%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET505-6 : 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 : n012.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 02:14:17 PM UTC 2026
% Result : Unsatisfiable 0.69s 0.52s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 46 ( 15 unt; 10 nHn; 29 RR)
% Number of literals : 89 ( 29 equ; 36 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
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(complement1,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(regularity1,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
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(intersection3,axiom,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(regularity2,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(cartesian_product1,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
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(unordered_pair2,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(prove_corollary_2_to_universal_class_not_set_1,negated_conjecture,
member(ordered_pair(universal_class,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_universal_class_not_set_1) ).
cnf(c_0_12,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_13,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_14,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_12 ).
cnf(c_0_15,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_13 ).
cnf(c_0_17,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_18,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_21,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_22,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_23,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_21 ).
cnf(c_0_25,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_22 ).
cnf(c_0_26,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
regularity2 ).
cnf(c_0_27,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_23]),c_0_18]) ).
cnf(c_0_28,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_24,c_0_17]) ).
cnf(c_0_29,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[cartesian_product1]) ).
cnf(c_0_30,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_31,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_32,plain,
( ~ member(X2,X1)
| ~ member(X2,regular(X1))
| X1 = null_class ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_33,plain,
( unordered_pair(X1,X1) = null_class
| regular(unordered_pair(X1,X1)) = X1 ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_28])]) ).
cnf(c_0_34,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[unordered_pair2]) ).
cnf(c_0_35,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
c_0_29 ).
cnf(c_0_36,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_30,c_0_31]),c_0_31]) ).
cnf(c_0_37,negated_conjecture,
member(ordered_pair(universal_class,y),cross_product(universal_class,universal_class)),
prove_corollary_2_to_universal_class_not_set_1 ).
cnf(c_0_38,plain,
( ~ member(X2,X1)
| ~ member(X2,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
c_0_34 ).
cnf(c_0_40,plain,
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4))
| member(X1,X3) ),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
member(unordered_pair(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,unordered_pair(y,y))),cross_product(universal_class,universal_class)),
inference(rw,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_42,plain,
( ~ member(X1,X1)
| unordered_pair(X1,X1) = null_class ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_18]) ).
cnf(c_0_43,negated_conjecture,
member(universal_class,universal_class),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
unordered_pair(universal_class,universal_class) = null_class,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_44]),c_0_43])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET505-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:22:25 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.69/0.52 % Version: 3.5.1
% 0.69/0.52 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.69/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.69/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.69/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.69/0.52 % Starting sh5l with 300s (1) cores
% 0.69/0.52 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1631443 completed with status 0
% 0.69/0.52 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.69/0.52 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.69/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.69/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.69/0.52 % No SInE strategy applied
% 0.69/0.52 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.69/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.69/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.69/0.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.69/0.52 % Starting new_bool_3 with 311s (1) cores
% 0.69/0.52 % Starting new_bool_1 with 308s (1) cores
% 0.69/0.52 % Starting sh5l with 304s (1) cores
% 0.69/0.52 % sh5l with pid 1631454 completed with status 0
% 0.69/0.52 % Result found by sh5l
% 0.69/0.52 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.69/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.69/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.69/0.52 % No SInE strategy applied
% 0.69/0.52 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.69/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.69/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.69/0.52 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.69/0.52 % Starting new_bool_3 with 311s (1) cores
% 0.69/0.52 % Starting new_bool_1 with 308s (1) cores
% 0.69/0.52 % Starting sh5l with 304s (1) cores
% 0.69/0.52 % Preprocessing time : 0.002 s
% 0.69/0.52 % Presaturation interreduction done
% 0.69/0.52
% 0.69/0.52 % Proof found!
