%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM095-1 : 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 : n016.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 01:44:21 PM UTC 2026
% Result : Unsatisfiable 5.44s 1.27s
% Output : CNFRefutation 5.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of clauses : 62 ( 19 unt; 14 nHn; 50 RR)
% Number of literals : 125 ( 17 equ; 61 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 102 ( 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(well_ordering2,axiom,
( ~ subclass(X3,X2)
| ~ well_ordering(X1,X2)
| member(least(X1,X3),X3)
| X3 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',well_ordering2) ).
cnf(intersection2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(intersection1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(prove_sections_property4_1,negated_conjecture,
well_ordering(xr,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sections_property4_1) ).
cnf(not_subclass_members2,axiom,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(not_subclass_members1,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(regularity1,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(prove_sections_property4_3,negated_conjecture,
~ member(least(xr,intersection(complement(w),y)),complement(w)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sections_property4_3) ).
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(complement2,axiom,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(section1,axiom,
( ~ section(X1,X2,X3)
| subclass(X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',section1) ).
cnf(subclass_implies_equal,axiom,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(prove_sections_property4_2,negated_conjecture,
section(xr,w,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sections_property4_2) ).
cnf(prove_sections_property4_4,negated_conjecture,
y != w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sections_property4_4) ).
cnf(c_0_17,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_18,plain,
( ~ subclass(X3,X2)
| ~ well_ordering(X1,X2)
| member(least(X1,X3),X3)
| X3 = null_class ),
inference(fof_simplification,[status(thm)],[well_ordering2]) ).
cnf(c_0_19,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_21,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_17 ).
cnf(c_0_22,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_23,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(fof_simplification,[status(thm)],[intersection1]) ).
cnf(c_0_24,plain,
( ~ subclass(X3,X2)
| ~ well_ordering(X1,X2)
| member(least(X1,X3),X3)
| X3 = null_class ),
c_0_18 ).
cnf(c_0_25,negated_conjecture,
well_ordering(xr,y),
prove_sections_property4_1 ).
cnf(c_0_26,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).
cnf(c_0_27,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_19 ).
cnf(c_0_28,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
not_subclass_members1 ).
cnf(c_0_29,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_20 ).
cnf(c_0_30,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_31,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_32,negated_conjecture,
~ member(least(xr,intersection(complement(w),y)),complement(w)),
inference(fof_simplification,[status(thm)],[prove_sections_property4_3]) ).
cnf(c_0_33,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
c_0_23 ).
cnf(c_0_34,negated_conjecture,
( ~ subclass(X1,y)
| member(least(xr,X1),X1)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_35,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
c_0_26 ).
cnf(c_0_36,plain,
( subclass(intersection(X1,X2),X3)
| member(not_subclass_element(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_39,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_40,negated_conjecture,
~ member(least(xr,intersection(complement(w),y)),complement(w)),
c_0_32 ).
cnf(c_0_41,negated_conjecture,
( ~ subclass(intersection(X1,X2),y)
| member(least(xr,intersection(X1,X2)),X1)
| intersection(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,plain,
subclass(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_39 ).
cnf(c_0_45,negated_conjecture,
intersection(complement(w),y) = null_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_46,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_43]),c_0_31]) ).
cnf(c_0_47,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
cnf(c_0_48,plain,
( ~ section(X1,X2,X3)
| subclass(X2,X3) ),
inference(fof_simplification,[status(thm)],[section1]) ).
cnf(c_0_49,negated_conjecture,
( ~ member(X1,y)
| ~ member(X1,complement(w)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_50,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_47 ).
cnf(c_0_51,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[subclass_implies_equal]) ).
cnf(c_0_52,plain,
( ~ section(X1,X2,X3)
| subclass(X2,X3) ),
c_0_48 ).
cnf(c_0_53,negated_conjecture,
section(xr,w,y),
prove_sections_property4_2 ).
cnf(c_0_54,negated_conjecture,
y != w,
inference(fof_simplification,[status(thm)],[prove_sections_property4_4]) ).
cnf(c_0_55,negated_conjecture,
( ~ member(X1,y)
| member(X1,w) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_31]) ).
cnf(c_0_56,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
c_0_51 ).
cnf(c_0_57,negated_conjecture,
subclass(w,y),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,negated_conjecture,
y != w,
c_0_54 ).
cnf(c_0_59,negated_conjecture,
( ~ member(not_subclass_element(X1,w),y)
| subclass(X1,w) ),
inference(spm,[status(thm)],[c_0_35,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
~ subclass(y,w),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_28]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM095-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n016.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 02:09:07 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 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
% 5.44/1.27 % Version: 3.5.1
% 5.44/1.27 % Preprocessing class: FSLSSMSMSSSNFFN.
% 5.44/1.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.44/1.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 5.44/1.27 % Starting new_bool_3 with 300s (1) cores
% 5.44/1.27 % Starting new_bool_1 with 300s (1) cores
% 5.44/1.27 % Starting sh5l with 300s (1) cores
% 5.44/1.27 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1338565 completed with status 0
% 5.44/1.27 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 5.44/1.27 % Preprocessing class: FSLSSMSMSSSNFFN.
