%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM030-1 : 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 : n019.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 01:44:17 PM UTC 2026
% Result : Unsatisfiable 22.85s 13.40s
% Output : CNFRefutation 23.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 50 ( 21 unt; 9 nHn; 29 RR)
% Number of literals : 88 ( 15 equ; 36 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 79 ( 7 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(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
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(complement2,axiom,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
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(complement1,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
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(intersection2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(prove_symmetrization_property3_1,negated_conjecture,
symmetrization_of(x) = x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetrization_property3_1) ).
cnf(symmetrization,axiom,
union(X1,inverse(X1)) = symmetrization_of(X1),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',symmetrization) ).
cnf(inverse,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inverse) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
cnf(prove_symmetrization_property3_2,negated_conjecture,
~ subclass(inverse(x),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetrization_property3_2) ).
cnf(c_0_13,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_14,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_13 ).
cnf(c_0_15,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
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,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
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,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
not_subclass_members1 ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_21,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
c_0_16 ).
cnf(c_0_22,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_17 ).
cnf(c_0_23,plain,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),universal_class) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_20 ).
cnf(c_0_25,plain,
( subclass(X1,complement(X2))
| member(not_subclass_element(X1,complement(X2)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_26,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[subclass_implies_equal]) ).
cnf(c_0_27,plain,
( ~ member(not_subclass_element(X1,complement(complement(X2))),X2)
| subclass(X1,complement(complement(X2))) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( ~ member(not_subclass_element(complement(X1),X2),X1)
| subclass(complement(X1),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
cnf(c_0_29,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
c_0_26 ).
cnf(c_0_30,plain,
subclass(X1,complement(complement(X1))),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_31,plain,
( subclass(complement(complement(X1)),X2)
| member(not_subclass_element(complement(complement(X1)),X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_22]),c_0_23]) ).
cnf(c_0_32,plain,
( ~ subclass(complement(complement(X1)),X1)
| complement(complement(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
subclass(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_34,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
cnf(c_0_35,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
cnf(c_0_36,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_34 ).
cnf(c_0_37,negated_conjecture,
symmetrization_of(x) = x,
prove_symmetrization_property3_1 ).
cnf(c_0_38,axiom,
union(X1,inverse(X1)) = symmetrization_of(X1),
symmetrization ).
cnf(c_0_39,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inverse ).
cnf(c_0_40,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_41,negated_conjecture,
~ subclass(inverse(x),x),
inference(fof_simplification,[status(thm)],[prove_symmetrization_property3_2]) ).
cnf(c_0_42,plain,
( ~ member(not_subclass_element(X1,X2),complement(X1))
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_35]) ).
cnf(c_0_43,plain,
( subclass(X1,complement(intersection(X2,X3)))
| member(not_subclass_element(X1,complement(intersection(X2,X3))),X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_44,negated_conjecture,
complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))) = x,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]) ).
cnf(c_0_45,negated_conjecture,
~ subclass(inverse(x),x),
c_0_41 ).
cnf(c_0_46,plain,
subclass(X1,complement(intersection(X2,complement(X1)))),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))) = complement(x),
inference(spm,[status(thm)],[c_0_35,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
~ subclass(domain_of(flip(cross_product(x,universal_class))),x),
inference(rw,[status(thm)],[c_0_45,c_0_39]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_35]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM030-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/10.38 % Computer : n019.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Mon Sep 21 01:59:46 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/10.43 Running first-order theorem proving
% 0.15/10.43 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
% 22.85/13.40 % Version: 3.5.1
% 22.85/13.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 22.85/13.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 22.85/13.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 22.85/13.40 % Starting new_bool_3 with 300s (1) cores
% 22.85/13.40 % Starting new_bool_1 with 300s (1) cores
% 22.85/13.40 % Starting sh5l with 300s (1) cores
% 22.85/13.40 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1454538 completed with status 0
% 22.85/13.40 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 22.85/13.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 22.85/13.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 22.85/13.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 22.85/13.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 22.85/13.40 % No SInE strategy applied
% 22.85/13.40 % Search class: FGHSM-FFLM31-DFFFFFNN
% 22.85/13.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 22.85/13.40 % Starting SubtermCWHack with 136s (1) cores
% 22.85/13.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 22.85/13.40 % Starting new_bool_3 with 311s (1) cores
% 22.85/13.40 % Starting new_bool_1 with 308s (1) cores
% 22.85/13.40 % Starting sh5l with 304s (1) cores
% 22.85/13.40 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1454546 completed with status 0
% 22.85/13.40 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 22.85/13.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 22.85/13.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 22.85/13.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 22.85/13.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 22.85/13.40 % No SInE strategy applied
% 22.85/13.40 % Search class: FGHSM-FFLM31-DFFFFFNN
% 22.85/13.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 22.85/13.40 % Starting SubtermCWHack with 136s (1) cores
% 22.85/13.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 22.85/13.40 % Preprocessing time : 0.004 s
% 22.85/13.40 % Presaturation interreduction done
% 22.85/13.40
% 22.85/13.40 % Proof found!
