%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET260-6 : 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 : n016.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 02:13:59 PM UTC 2026
% Result : Unsatisfiable 2.94s 0.89s
% Output : CNFRefutation 2.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of clauses : 59 ( 23 unt; 7 nHn; 40 RR)
% Number of literals : 115 ( 16 equ; 56 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 117 ( 21 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(domain2,axiom,
( ~ member(X1,universal_class)
| member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain2) ).
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(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(cartesian_product3,axiom,
( ~ member(X3,X4)
| ~ member(X1,X2)
| member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
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(cartesian_product2,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
cnf(prove_domain_alternate_defn3_2,negated_conjecture,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_alternate_defn3_2) ).
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(prove_domain_alternate_defn3_1,negated_conjecture,
member(ordered_pair(x,y),xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_alternate_defn3_1) ).
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_domain_alternate_defn3_3,negated_conjecture,
~ member(x,domain_of(xr)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_alternate_defn3_3) ).
cnf(c_0_16,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_17,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_18,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_16 ).
cnf(c_0_19,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_17 ).
cnf(c_0_21,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_22,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ member(X1,universal_class)
| member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class ),
inference(fof_simplification,[status(thm)],[domain2]) ).
cnf(c_0_24,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_26,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_27,plain,
( ~ member(X1,universal_class)
| member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class ),
c_0_23 ).
cnf(c_0_28,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_29,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_30,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( ~ member(X3,X4)
| ~ member(X1,X2)
| member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
inference(fof_simplification,[status(thm)],[cartesian_product3]) ).
cnf(c_0_32,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_33,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X2,X4) ),
inference(fof_simplification,[status(thm)],[cartesian_product2]) ).
cnf(c_0_34,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_26 ).
cnf(c_0_35,plain,
( ~ member(X1,universal_class)
| member(X1,domain_of(X2))
| intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)) = null_class ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_36,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_30]),c_0_22]) ).
cnf(c_0_37,plain,
( ~ member(X3,X4)
| ~ member(X1,X2)
| member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
c_0_31 ).
cnf(c_0_38,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_32,c_0_28]),c_0_28]) ).
cnf(c_0_39,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X2,X4) ),
c_0_33 ).
cnf(c_0_40,negated_conjecture,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
prove_domain_alternate_defn3_2 ).
cnf(c_0_41,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[cartesian_product1]) ).
cnf(c_0_42,plain,
( ~ member(X3,X2)
| ~ member(X1,universal_class)
| ~ member(X3,cross_product(unordered_pair(X1,X1),universal_class))
| member(X1,domain_of(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_43,plain,
( ~ member(X1,X2)
| ~ member(X3,X4)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(X2,X4)) ),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
member(ordered_pair(x,y),xr),
prove_domain_alternate_defn3_1 ).
cnf(c_0_45,plain,
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4))
| member(X2,X4) ),
inference(rw,[status(thm)],[c_0_39,c_0_38]) ).
cnf(c_0_46,negated_conjecture,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(universal_class,universal_class)),
inference(rw,[status(thm)],[c_0_40,c_0_38]) ).
cnf(c_0_47,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
c_0_41 ).
cnf(c_0_48,plain,
( ~ member(X4,universal_class)
| ~ member(X1,universal_class)
| ~ member(X3,unordered_pair(X1,X1))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),X2)
| member(X1,domain_of(X2)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),xr),
inference(rw,[status(thm)],[c_0_44,c_0_38]) ).
cnf(c_0_50,negated_conjecture,
member(y,universal_class),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[unordered_pair2]) ).
cnf(c_0_52,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_47,c_0_38]) ).
cnf(c_0_53,negated_conjecture,
~ member(x,domain_of(xr)),
inference(fof_simplification,[status(thm)],[prove_domain_alternate_defn3_3]) ).
cnf(c_0_54,negated_conjecture,
( ~ member(X1,universal_class)
| ~ member(x,unordered_pair(X1,X1))
| member(X1,domain_of(xr)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).
cnf(c_0_55,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
c_0_51 ).
cnf(c_0_56,negated_conjecture,
member(x,universal_class),
inference(spm,[status(thm)],[c_0_52,c_0_46]) ).
cnf(c_0_57,negated_conjecture,
~ member(x,domain_of(xr)),
c_0_53 ).
cnf(c_0_58,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET260-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n016.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:08:22 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 2.94/0.89 % Version: 3.5.1
% 2.94/0.89 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.94/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.94/0.89 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.94/0.89 % Starting new_bool_3 with 300s (1) cores
% 2.94/0.89 % Starting new_bool_1 with 300s (1) cores
% 2.94/0.89 % Starting sh5l with 300s (1) cores
% 2.94/0.89 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1622176 completed with status 0
% 2.94/0.89 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 2.94/0.89 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.94/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.94/0.89 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.94/0.89 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.94/0.89 % No SInE strategy applied
% 2.94/0.89 % Search class: FGHSM-FFLM31-DFFFFFNN
% 2.94/0.89 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.94/0.89 % Starting SubtermCWHack with 136s (1) cores
% 2.94/0.89 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 2.94/0.89 % Starting new_bool_3 with 311s (1) cores
% 2.94/0.89 % Starting new_bool_1 with 308s (1) cores
% 2.94/0.89 % Starting sh5l with 304s (1) cores
% 2.94/0.89 % sh5l with pid 1622187 completed with status 0
% 2.94/0.89 % Result found by sh5l
% 2.94/0.89 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.94/0.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.94/0.89 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.94/0.89 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.94/0.89 % No SInE strategy applied
% 2.94/0.89 % Search class: FGHSM-FFLM31-DFFFFFNN
% 2.94/0.89 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.94/0.89 % Starting SubtermCWHack with 136s (1) cores
% 2.94/0.89 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 2.94/0.89 % Starting new_bool_3 with 311s (1) cores
% 2.94/0.89 % Starting new_bool_1 with 308s (1) cores
% 2.94/0.89 % Starting sh5l with 304s (1) cores
% 2.94/0.89 % Preprocessing time : 0.003 s
% 2.94/0.89 % Presaturation interreduction done
% 2.94/0.89
% 2.94/0.89 % Proof found!
