%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET129-6 : 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 : n018.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 02:13:41 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of clauses : 59 ( 27 unt; 12 nHn; 44 RR)
% Number of literals : 115 ( 27 equ; 62 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 59 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(definition_of_set_builder,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_set_builder) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(complement1,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(prove_members_of_built_triple_1,negated_conjecture,
member(u,set_builder(x,set_builder(y,set_builder(z,null_class)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_members_of_built_triple_1) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
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(intersection3,axiom,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
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(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(prove_members_of_built_triple_4,negated_conjecture,
u != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_members_of_built_triple_4) ).
cnf(prove_members_of_built_triple_3,negated_conjecture,
u != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_members_of_built_triple_3) ).
cnf(prove_members_of_built_triple_2,negated_conjecture,
u != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_members_of_built_triple_2) ).
cnf(c_0_14,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
definition_of_set_builder ).
cnf(c_0_15,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_17,negated_conjecture,
member(u,set_builder(x,set_builder(y,set_builder(z,null_class)))),
prove_members_of_built_triple_1 ).
cnf(c_0_18,plain,
union(unordered_pair(X1,X1),X2) = set_builder(X1,X2),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_20,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_21,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_16 ).
cnf(c_0_22,negated_conjecture,
member(u,complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]),c_0_18]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_23,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_24,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_20 ).
cnf(c_0_25,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_26,negated_conjecture,
~ member(u,intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_23 ).
cnf(c_0_28,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
cnf(c_0_29,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( ~ member(u,complement(unordered_pair(x,x)))
| ~ member(u,complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_28 ).
cnf(c_0_32,negated_conjecture,
member(u,universal_class),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_33,negated_conjecture,
( ~ member(u,complement(unordered_pair(x,x)))
| member(u,complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_34,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_35,negated_conjecture,
( ~ member(u,complement(unordered_pair(x,x)))
| ~ member(u,intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))) ),
inference(spm,[status(thm)],[c_0_21,c_0_33]) ).
cnf(c_0_36,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_37,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( ~ member(u,complement(unordered_pair(y,y)))
| ~ member(u,complement(unordered_pair(x,x)))
| ~ member(u,complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))) ),
inference(spm,[status(thm)],[c_0_35,c_0_27]) ).
cnf(c_0_39,plain,
null_class = complement(universal_class),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( ~ member(u,complement(unordered_pair(y,y)))
| ~ member(u,complement(unordered_pair(x,x)))
| member(u,complement(intersection(complement(unordered_pair(z,z)),complement(complement(universal_class))))) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_31]),c_0_32])]),c_0_39]) ).
cnf(c_0_41,negated_conjecture,
( ~ member(u,complement(unordered_pair(y,y)))
| ~ member(u,complement(unordered_pair(x,x)))
| ~ member(u,intersection(complement(unordered_pair(z,z)),complement(complement(universal_class)))) ),
inference(spm,[status(thm)],[c_0_21,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
( ~ member(u,complement(complement(universal_class)))
| ~ member(u,complement(unordered_pair(z,z)))
| ~ member(u,complement(unordered_pair(y,y)))
| ~ member(u,complement(unordered_pair(x,x))) ),
inference(spm,[status(thm)],[c_0_41,c_0_27]) ).
cnf(c_0_43,negated_conjecture,
( ~ member(u,complement(complement(universal_class)))
| ~ member(u,complement(unordered_pair(y,y)))
| ~ member(u,complement(unordered_pair(x,x)))
| member(u,unordered_pair(z,z)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_31]),c_0_32])]) ).
cnf(c_0_44,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_45,negated_conjecture,
( ~ member(u,complement(complement(universal_class)))
| ~ member(u,complement(unordered_pair(x,x)))
| member(u,unordered_pair(z,z))
| member(u,unordered_pair(y,y)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_31]),c_0_32])]) ).
cnf(c_0_46,negated_conjecture,
u != z,
inference(fof_simplification,[status(thm)],[prove_members_of_built_triple_4]) ).
cnf(c_0_47,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_44 ).
cnf(c_0_48,negated_conjecture,
( ~ member(u,complement(complement(universal_class)))
| member(u,unordered_pair(y,y))
| member(u,unordered_pair(z,z))
| member(u,unordered_pair(x,x)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_31]),c_0_32])]) ).
cnf(c_0_49,negated_conjecture,
u != z,
c_0_46 ).
cnf(c_0_50,negated_conjecture,
u != y,
inference(fof_simplification,[status(thm)],[prove_members_of_built_triple_3]) ).
cnf(c_0_51,negated_conjecture,
( ~ member(u,complement(complement(universal_class)))
| member(u,unordered_pair(x,x))
| member(u,unordered_pair(y,y)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_52,negated_conjecture,
u != y,
c_0_50 ).
cnf(c_0_53,negated_conjecture,
u != x,
inference(fof_simplification,[status(thm)],[prove_members_of_built_triple_2]) ).
cnf(c_0_54,negated_conjecture,
( ~ member(u,complement(complement(universal_class)))
| member(u,unordered_pair(x,x)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_51]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
u != x,
c_0_53 ).
