%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM071-1 : 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 : n008.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 01:44:20 PM UTC 2026
% Result : Unsatisfiable 277.87s 36.78s
% Output : CNFRefutation 277.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 49 ( 20 unt; 7 nHn; 34 RR)
% Number of literals : 101 ( 15 equ; 50 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(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(subclass_members,axiom,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(well_ordering3,axiom,
( ~ member(X4,X3)
| ~ subclass(X3,X2)
| ~ well_ordering(X1,X2)
| member(least(X1,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',well_ordering3) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(prove_well_ordering_is_irreflexive_1,negated_conjecture,
well_ordering(xr,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_well_ordering_is_irreflexive_1) ).
cnf(prove_well_ordering_is_irreflexive_3,negated_conjecture,
member(u,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_well_ordering_is_irreflexive_3) ).
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(well_ordering5,axiom,
( ~ member(ordered_pair(X4,least(X1,X3)),X1)
| ~ member(X4,X3)
| ~ subclass(X3,X2)
| ~ well_ordering(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',well_ordering5) ).
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_well_ordering_is_irreflexive_2,negated_conjecture,
member(ordered_pair(u,u),xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_well_ordering_is_irreflexive_2) ).
cnf(c_0_13,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_14,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_13 ).
cnf(c_0_15,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
not_subclass_members1 ).
cnf(c_0_16,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).
cnf(c_0_17,plain,
( subclass(unordered_pair(X1,X2),X3)
| not_subclass_element(unordered_pair(X1,X2),X3) = X2
| not_subclass_element(unordered_pair(X1,X2),X3) = X1 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_19,plain,
( ~ member(X4,X3)
| ~ subclass(X3,X2)
| ~ well_ordering(X1,X2)
| member(least(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[well_ordering3]) ).
cnf(c_0_20,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
c_0_16 ).
cnf(c_0_21,plain,
( subclass(unordered_pair(X1,X1),X2)
| not_subclass_element(unordered_pair(X1,X1),X2) = X1 ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_17])]) ).
cnf(c_0_22,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_18 ).
cnf(c_0_23,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_24,plain,
( ~ member(X4,X3)
| ~ subclass(X3,X2)
| ~ well_ordering(X1,X2)
| member(least(X1,X3),X3) ),
c_0_19 ).
cnf(c_0_25,negated_conjecture,
well_ordering(xr,y),
prove_well_ordering_is_irreflexive_1 ).
cnf(c_0_26,plain,
( ~ member(X1,X2)
| subclass(unordered_pair(X1,X1),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
member(u,y),
prove_well_ordering_is_irreflexive_3 ).
cnf(c_0_28,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
inference(fof_simplification,[status(thm)],[unordered_pair3]) ).
cnf(c_0_29,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( ~ member(ordered_pair(X4,least(X1,X3)),X1)
| ~ member(X4,X3)
| ~ subclass(X3,X2)
| ~ well_ordering(X1,X2) ),
inference(fof_simplification,[status(thm)],[well_ordering5]) ).
cnf(c_0_31,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_32,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_33,negated_conjecture,
( ~ subclass(X1,y)
| ~ member(X2,X1)
| member(least(xr,X1),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_34,negated_conjecture,
subclass(unordered_pair(u,u),y),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
c_0_28 ).
cnf(c_0_36,negated_conjecture,
member(u,universal_class),
inference(spm,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_37,plain,
( ~ member(ordered_pair(X4,least(X1,X3)),X1)
| ~ member(X4,X3)
| ~ subclass(X3,X2)
| ~ well_ordering(X1,X2) ),
c_0_30 ).
cnf(c_0_38,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_31,c_0_32]),c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( ~ member(X1,unordered_pair(u,u))
| member(least(xr,unordered_pair(u,u)),unordered_pair(u,u)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
member(u,unordered_pair(X1,u)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
( ~ member(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(least(X1,X3),least(X1,X3)))),X1)
| ~ well_ordering(X1,X2)
| ~ member(X4,X3)
| ~ subclass(X3,X2) ),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
member(least(xr,unordered_pair(u,u)),unordered_pair(u,u)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( ~ subclass(X2,y)
| ~ member(X1,X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(least(xr,X2),least(xr,X2)))),xr) ),
inference(spm,[status(thm)],[c_0_41,c_0_25]) ).
cnf(c_0_44,negated_conjecture,
least(xr,unordered_pair(u,u)) = u,
inference(spm,[status(thm)],[c_0_14,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
member(ordered_pair(u,u),xr),
prove_well_ordering_is_irreflexive_2 ).
cnf(c_0_46,negated_conjecture,
( ~ member(X1,unordered_pair(u,u))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(u,u))),xr) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_34]),c_0_44]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(u,u))),xr),
inference(rw,[status(thm)],[c_0_45,c_0_38]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_40]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM071-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 02:02:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 277.87/36.78 % Version: 3.5.1
% 277.87/36.78 % Preprocessing class: FSLSSMSMSSSNFFN.
% 277.87/36.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 277.87/36.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 277.87/36.78 % Starting new_bool_3 with 300s (1) cores
% 277.87/36.78 % Starting new_bool_1 with 300s (1) cores
% 277.87/36.78 % Starting sh5l with 300s (1) cores
% 277.87/36.78 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 4114250 completed with status 0
% 277.87/36.78 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 277.87/36.78 % Preprocessing class: FSLSSMSMSSSNFFN.