% 5.44/1.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.44/1.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 5.44/1.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.44/1.27 % No SInE strategy applied
% 5.44/1.27 % Search class: FGHSM-FFLM31-DFFFFFNN
% 5.44/1.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.44/1.27 % Starting SubtermCWHack with 136s (1) cores
% 5.44/1.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 5.44/1.27 % Starting new_bool_3 with 311s (1) cores
% 5.44/1.27 % Starting new_bool_1 with 308s (1) cores
% 5.44/1.27 % Starting sh5l with 304s (1) cores
% 5.44/1.27 % SubtermCWHack with pid 1338572 completed with status 0
% 5.44/1.27 % Result found by SubtermCWHack
% 5.44/1.27 % Preprocessing class: FSLSSMSMSSSNFFN.
% 5.44/1.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.44/1.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 5.44/1.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.44/1.27 % No SInE strategy applied
% 5.44/1.27 % Search class: FGHSM-FFLM31-DFFFFFNN
% 5.44/1.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.44/1.27 % Starting SubtermCWHack with 136s (1) cores
% 5.44/1.27 % Preprocessing time : 0.005 s
% 5.44/1.27
% 5.44/1.27 % Proof found!
% 5.44/1.27 % SZS status Unsatisfiable
% 5.44/1.27 % SZS output start CNFRefutation
% See solution above
% 5.44/1.27 % Parsed axioms : 162
% 5.44/1.27 % Removed by relevancy pruning/SinE : 0
% 5.44/1.27 % Initial clauses : 162
% 5.44/1.27 % Removed in clause preprocessing : 19
% 5.44/1.27 % Initial clauses in saturation : 143
% 5.44/1.27 % Processed clauses : 4295
% 5.44/1.27 % ...of these trivial : 3
% 5.44/1.27 % ...subsumed : 3024
% 5.44/1.27 % ...remaining for further processing : 1268
% 5.44/1.27 % Other redundant clauses eliminated : 14
% 5.44/1.27 % Clauses deleted for lack of memory : 0
% 5.44/1.27 % Backward-subsumed : 102
% 5.44/1.27 % Backward-rewritten : 30
% 5.44/1.27 % Generated clauses : 21953
% 5.44/1.27 % ...of the previous two non-redundant : 18965
% 5.44/1.27 % ...aggressively subsumed : 0
% 5.44/1.27 % Contextual simplify-reflections : 18
% 5.44/1.27 % Paramodulations : 21931
% 5.44/1.27 % Factorizations : 8
% 5.44/1.27 % NegExts : 0
% 5.44/1.27 % Equation resolutions : 14
% 5.44/1.27 % Disequality decompositions : 0
% 5.44/1.27 % Total rewrite steps : 6175
% 5.44/1.27 % ...of those cached : 5684
% 5.44/1.27 % Propositional unsat checks : 0
% 5.44/1.27 % Propositional check models : 0
% 5.44/1.27 % Propositional check unsatisfiable : 0
% 5.44/1.27 % Propositional clauses : 0
% 5.44/1.27 % Propositional clauses after purity: 0
% 5.44/1.27 % Propositional unsat core size : 0
% 5.44/1.27 % Propositional preprocessing time : 0.000
% 5.44/1.27 % Propositional encoding time : 0.000
% 5.44/1.27 % Propositional solver time : 0.000
% 5.44/1.27 % Success case prop preproc time : 0.000
% 5.44/1.27 % Success case prop encoding time : 0.000
% 5.44/1.27 % Success case prop solver time : 0.000
% 5.44/1.27 % Current number of processed clauses : 1130
% 5.44/1.27 % Positive orientable unit clauses : 146
% 5.44/1.27 % Positive unorientable unit clauses: 3
% 5.44/1.27 % Negative unit clauses : 13
% 5.44/1.27 % Non-unit-clauses : 968
% 5.44/1.27 % Current number of unprocessed clauses: 14684
% 5.44/1.27 % ...number of literals in the above : 48595
% 5.44/1.27 % Current number of archived formulas : 0
% 5.44/1.27 % Current number of archived clauses : 151
% 5.44/1.27 % Clause-clause subsumption calls (NU) : 65413
% 5.44/1.27 % Rec. Clause-clause subsumption calls : 46163
% 5.44/1.27 % Non-unit clause-clause subsumptions : 2014
% 5.44/1.27 % Unit Clause-clause subsumption calls : 3721
% 5.44/1.27 % Rewrite failures with RHS unbound : 14
% 5.44/1.27 % BW rewrite match attempts : 81
% 5.44/1.27 % BW rewrite match successes : 13
% 5.44/1.27 % Condensation attempts : 0
% 5.44/1.27 % Condensation successes : 0
% 5.44/1.27 % Termbank termtop insertions : 379157
% 5.44/1.27 % Search garbage collected termcells : 289
% 5.44/1.27
% 5.44/1.27 % -------------------------------------------------
% 5.44/1.27 % User time : 0.682 s
% 5.44/1.27 % System time : 0.033 s
% 5.44/1.27 % Total time : 0.715 s
% 5.44/1.27 % Maximum resident set size: 4036 pages
% 5.44/1.27
% 5.44/1.27 % -------------------------------------------------
% 5.44/1.27 % User time : 3.438 s
% 5.44/1.27 % System time : 0.125 s
% 5.44/1.27 % Total time : 3.563 s
% 5.44/1.27 % Maximum resident set size: 4864 pages
% 5.44/1.27 % E exiting
%------------------------------------------------------------------------------