cnf(c_0_56,negated_conjecture,
~ member(u,complement(complement(universal_class))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_54]),c_0_55]) ).
cnf(c_0_57,negated_conjecture,
member(u,complement(universal_class)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_31]),c_0_32])]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_57]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET129-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n018.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 04:57:44 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.45 % Version: 3.5.1
% 0.11/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % Starting sh5l with 300s (1) cores
% 0.11/0.45 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1010057 completed with status 0
% 0.11/0.45 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.11/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.11/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.45 % No SInE strategy applied
% 0.11/0.45 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.11/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.11/0.45 % Starting new_bool_3 with 311s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 308s (1) cores
% 0.11/0.45 % Starting sh5l with 304s (1) cores
% 0.11/0.45 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1010065 completed with status 0
% 0.11/0.45 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.11/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.11/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.45 % No SInE strategy applied
% 0.11/0.45 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.11/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.11/0.45 % Preprocessing time : 0.003 s
% 0.11/0.45 % Presaturation interreduction done
% 0.11/0.45
% 0.11/0.45 % Proof found!
% 0.11/0.45 % SZS status Unsatisfiable
% 0.11/0.45 % SZS output start CNFRefutation
% See solution above
% 0.11/0.45 % Parsed axioms : 96
% 0.11/0.45 % Removed by relevancy pruning/SinE : 0
% 0.11/0.45 % Initial clauses : 96
% 0.11/0.45 % Removed in clause preprocessing : 16
% 0.11/0.45 % Initial clauses in saturation : 80
% 0.11/0.45 % Processed clauses : 180
% 0.11/0.45 % ...of these trivial : 0
% 0.11/0.45 % ...subsumed : 2
% 0.11/0.45 % ...remaining for further processing : 178
% 0.11/0.45 % Other redundant clauses eliminated : 3
% 0.11/0.45 % Clauses deleted for lack of memory : 0
% 0.11/0.45 % Backward-subsumed : 6
% 0.11/0.45 % Backward-rewritten : 16
% 0.11/0.45 % Generated clauses : 151
% 0.11/0.45 % ...of the previous two non-redundant : 140
% 0.11/0.45 % ...aggressively subsumed : 0
% 0.11/0.45 % Contextual simplify-reflections : 0
% 0.11/0.45 % Paramodulations : 148
% 0.11/0.45 % Factorizations : 0
% 0.11/0.45 % NegExts : 0
% 0.11/0.45 % Equation resolutions : 3
% 0.11/0.45 % Disequality decompositions : 0
% 0.11/0.45 % Total rewrite steps : 44
% 0.11/0.45 % ...of those cached : 37
% 0.11/0.45 % Propositional unsat checks : 0
% 0.11/0.45 % Propositional check models : 0
% 0.11/0.45 % Propositional check unsatisfiable : 0
% 0.11/0.45 % Propositional clauses : 0
% 0.11/0.45 % Propositional clauses after purity: 0
% 0.11/0.45 % Propositional unsat core size : 0
% 0.11/0.45 % Propositional preprocessing time : 0.000
% 0.11/0.45 % Propositional encoding time : 0.000
% 0.11/0.45 % Propositional solver time : 0.000
% 0.11/0.45 % Success case prop preproc time : 0.000
% 0.11/0.45 % Success case prop encoding time : 0.000
% 0.11/0.45 % Success case prop solver time : 0.000
% 0.11/0.45 % Current number of processed clauses : 74
% 0.11/0.45 % Positive orientable unit clauses : 19
% 0.11/0.45 % Positive unorientable unit clauses: 1
% 0.11/0.45 % Negative unit clauses : 5
% 0.11/0.45 % Non-unit-clauses : 49
% 0.11/0.45 % Current number of unprocessed clauses: 118
% 0.11/0.45 % ...number of literals in the above : 303
% 0.11/0.45 % Current number of archived formulas : 0
% 0.11/0.45 % Current number of archived clauses : 117
% 0.11/0.45 % Clause-clause subsumption calls (NU) : 1547
% 0.11/0.45 % Rec. Clause-clause subsumption calls : 970
% 0.11/0.45 % Non-unit clause-clause subsumptions : 4
% 0.11/0.45 % Unit Clause-clause subsumption calls : 20
% 0.11/0.45 % Rewrite failures with RHS unbound : 0
% 0.11/0.45 % BW rewrite match attempts : 6
% 0.11/0.45 % BW rewrite match successes : 4
% 0.11/0.45 % Condensation attempts : 0
% 0.11/0.45 % Condensation successes : 0
% 0.11/0.45 % Termbank termtop insertions : 8436
% 0.11/0.45 % Search garbage collected termcells : 160
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.019 s
% 0.11/0.45 % System time : 0.007 s
% 0.11/0.45 % Total time : 0.026 s
% 0.11/0.45 % Maximum resident set size: 3720 pages
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.089 s
% 0.11/0.45 % System time : 0.028 s
% 0.11/0.45 % Total time : 0.117 s
% 0.11/0.45 % Maximum resident set size: 4864 pages
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------