%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM045-1 : 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 01:44:18 PM UTC 2026
% Result : Unsatisfiable 24.06s 3.94s
% Output : CNFRefutation 24.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of clauses : 58 ( 18 unt; 12 nHn; 39 RR)
% Number of literals : 110 ( 14 equ; 48 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 105 ( 10 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(prove_irreflexive_class_property7_1,negated_conjecture,
restrict(intersection(x,identity_relation),y,y) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_irreflexive_class_property7_1) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(restriction2,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction2) ).
cnf(regularity1,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
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(intersection1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
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(intersection2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(irreflexive2,axiom,
( ~ subclass(restrict(X1,X2,X2),complement(identity_relation))
| irreflexive(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',irreflexive2) ).
cnf(prove_irreflexive_class_property7_2,negated_conjecture,
~ irreflexive(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_irreflexive_class_property7_2) ).
cnf(c_0_15,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_17,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_15 ).
cnf(c_0_18,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_19,negated_conjecture,
restrict(intersection(x,identity_relation),y,y) = null_class,
prove_irreflexive_class_property7_1 ).
cnf(c_0_20,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_21,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
restriction2 ).
cnf(c_0_22,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_16 ).
cnf(c_0_23,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_24,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_26,negated_conjecture,
intersection(intersection(x,identity_relation),cross_product(y,y)) = null_class,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(rw,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_28,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_30,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_25 ).
cnf(c_0_31,negated_conjecture,
intersection(cross_product(y,y),intersection(x,identity_relation)) = null_class,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(fof_simplification,[status(thm)],[intersection1]) ).
cnf(c_0_34,negated_conjecture,
( ~ member(X1,cross_product(y,y))
| ~ member(X1,intersection(x,identity_relation))
| member(X1,null_class) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_32]),c_0_24]) ).
cnf(c_0_36,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
c_0_33 ).
cnf(c_0_37,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
not_subclass_members1 ).
cnf(c_0_38,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
cnf(c_0_39,negated_conjecture,
( ~ member(X1,x)
| ~ member(X1,identity_relation)
| ~ member(X1,cross_product(y,y)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_30]),c_0_35]) ).
cnf(c_0_40,plain,
( subclass(intersection(X1,X2),X3)
| member(not_subclass_element(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_38 ).
cnf(c_0_42,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).
cnf(c_0_43,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
cnf(c_0_44,plain,
( ~ subclass(restrict(X1,X2,X2),complement(identity_relation))
| irreflexive(X1,X2) ),
inference(fof_simplification,[status(thm)],[irreflexive2]) ).
cnf(c_0_45,negated_conjecture,
( ~ member(not_subclass_element(intersection(cross_product(y,y),X1),X2),x)
| ~ member(not_subclass_element(intersection(cross_product(y,y),X1),X2),identity_relation)
| subclass(intersection(cross_product(y,y),X1),X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,plain,
( subclass(intersection(X1,X2),X3)
| member(not_subclass_element(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_37]) ).
cnf(c_0_47,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
c_0_42 ).
cnf(c_0_48,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_43 ).
cnf(c_0_49,plain,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),universal_class) ),
inference(spm,[status(thm)],[c_0_24,c_0_37]) ).
cnf(c_0_50,plain,
( ~ subclass(restrict(X1,X2,X2),complement(identity_relation))
| irreflexive(X1,X2) ),
c_0_44 ).
cnf(c_0_51,negated_conjecture,
( ~ member(not_subclass_element(intersection(x,cross_product(y,y)),X1),identity_relation)
| subclass(intersection(x,cross_product(y,y)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_27]),c_0_27]) ).
cnf(c_0_52,plain,
( subclass(X1,complement(X2))
| member(not_subclass_element(X1,complement(X2)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_53,negated_conjecture,
~ irreflexive(x,y),
inference(fof_simplification,[status(thm)],[prove_irreflexive_class_property7_2]) ).
cnf(c_0_54,plain,
( ~ subclass(intersection(X1,cross_product(X2,X2)),complement(identity_relation))
| irreflexive(X1,X2) ),
inference(rw,[status(thm)],[c_0_50,c_0_20]) ).
cnf(c_0_55,negated_conjecture,
subclass(intersection(x,cross_product(y,y)),complement(identity_relation)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
~ irreflexive(x,y),
c_0_53 ).
cnf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM045-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n020.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 21 02:01:32 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 24.06/3.94 % Version: 3.5.1
% 24.06/3.94 % Preprocessing class: FSLSSMSMSSSNFFN.
% 24.06/3.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.06/3.94 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 24.06/3.94 % Starting new_bool_3 with 300s (1) cores
% 24.06/3.94 % Starting new_bool_1 with 300s (1) cores
% 24.06/3.94 % Starting sh5l with 300s (1) cores
% 24.06/3.94 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1761220 completed with status 0
% 24.06/3.94 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 24.06/3.94 % Preprocessing class: FSLSSMSMSSSNFFN.
% 24.06/3.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.06/3.94 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 24.06/3.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 24.06/3.94 % No SInE strategy applied
% 24.06/3.94 % Search class: FGHSM-FFLM31-DFFFFFNN
% 24.06/3.94 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 24.06/3.94 % Starting SubtermCWHack with 136s (1) cores
% 24.06/3.94 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 24.06/3.94 % Starting new_bool_3 with 311s (1) cores
% 24.06/3.94 % Starting new_bool_1 with 308s (1) cores
% 24.06/3.94 % Starting sh5l with 304s (1) cores
% 24.06/3.94 % sh5l with pid 1761234 completed with status 0
% 24.06/3.94 % Result found by sh5l
% 24.06/3.94 % Preprocessing class: FSLSSMSMSSSNFFN.
