%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM154-1 : 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 : n020.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 01:44:26 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.61s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of clauses : 51 ( 22 unt; 6 nHn; 33 RR)
% Number of literals : 86 ( 16 equ; 35 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 71 ( 15 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(successor,axiom,
union(X1,singleton(X1)) = successor(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',successor) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
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(prove_corollary_5_to_successor_property1_1,negated_conjecture,
successor(x) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_5_to_successor_property1_1) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
cnf(intersection1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(intersection2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(inductive1,axiom,
( ~ inductive(X1)
| member(null_class,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive1) ).
cnf(omega_is_inductive1,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
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(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,axiom,
union(X1,singleton(X1)) = successor(X1),
successor ).
cnf(c_0_22,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_23,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_25,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
cnf(c_0_26,negated_conjecture,
successor(x) = null_class,
prove_corollary_5_to_successor_property1_1 ).
cnf(c_0_27,plain,
union(X1,unordered_pair(X1,X1)) = successor(X1),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_29,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
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(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_25 ).
cnf(c_0_32,negated_conjecture,
complement(intersection(complement(x),complement(unordered_pair(x,x)))) = null_class,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_33,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_29]),c_0_20]) ).
cnf(c_0_34,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
c_0_30 ).
cnf(c_0_35,negated_conjecture,
( ~ member(X1,universal_class)
| member(X1,intersection(complement(x),complement(unordered_pair(x,x)))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( ~ member(X1,universal_class)
| member(X1,complement(x)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
cnf(c_0_38,negated_conjecture,
~ member(X1,x),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_36]),c_0_20]) ).
cnf(c_0_39,plain,
( ~ inductive(X1)
| member(null_class,X1) ),
inference(fof_simplification,[status(thm)],[inductive1]) ).
cnf(c_0_40,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_37 ).
cnf(c_0_41,negated_conjecture,
x = null_class,
inference(spm,[status(thm)],[c_0_38,c_0_19]) ).
cnf(c_0_42,plain,
( ~ inductive(X1)
| member(null_class,X1) ),
c_0_39 ).
cnf(c_0_43,axiom,
inductive(omega),
omega_is_inductive1 ).
cnf(c_0_44,negated_conjecture,
( ~ member(X1,universal_class)
| member(X1,complement(unordered_pair(null_class,null_class))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_35]),c_0_41]),c_0_41]) ).
cnf(c_0_45,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[unordered_pair2]) ).
cnf(c_0_46,plain,
member(null_class,omega),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
~ member(X1,unordered_pair(null_class,null_class)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_44]),c_0_20]) ).
cnf(c_0_48,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
c_0_45 ).
cnf(c_0_49,plain,
member(null_class,universal_class),
inference(spm,[status(thm)],[c_0_20,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM154-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n020.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 02:10:04 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 0.23/0.61 % Version: 3.5.1
% 0.23/0.61 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.23/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.61 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.23/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.61 % Starting sh5l with 300s (1) cores
% 0.23/0.61 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1771014 completed with status 0
% 0.23/0.61 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.23/0.61 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.23/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.61 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.23/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.61 % No SInE strategy applied
% 0.23/0.61 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.23/0.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.61 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.23/0.61 % Starting new_bool_3 with 311s (1) cores
% 0.23/0.61 % Starting new_bool_1 with 308s (1) cores
% 0.23/0.61 % Starting sh5l with 304s (1) cores
% 0.23/0.61 % sh5l with pid 1771025 completed with status 0
% 0.23/0.61 % Result found by sh5l
% 0.23/0.61 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.23/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.61 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.23/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.61 % No SInE strategy applied
% 0.23/0.61 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.23/0.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.61 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.23/0.61 % Starting new_bool_3 with 311s (1) cores
% 0.23/0.61 % Starting new_bool_1 with 308s (1) cores
% 0.23/0.61 % Starting sh5l with 304s (1) cores
% 0.23/0.61 % Preprocessing time : 0.006 s
% 0.23/0.61 % Presaturation interreduction done
% 0.23/0.61
% 0.23/0.61 % Proof found!
