfiable : 0
% 0.13/0.53 % Propositional clauses : 0
% 0.13/0.53 % Propositional clauses after purity: 0
% 0.13/0.53 % Propositional unsat core size : 0
% 0.13/0.53 % Propositional preprocessing time : 0.000
% 0.13/0.53 % Propositional encoding time : 0.000
% 0.13/0.53 % Propositional solver time : 0.000
% 0.13/0.53 % Success case prop preproc time : 0.000
% 0.13/0.53 % Success case prop encoding time : 0.000
% 0.13/0.53 % Success case prop solver time : 0.000
% 0.13/0.53 % Current number of processed clauses : 202
% 0.13/0.53 % Positive orientable unit clauses : 61
% 0.13/0.53 % Positive unorientable unit clauses: 1
% 0.13/0.53 % Negative unit clauses : 35
% 0.13/0.53 % Non-unit-clauses : 105
% 0.13/0.53 % Current number of unprocessed clauses: 569
% 0.13/0.53 % ...number of literals in the above : 981
% 0.13/0.53 % Current number of archived formulas : 0
% 0.13/0.53 % Current number of archived clauses : 131
% 0.13/0.53 % Clause-clause subsumption calls (NU) : 2914
% 0.13/0.53 % Rec. Clause-clause subsumption calls : 1610
% 0.13/0.53 % Non-unit clause-clause subsumptions : 13
% 0.13/0.53 % Unit Clause-clause subsumption calls : 343
% 0.13/0.53 % Rewrite failures with RHS unbound : 0
% 0.13/0.53 % BW rewrite match attempts : 36
% 0.13/0.53 % BW rewrite match successes : 5
% 0.13/0.53 % Condensation attempts : 0
% 0.13/0.53 % Condensation successes : 0
% 0.13/0.53 % Termbank termtop insertions : 22467
% 0.13/0.53 % Search garbage collected termcells : 185
% 0.13/0.53
% 0.13/0.53 % -------------------------------------------------
% 0.13/0.53 % User time : 0.059 s
% 0.13/0.53 % System time : 0.007 s
% 0.13/0.53 % Total time : 0.066 s
% 0.13/0.53 % Maximum resident set size: 3940 pages
% 0.13/0.53
% 0.13/0.53 % -------------------------------------------------
% 0.13/0.53 % User time : 0.116 s
% 0.13/0.53 % System time : 0.022 s
% 0.13/0.53 % Total time : 0.138 s
% 0.13/0.53 % Maximum resident set size: 4864 pages
% 0.13/0.53 % E exiting
%------------------------------------------------------------------------------