% 22.85/13.40 % SZS status Unsatisfiable
% 22.85/13.40 % SZS output start CNFRefutation
% See solution above
% 23.49/13.40 % Parsed axioms : 160
% 23.49/13.40 % Removed by relevancy pruning/SinE : 0
% 23.49/13.40 % Initial clauses : 160
% 23.49/13.40 % Removed in clause preprocessing : 19
% 23.49/13.40 % Initial clauses in saturation : 141
% 23.49/13.40 % Processed clauses : 13322
% 23.49/13.40 % ...of these trivial : 87
% 23.49/13.40 % ...subsumed : 10356
% 23.49/13.40 % ...remaining for further processing : 2879
% 23.49/13.40 % Other redundant clauses eliminated : 22
% 23.49/13.40 % Clauses deleted for lack of memory : 0
% 23.49/13.40 % Backward-subsumed : 203
% 23.49/13.40 % Backward-rewritten : 357
% 23.49/13.40 % Generated clauses : 84449
% 23.49/13.40 % ...of the previous two non-redundant : 69090
% 23.49/13.40 % ...aggressively subsumed : 0
% 23.49/13.40 % Contextual simplify-reflections : 59
% 23.49/13.40 % Paramodulations : 84411
% 23.49/13.40 % Factorizations : 16
% 23.49/13.40 % NegExts : 0
% 23.49/13.40 % Equation resolutions : 22
% 23.49/13.40 % Disequality decompositions : 0
% 23.49/13.40 % Total rewrite steps : 38331
% 23.49/13.40 % ...of those cached : 35640
% 23.49/13.40 % Propositional unsat checks : 0
% 23.49/13.40 % Propositional check models : 0
% 23.49/13.40 % Propositional check unsatisfiable : 0
% 23.49/13.40 % Propositional clauses : 0
% 23.49/13.40 % Propositional clauses after purity: 0
% 23.49/13.40 % Propositional unsat core size : 0
% 23.49/13.40 % Propositional preprocessing time : 0.000
% 23.49/13.40 % Propositional encoding time : 0.000
% 23.49/13.40 % Propositional solver time : 0.000
% 23.49/13.40 % Success case prop preproc time : 0.000
% 23.49/13.40 % Success case prop encoding time : 0.000
% 23.49/13.40 % Success case prop solver time : 0.000
% 23.49/13.40 % Current number of processed clauses : 2173
% 23.49/13.40 % Positive orientable unit clauses : 252
% 23.49/13.40 % Positive unorientable unit clauses: 4
% 23.49/13.40 % Negative unit clauses : 5
% 23.49/13.40 % Non-unit-clauses : 1912
% 23.49/13.40 % Current number of unprocessed clauses: 55118
% 23.49/13.40 % ...number of literals in the above : 199331
% 23.49/13.40 % Current number of archived formulas : 0
% 23.49/13.40 % Current number of archived clauses : 719
% 23.49/13.40 % Clause-clause subsumption calls (NU) : 1012241
% 23.49/13.40 % Rec. Clause-clause subsumption calls : 568031
% 23.49/13.40 % Non-unit clause-clause subsumptions : 7484
% 23.49/13.40 % Unit Clause-clause subsumption calls : 30977
% 23.49/13.40 % Rewrite failures with RHS unbound : 16
% 23.49/13.40 % BW rewrite match attempts : 1226
% 23.49/13.40 % BW rewrite match successes : 923
% 23.49/13.40 % Condensation attempts : 0
% 23.49/13.40 % Condensation successes : 0
% 23.49/13.40 % Termbank termtop insertions : 3174924
% 23.49/13.40 % Search garbage collected termcells : 287
% 23.49/13.40
% 23.49/13.40 % -------------------------------------------------
% 23.49/13.40 % User time : 2.839 s
% 23.49/13.40 % System time : 0.069 s
% 23.49/13.40 % Total time : 2.908 s
% 23.49/13.40 % Maximum resident set size: 4036 pages
% 23.49/13.40
% 23.49/13.40 % -------------------------------------------------
% 23.49/13.40 % User time : 14.073 s
% 23.49/13.40 % System time : 0.392 s
% 23.49/13.40 % Total time : 14.465 s
% 23.49/13.40 % Maximum resident set size: 4864 pages
% 23.49/13.40 % E exiting
%------------------------------------------------------------------------------