% 2.94/0.89 % SZS status Unsatisfiable
% 2.94/0.89 % SZS output start CNFRefutation
% See solution above
% 2.94/0.89 % Parsed axioms : 115
% 2.94/0.89 % Removed by relevancy pruning/SinE : 0
% 2.94/0.89 % Initial clauses : 115
% 2.94/0.89 % Removed in clause preprocessing : 17
% 2.94/0.89 % Initial clauses in saturation : 98
% 2.94/0.89 % Processed clauses : 2373
% 2.94/0.89 % ...of these trivial : 2
% 2.94/0.89 % ...subsumed : 1514
% 2.94/0.89 % ...remaining for further processing : 857
% 2.94/0.89 % Other redundant clauses eliminated : 8
% 2.94/0.89 % Clauses deleted for lack of memory : 0
% 2.94/0.89 % Backward-subsumed : 43
% 2.94/0.89 % Backward-rewritten : 45
% 2.94/0.89 % Generated clauses : 8241
% 2.94/0.89 % ...of the previous two non-redundant : 7238
% 2.94/0.89 % ...aggressively subsumed : 0
% 2.94/0.89 % Contextual simplify-reflections : 24
% 2.94/0.89 % Paramodulations : 8229
% 2.94/0.89 % Factorizations : 4
% 2.94/0.89 % NegExts : 0
% 2.94/0.89 % Equation resolutions : 8
% 2.94/0.89 % Disequality decompositions : 0
% 2.94/0.89 % Total rewrite steps : 4106
% 2.94/0.89 % ...of those cached : 3862
% 2.94/0.89 % Propositional unsat checks : 0
% 2.94/0.89 % Propositional check models : 0
% 2.94/0.89 % Propositional check unsatisfiable : 0
% 2.94/0.89 % Propositional clauses : 0
% 2.94/0.89 % Propositional clauses after purity: 0
% 2.94/0.89 % Propositional unsat core size : 0
% 2.94/0.89 % Propositional preprocessing time : 0.000
% 2.94/0.89 % Propositional encoding time : 0.000
% 2.94/0.89 % Propositional solver time : 0.000
% 2.94/0.89 % Success case prop preproc time : 0.000
% 2.94/0.89 % Success case prop encoding time : 0.000
% 2.94/0.89 % Success case prop solver time : 0.000
% 2.94/0.89 % Current number of processed clauses : 668
% 2.94/0.89 % Positive orientable unit clauses : 74
% 2.94/0.89 % Positive unorientable unit clauses: 1
% 2.94/0.89 % Negative unit clauses : 3
% 2.94/0.89 % Non-unit-clauses : 590
% 2.94/0.89 % Current number of unprocessed clauses: 4973
% 2.94/0.89 % ...number of literals in the above : 16472
% 2.94/0.89 % Current number of archived formulas : 0
% 2.94/0.89 % Current number of archived clauses : 202
% 2.94/0.89 % Clause-clause subsumption calls (NU) : 70304
% 2.94/0.89 % Rec. Clause-clause subsumption calls : 51506
% 2.94/0.89 % Non-unit clause-clause subsumptions : 1374
% 2.94/0.89 % Unit Clause-clause subsumption calls : 1278
% 2.94/0.89 % Rewrite failures with RHS unbound : 0
% 2.94/0.89 % BW rewrite match attempts : 58
% 2.94/0.89 % BW rewrite match successes : 20
% 2.94/0.89 % Condensation attempts : 2373
% 2.94/0.89 % Condensation successes : 58
% 2.94/0.89 % Termbank termtop insertions : 177170
% 2.94/0.89 % Search garbage collected termcells : 185
% 2.94/0.89
% 2.94/0.89 % -------------------------------------------------
% 2.94/0.89 % User time : 0.314 s
% 2.94/0.89 % System time : 0.012 s
% 2.94/0.89 % Total time : 0.326 s
% 2.94/0.89 % Maximum resident set size: 3744 pages
% 2.94/0.89
% 2.94/0.89 % -------------------------------------------------
% 2.94/0.89 % User time : 2.072 s
% 2.94/0.89 % System time : 0.085 s
% 2.94/0.89 % Total time : 2.157 s
% 2.94/0.89 % Maximum resident set size: 4608 pages
% 2.94/0.89 % E exiting
%------------------------------------------------------------------------------