% 24.06/3.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.06/3.94 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 24.06/3.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 24.06/3.94 % No SInE strategy applied
% 24.06/3.94 % Search class: FGHSM-FFLM31-DFFFFFNN
% 24.06/3.94 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 24.06/3.94 % Starting SubtermCWHack with 136s (1) cores
% 24.06/3.94 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 24.06/3.94 % Starting new_bool_3 with 311s (1) cores
% 24.06/3.94 % Starting new_bool_1 with 308s (1) cores
% 24.06/3.94 % Starting sh5l with 304s (1) cores
% 24.06/3.94 % Preprocessing time : 0.004 s
% 24.06/3.94 % Presaturation interreduction done
% 24.06/3.94
% 24.06/3.94 % Proof found!
% 24.06/3.94 % SZS status Unsatisfiable
% 24.06/3.94 % SZS output start CNFRefutation
% See solution above
% 24.06/3.94 % Parsed axioms : 160
% 24.06/3.94 % Removed by relevancy pruning/SinE : 0
% 24.06/3.94 % Initial clauses : 160
% 24.06/3.94 % Removed in clause preprocessing : 19
% 24.06/3.94 % Initial clauses in saturation : 141
% 24.06/3.94 % Processed clauses : 13401
% 24.06/3.94 % ...of these trivial : 42
% 24.06/3.94 % ...subsumed : 10906
% 24.06/3.94 % ...remaining for further processing : 2453
% 24.06/3.94 % Other redundant clauses eliminated : 22
% 24.06/3.94 % Clauses deleted for lack of memory : 0
% 24.06/3.94 % Backward-subsumed : 170
% 24.06/3.94 % Backward-rewritten : 84
% 24.06/3.94 % Generated clauses : 74197
% 24.06/3.94 % ...of the previous two non-redundant : 54272
% 24.06/3.94 % ...aggressively subsumed : 0
% 24.06/3.94 % Contextual simplify-reflections : 42
% 24.06/3.94 % Paramodulations : 74159
% 24.06/3.94 % Factorizations : 16
% 24.06/3.94 % NegExts : 0
% 24.06/3.94 % Equation resolutions : 22
% 24.06/3.94 % Disequality decompositions : 0
% 24.06/3.94 % Total rewrite steps : 54005
% 24.06/3.94 % ...of those cached : 52416
% 24.06/3.94 % Propositional unsat checks : 0
% 24.06/3.94 % Propositional check models : 0
% 24.06/3.94 % Propositional check unsatisfiable : 0
% 24.06/3.94 % Propositional clauses : 0
% 24.06/3.94 % Propositional clauses after purity: 0
% 24.06/3.94 % Propositional unsat core size : 0
% 24.06/3.94 % Propositional preprocessing time : 0.000
% 24.06/3.94 % Propositional encoding time : 0.000
% 24.06/3.94 % Propositional solver time : 0.000
% 24.06/3.94 % Success case prop preproc time : 0.000
% 24.06/3.94 % Success case prop encoding time : 0.000
% 24.06/3.94 % Success case prop solver time : 0.000
% 24.06/3.94 % Current number of processed clauses : 2053
% 24.06/3.94 % Positive orientable unit clauses : 234
% 24.06/3.94 % Positive unorientable unit clauses: 3
% 24.06/3.94 % Negative unit clauses : 33
% 24.06/3.94 % Non-unit-clauses : 1783
% 24.06/3.94 % Current number of unprocessed clauses: 40702
% 24.06/3.94 % ...number of literals in the above : 160766
% 24.06/3.94 % Current number of archived formulas : 0
% 24.06/3.94 % Current number of archived clauses : 413
% 24.06/3.94 % Clause-clause subsumption calls (NU) : 376281
% 24.06/3.94 % Rec. Clause-clause subsumption calls : 206128
% 24.06/3.94 % Non-unit clause-clause subsumptions : 7251
% 24.06/3.94 % Unit Clause-clause subsumption calls : 8585
% 24.06/3.94 % Rewrite failures with RHS unbound : 32
% 24.06/3.94 % BW rewrite match attempts : 138
% 24.06/3.94 % BW rewrite match successes : 58
% 24.06/3.94 % Condensation attempts : 13401
% 24.06/3.94 % Condensation successes : 611
% 24.06/3.94 % Termbank termtop insertions : 3137415
% 24.06/3.94 % Search garbage collected termcells : 287
% 24.06/3.94
% 24.06/3.94 % -------------------------------------------------
% 24.06/3.94 % User time : 3.310 s
% 24.06/3.94 % System time : 0.078 s
% 24.06/3.94 % Total time : 3.388 s
% 24.06/3.94 % Maximum resident set size: 4036 pages
% 24.06/3.94
% 24.06/3.94 % -------------------------------------------------
% 24.06/3.94 % User time : 16.247 s
% 24.06/3.94 % System time : 0.594 s
% 24.06/3.94 % Total time : 16.840 s
% 24.06/3.94 % Maximum resident set size: 4864 pages
% 24.06/3.94 % E exiting
%------------------------------------------------------------------------------