% 0.69/0.52 % SZS status Unsatisfiable
% 0.69/0.52 % SZS output start CNFRefutation
% See solution above
% 0.69/0.52 % Parsed axioms : 113
% 0.69/0.52 % Removed by relevancy pruning/SinE : 0
% 0.69/0.52 % Initial clauses : 113
% 0.69/0.52 % Removed in clause preprocessing : 17
% 0.69/0.52 % Initial clauses in saturation : 96
% 0.69/0.52 % Processed clauses : 1254
% 0.69/0.52 % ...of these trivial : 1
% 0.69/0.52 % ...subsumed : 666
% 0.69/0.52 % ...remaining for further processing : 587
% 0.69/0.52 % Other redundant clauses eliminated : 8
% 0.69/0.52 % Clauses deleted for lack of memory : 0
% 0.69/0.52 % Backward-subsumed : 30
% 0.69/0.52 % Backward-rewritten : 36
% 0.69/0.52 % Generated clauses : 3405
% 0.69/0.52 % ...of the previous two non-redundant : 2856
% 0.69/0.52 % ...aggressively subsumed : 0
% 0.69/0.52 % Contextual simplify-reflections : 14
% 0.69/0.52 % Paramodulations : 3393
% 0.69/0.52 % Factorizations : 4
% 0.69/0.52 % NegExts : 0
% 0.69/0.52 % Equation resolutions : 8
% 0.69/0.52 % Disequality decompositions : 0
% 0.69/0.52 % Total rewrite steps : 1088
% 0.69/0.52 % ...of those cached : 949
% 0.69/0.52 % Propositional unsat checks : 0
% 0.69/0.52 % Propositional check models : 0
% 0.69/0.52 % Propositional check unsatisfiable : 0
% 0.69/0.52 % Propositional clauses : 0
% 0.69/0.52 % Propositional clauses after purity: 0
% 0.69/0.52 % Propositional unsat core size : 0
% 0.69/0.52 % Propositional preprocessing time : 0.000
% 0.69/0.52 % Propositional encoding time : 0.000
% 0.69/0.52 % Propositional solver time : 0.000
% 0.69/0.52 % Success case prop preproc time : 0.000
% 0.69/0.52 % Success case prop encoding time : 0.000
% 0.69/0.52 % Success case prop solver time : 0.000
% 0.69/0.52 % Current number of processed clauses : 422
% 0.69/0.52 % Positive orientable unit clauses : 69
% 0.69/0.52 % Positive unorientable unit clauses: 1
% 0.69/0.52 % Negative unit clauses : 2
% 0.69/0.52 % Non-unit-clauses : 350
% 0.69/0.52 % Current number of unprocessed clauses: 1739
% 0.69/0.52 % ...number of literals in the above : 5204
% 0.69/0.52 % Current number of archived formulas : 0
% 0.69/0.52 % Current number of archived clauses : 178
% 0.69/0.52 % Clause-clause subsumption calls (NU) : 20350
% 0.69/0.52 % Rec. Clause-clause subsumption calls : 13927
% 0.69/0.52 % Non-unit clause-clause subsumptions : 557
% 0.69/0.52 % Unit Clause-clause subsumption calls : 1158
% 0.69/0.52 % Rewrite failures with RHS unbound : 0
% 0.69/0.52 % BW rewrite match attempts : 53
% 0.69/0.52 % BW rewrite match successes : 24
% 0.69/0.52 % Condensation attempts : 1254
% 0.69/0.52 % Condensation successes : 39
% 0.69/0.52 % Termbank termtop insertions : 74969
% 0.69/0.52 % Search garbage collected termcells : 183
% 0.69/0.52
% 0.69/0.52 % -------------------------------------------------
% 0.69/0.52 % User time : 0.094 s
% 0.69/0.52 % System time : 0.012 s
% 0.69/0.52 % Total time : 0.106 s
% 0.69/0.52 % Maximum resident set size: 3992 pages
% 0.69/0.52
% 0.69/0.52 % -------------------------------------------------
% 0.69/0.52 % User time : 0.485 s
% 0.69/0.52 % System time : 0.038 s
% 0.69/0.52 % Total time : 0.523 s
% 0.69/0.52 % Maximum resident set size: 4608 pages
% 0.69/0.52 % E exiting
%------------------------------------------------------------------------------