% 0.23/0.61 % SZS status Unsatisfiable
% 0.23/0.61 % SZS output start CNFRefutation
% See solution above
% 0.23/0.61 % Parsed axioms : 159
% 0.23/0.61 % Removed by relevancy pruning/SinE : 0
% 0.23/0.61 % Initial clauses : 159
% 0.23/0.61 % Removed in clause preprocessing : 19
% 0.23/0.61 % Initial clauses in saturation : 140
% 0.23/0.61 % Processed clauses : 302
% 0.23/0.61 % ...of these trivial : 0
% 0.23/0.61 % ...subsumed : 26
% 0.23/0.61 % ...remaining for further processing : 276
% 0.23/0.61 % Other redundant clauses eliminated : 6
% 0.23/0.61 % Clauses deleted for lack of memory : 0
% 0.23/0.61 % Backward-subsumed : 7
% 0.23/0.61 % Backward-rewritten : 7
% 0.23/0.61 % Generated clauses : 237
% 0.23/0.61 % ...of the previous two non-redundant : 195
% 0.23/0.61 % ...aggressively subsumed : 0
% 0.23/0.61 % Contextual simplify-reflections : 7
% 0.23/0.61 % Paramodulations : 231
% 0.23/0.61 % Factorizations : 0
% 0.23/0.61 % NegExts : 0
% 0.23/0.61 % Equation resolutions : 6
% 0.23/0.61 % Disequality decompositions : 0
% 0.23/0.61 % Total rewrite steps : 52
% 0.23/0.61 % ...of those cached : 37
% 0.23/0.61 % Propositional unsat checks : 0
% 0.23/0.61 % Propositional check models : 0
% 0.23/0.61 % Propositional check unsatisfiable : 0
% 0.23/0.61 % Propositional clauses : 0
% 0.23/0.61 % Propositional clauses after purity: 0
% 0.23/0.61 % Propositional unsat core size : 0
% 0.23/0.61 % Propositional preprocessing time : 0.000
% 0.23/0.61 % Propositional encoding time : 0.000
% 0.23/0.61 % Propositional solver time : 0.000
% 0.23/0.61 % Success case prop preproc time : 0.000
% 0.23/0.61 % Success case prop encoding time : 0.000
% 0.23/0.61 % Success case prop solver time : 0.000
% 0.23/0.61 % Current number of processed clauses : 117
% 0.23/0.61 % Positive orientable unit clauses : 38
% 0.23/0.61 % Positive unorientable unit clauses: 0
% 0.23/0.61 % Negative unit clauses : 2
% 0.23/0.61 % Non-unit-clauses : 77
% 0.23/0.61 % Current number of unprocessed clauses: 162
% 0.23/0.61 % ...number of literals in the above : 402
% 0.23/0.61 % Current number of archived formulas : 0
% 0.23/0.61 % Current number of archived clauses : 172
% 0.23/0.61 % Clause-clause subsumption calls (NU) : 2449
% 0.23/0.61 % Rec. Clause-clause subsumption calls : 1601
% 0.23/0.61 % Non-unit clause-clause subsumptions : 21
% 0.23/0.61 % Unit Clause-clause subsumption calls : 85
% 0.23/0.61 % Rewrite failures with RHS unbound : 0
% 0.23/0.61 % BW rewrite match attempts : 13
% 0.23/0.61 % BW rewrite match successes : 4
% 0.23/0.61 % Condensation attempts : 302
% 0.23/0.61 % Condensation successes : 1
% 0.23/0.61 % Termbank termtop insertions : 13543
% 0.23/0.61 % Search garbage collected termcells : 285
% 0.23/0.61
% 0.23/0.61 % -------------------------------------------------
% 0.23/0.61 % User time : 0.046 s
% 0.23/0.61 % System time : 0.011 s
% 0.23/0.61 % Total time : 0.057 s
% 0.23/0.61 % Maximum resident set size: 4036 pages
% 0.23/0.61
% 0.23/0.61 % -------------------------------------------------
% 0.23/0.61 % User time : 0.225 s
% 0.23/0.61 % System time : 0.034 s
% 0.23/0.61 % Total time : 0.259 s
% 0.23/0.61 % Maximum resident set size: 4864 pages
% 0.23/0.61 % E exiting
%------------------------------------------------------------------------------