% 277.87/36.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 277.87/36.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 277.87/36.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 277.87/36.78 % No SInE strategy applied
% 277.87/36.78 % Search class: FGHSM-FFLM31-DFFFFFNN
% 277.87/36.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 277.87/36.78 % Starting SubtermCWHack with 136s (1) cores
% 277.87/36.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 277.87/36.78 % Starting new_bool_3 with 311s (1) cores
% 277.87/36.78 % Starting new_bool_1 with 308s (1) cores
% 277.87/36.78 % Starting sh5l with 304s (1) cores
% 277.87/36.78 % new_bool_3 with pid 4114259 completed with status 0
% 277.87/36.78 % Result found by new_bool_3
% 277.87/36.78 % Preprocessing class: FSLSSMSMSSSNFFN.
% 277.87/36.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 277.87/36.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 277.87/36.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 277.87/36.78 % No SInE strategy applied
% 277.87/36.78 % Search class: FGHSM-FFLM31-DFFFFFNN
% 277.87/36.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 277.87/36.78 % Starting SubtermCWHack with 136s (1) cores
% 277.87/36.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 277.87/36.78 % Starting new_bool_3 with 311s (1) cores
% 277.87/36.78 % Preprocessing time : 0.004 s
% 277.87/36.78 % Presaturation interreduction done
% 277.87/36.78
% 277.87/36.78 % Proof found!
% 277.87/36.78 % SZS status Unsatisfiable
% 277.87/36.78 % SZS output start CNFRefutation
% See solution above
% 277.87/36.78 % Parsed axioms : 161
% 277.87/36.78 % Removed by relevancy pruning/SinE : 0
% 277.87/36.78 % Initial clauses : 161
% 277.87/36.78 % Removed in clause preprocessing : 19
% 277.87/36.78 % Initial clauses in saturation : 142
% 277.87/36.78 % Processed clauses : 16557
% 277.87/36.78 % ...of these trivial : 310
% 277.87/36.78 % ...subsumed : 7375
% 277.87/36.78 % ...remaining for further processing : 8872
% 277.87/36.78 % Other redundant clauses eliminated : 10
% 277.87/36.78 % Clauses deleted for lack of memory : 0
% 277.87/36.78 % Backward-subsumed : 233
% 277.87/36.78 % Backward-rewritten : 140
% 277.87/36.78 % Generated clauses : 1331083
% 277.87/36.78 % ...of the previous two non-redundant : 1315210
% 277.87/36.78 % ...aggressively subsumed : 0
% 277.87/36.78 % Contextual simplify-reflections : 4
% 277.87/36.78 % Paramodulations : 1331067
% 277.87/36.78 % Factorizations : 4
% 277.87/36.78 % NegExts : 0
% 277.87/36.78 % Equation resolutions : 12
% 277.87/36.78 % Disequality decompositions : 0
% 277.87/36.78 % Total rewrite steps : 75486
% 277.87/36.78 % ...of those cached : 72217
% 277.87/36.78 % Propositional unsat checks : 1
% 277.87/36.78 % Propositional check models : 0
% 277.87/36.78 % Propositional check unsatisfiable : 0
% 277.87/36.78 % Propositional clauses : 0
% 277.87/36.78 % Propositional clauses after purity: 0
% 277.87/36.78 % Propositional unsat core size : 0
% 277.87/36.78 % Propositional preprocessing time : 0.000
% 277.87/36.78 % Propositional encoding time : 1.786
% 277.87/36.78 % Propositional solver time : 1.422
% 277.87/36.78 % Success case prop preproc time : 0.000
% 277.87/36.78 % Success case prop encoding time : 0.000
% 277.87/36.78 % Success case prop solver time : 0.000
% 277.87/36.78 % Current number of processed clauses : 8352
% 277.87/36.78 % Positive orientable unit clauses : 2656
% 277.87/36.78 % Positive unorientable unit clauses: 3
% 277.87/36.78 % Negative unit clauses : 2489
% 277.87/36.78 % Non-unit-clauses : 3204
% 277.87/36.78 % Current number of unprocessed clauses: 1298628
% 277.87/36.78 % ...number of literals in the above : 1798629
% 277.87/36.78 % Current number of archived formulas : 0
% 277.87/36.78 % Current number of archived clauses : 533
% 277.87/36.78 % Clause-clause subsumption calls (NU) : 520459
% 277.87/36.78 % Rec. Clause-clause subsumption calls : 404093
% 277.87/36.78 % Non-unit clause-clause subsumptions : 4840
% 277.87/36.78 % Unit Clause-clause subsumption calls : 371285
% 277.87/36.78 % Rewrite failures with RHS unbound : 14
% 277.87/36.78 % BW rewrite match attempts : 299456
% 277.87/36.78 % BW rewrite match successes : 104
% 277.87/36.78 % Condensation attempts : 0
% 277.87/36.78 % Condensation successes : 0
% 277.87/36.78 % Termbank termtop insertions : 34792875
% 277.87/36.78 % Search garbage collected termcells : 285
% 277.87/36.78
% 277.87/36.78 % -------------------------------------------------
% 277.87/36.78 % User time : 33.918 s
% 277.87/36.78 % System time : 1.766 s
% 277.87/36.78 % Total time : 35.684 s
% 277.87/36.78 % Maximum resident set size: 4036 pages
% 277.87/36.78
% 277.87/36.78 % -------------------------------------------------
% 277.87/36.78 % User time : 171.224 s
% 277.87/36.78 % System time : 5.821 s
% 277.87/36.78 % Total time : 177.045 s
% 277.87/36.78 % Maximum resident set size: 4864 pages
% 277.87/36.78 % E exiting
%------------------------------------------------------------------------------