%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM078-1 : 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 : n014.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 01:51:17 PM UTC 2026
% Result : Unsatisfiable 1.99s 0.74s
% Output : CNFRefutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 40 ( 10 unt; 10 nHn; 28 RR)
% Number of literals : 82 ( 24 equ; 35 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 10 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(unordered_pair_member,axiom,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(intersection3,axiom,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(regularity2,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(unordered_pair2,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(intersection1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(prove_corollary_2_to_well_ordering_property7_3,negated_conjecture,
member(u,intersection(u,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_well_ordering_property7_3) ).
cnf(c_0_10,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_11,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_12,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_10 ).
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)) ),
c_0_11 ).
cnf(c_0_15,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_19,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_20,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_21,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_19 ).
cnf(c_0_23,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_20 ).
cnf(c_0_24,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
regularity2 ).
cnf(c_0_25,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_21]),c_0_16]) ).
cnf(c_0_26,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_22,c_0_15]) ).
cnf(c_0_27,plain,
( ~ member(X2,X1)
| ~ member(X2,regular(X1))
| X1 = null_class ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_28,plain,
( unordered_pair(X1,X1) = null_class
| regular(unordered_pair(X1,X1)) = X1 ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_26])]) ).
cnf(c_0_29,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[unordered_pair2]) ).
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(X2,X1)
| ~ member(X2,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
c_0_29 ).
cnf(c_0_33,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
c_0_30 ).
cnf(c_0_34,negated_conjecture,
member(u,intersection(u,y)),
prove_corollary_2_to_well_ordering_property7_3 ).
cnf(c_0_35,plain,
( ~ member(X1,X1)
| unordered_pair(X1,X1) = null_class ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_16]) ).
cnf(c_0_36,negated_conjecture,
member(u,u),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
unordered_pair(u,u) = null_class,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
member(u,universal_class),
inference(spm,[status(thm)],[c_0_16,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_37]),c_0_38])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM078-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n014.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 02:02:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 1.99/0.74 % Version: 3.5.1
% 1.99/0.74 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.99/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.99/0.74 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.99/0.74 % Starting new_bool_3 with 300s (1) cores
% 1.99/0.74 % Starting new_bool_1 with 300s (1) cores
% 1.99/0.74 % Starting sh5l with 300s (1) cores
% 1.99/0.74 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2912692 completed with status 0
% 1.99/0.74 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.99/0.74 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.99/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.99/0.74 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.99/0.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.99/0.74 % No SInE strategy applied
% 1.99/0.74 % Search class: FGHSM-FFLM31-DFFFFFNN
% 1.99/0.74 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.99/0.74 % Starting SubtermCWHack with 136s (1) cores
% 1.99/0.74 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.99/0.74 % Starting new_bool_3 with 311s (1) cores
% 1.99/0.74 % Starting new_bool_1 with 308s (1) cores
% 1.99/0.74 % Starting sh5l with 304s (1) cores
% 1.99/0.74 % sh5l with pid 2912702 completed with status 0
% 1.99/0.74 % Result found by sh5l
% 1.99/0.74 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.99/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.99/0.74 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.99/0.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.99/0.74 % No SInE strategy applied
% 1.99/0.74 % Search class: FGHSM-FFLM31-DFFFFFNN
% 1.99/0.74 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.99/0.74 % Starting SubtermCWHack with 136s (1) cores
% 1.99/0.74 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.99/0.74 % Starting new_bool_3 with 311s (1) cores
% 1.99/0.74 % Starting new_bool_1 with 308s (1) cores
% 1.99/0.74 % Starting sh5l with 304s (1) cores
% 1.99/0.74 % Preprocessing time : 0.002 s
% 1.99/0.74 % Presaturation interreduction done
% 1.99/0.74
% 1.99/0.74 % Proof found!
% 1.99/0.74 % SZS status Unsatisfiable
% 1.99/0.74 % SZS output start CNFRefutation
% See solution above
% 1.99/0.74 % Parsed axioms : 161
% 1.99/0.74 % Removed by relevancy pruning/SinE : 0
% 1.99/0.74 % Initial clauses : 161
% 1.99/0.74 % Removed in clause preprocessing : 19
% 1.99/0.74 % Initial clauses in saturation : 142
% 1.99/0.74 % Processed clauses : 3784
% 1.99/0.74 % ...of these trivial : 17
% 1.99/0.74 % ...subsumed : 2366
% 1.99/0.74 % ...remaining for further processing : 1401
% 1.99/0.74 % Other redundant clauses eliminated : 10
% 1.99/0.74 % Clauses deleted for lack of memory : 0
% 1.99/0.74 % Backward-subsumed : 55
% 1.99/0.74 % Backward-rewritten : 60
% 1.99/0.74 % Generated clauses : 13571
% 1.99/0.74 % ...of the previous two non-redundant : 12073
% 1.99/0.74 % ...aggressively subsumed : 0
% 1.99/0.74 % Contextual simplify-reflections : 25
% 1.99/0.74 % Paramodulations : 13557
% 1.99/0.74 % Factorizations : 4
% 1.99/0.74 % NegExts : 0
% 1.99/0.74 % Equation resolutions : 10
% 1.99/0.74 % Disequality decompositions : 0
% 1.99/0.74 % Total rewrite steps : 4605
% 1.99/0.74 % ...of those cached : 4277
% 1.99/0.74 % Propositional unsat checks : 0
% 1.99/0.74 % Propositional check models : 0
% 1.99/0.74 % Propositional check unsatisfiable : 0
% 1.99/0.74 % Propositional clauses : 0
% 1.99/0.74 % Propositional clauses after purity: 0
% 1.99/0.74 % Propositional unsat core size : 0
% 1.99/0.74 % Propositional preprocessing time : 0.000
% 1.99/0.74 % Propositional encoding time : 0.000
% 1.99/0.74 % Propositional solver time : 0.000
% 1.99/0.74 % Success case prop preproc time : 0.000
% 1.99/0.74 % Success case prop encoding time : 0.000
% 1.99/0.74 % Success case prop solver time : 0.000
% 1.99/0.74 % Current number of processed clauses : 1139
% 1.99/0.74 % Positive orientable unit clauses : 125
% 1.99/0.74 % Positive unorientable unit clauses: 3
% 1.99/0.74 % Negative unit clauses : 4
% 1.99/0.74 % Non-unit-clauses : 1007
% 1.99/0.74 % Current number of unprocessed clauses: 8312
% 1.99/0.74 % ...number of literals in the above : 27236
% 1.99/0.74 % Current number of archived formulas : 0
% 1.99/0.74 % Current number of archived clauses : 275
% 1.99/0.74 % Clause-clause subsumption calls (NU) : 83724
% 1.99/0.74 % Rec. Clause-clause subsumption calls : 66487
% 1.99/0.74 % Non-unit clause-clause subsumptions : 2028
% 1.99/0.74 % Unit Clause-clause subsumption calls : 1744
% 1.99/0.74 % Rewrite failures with RHS unbound : 20
% 1.99/0.74 % BW rewrite match attempts : 100
% 1.99/0.74 % BW rewrite match successes : 29
% 1.99/0.74 % Condensation attempts : 3784
% 1.99/0.74 % Condensation successes : 101
% 1.99/0.74 % Termbank termtop insertions : 278543
% 1.99/0.74 % Search garbage collected termcells : 285
% 1.99/0.74
% 1.99/0.74 % -------------------------------------------------
% 1.99/0.74 % User time : 0.271 s
% 1.99/0.74 % System time : 0.023 s
% 1.99/0.74 % Total time : 0.294 s
% 1.99/0.74 % Maximum resident set size: 4036 pages
% 1.99/0.74
% 1.99/0.74 % -------------------------------------------------
% 1.99/0.74 % User time : 1.398 s
% 1.99/0.74 % System time : 0.097 s
% 1.99/0.74 % Total time : 1.495 s
% 1.99/0.74 % Maximum resident set size: 4864 pages
% 1.99/0.74 % E exiting
%------------------------------------------------------------------------------