%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET245-6 : 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 : n010.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 02:13:58 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.47s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 31 ( 16 unt; 4 nHn; 18 RR)
% Number of literals : 49 ( 17 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 53 ( 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(regularity1,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(intersection2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(prove_restriction_with_null_class1_1,negated_conjecture,
restrict(null_class,x,y) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_restriction_with_null_class1_1) ).
cnf(restriction2,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction2) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(c_0_8,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_9,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_10,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_8 ).
cnf(c_0_11,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_12,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_9 ).
cnf(c_0_13,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_14,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_17,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
cnf(c_0_18,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_17 ).
cnf(c_0_20,negated_conjecture,
restrict(null_class,x,y) != null_class,
inference(fof_simplification,[status(thm)],[prove_restriction_with_null_class1_1]) ).
cnf(c_0_21,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
restriction2 ).
cnf(c_0_22,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_23,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_18]),c_0_14]) ).
cnf(c_0_24,plain,
( member(regular(intersection(X1,X2)),X2)
| intersection(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_25,negated_conjecture,
restrict(null_class,x,y) != null_class,
c_0_20 ).
cnf(c_0_26,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
intersection(X1,null_class) = null_class,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
intersection(null_class,cross_product(x,y)) != null_class,
inference(rw,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_29,plain,
intersection(null_class,cross_product(X1,X2)) = null_class,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET245-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n010.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 21 05:03:25 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 0.13/0.47 % Version: 3.5.1
% 0.13/0.47 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.13/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.47 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.13/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.47 % Starting sh5l with 300s (1) cores
% 0.13/0.47 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 78905 completed with status 0
% 0.13/0.47 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.13/0.47 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.13/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.47 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.13/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.47 % No SInE strategy applied
% 0.13/0.47 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.13/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.47 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.13/0.47 % Starting new_bool_3 with 311s (1) cores
% 0.13/0.47 % Starting new_bool_1 with 308s (1) cores
% 0.13/0.47 % Starting sh5l with 304s (1) cores
% 0.13/0.47 % SubtermCWHack with pid 78912 completed with status 0
% 0.13/0.47 % Result found by SubtermCWHack
% 0.13/0.47 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.13/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.47 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.13/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.47 % No SInE strategy applied
% 0.13/0.47 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.13/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.47 % Preprocessing time : 0.003 s
% 0.13/0.47
% 0.13/0.47 % Proof found!
% 0.13/0.47 % SZS status Unsatisfiable
% 0.13/0.47 % SZS output start CNFRefutation
% See solution above
% 0.13/0.47 % Parsed axioms : 113
% 0.13/0.47 % Removed by relevancy pruning/SinE : 0
% 0.13/0.47 % Initial clauses : 113
% 0.13/0.47 % Removed in clause preprocessing : 17
% 0.13/0.47 % Initial clauses in saturation : 96
% 0.13/0.47 % Processed clauses : 129
% 0.13/0.47 % ...of these trivial : 0
% 0.13/0.47 % ...subsumed : 22
% 0.13/0.47 % ...remaining for further processing : 107
% 0.13/0.47 % Other redundant clauses eliminated : 2
% 0.13/0.47 % Clauses deleted for lack of memory : 0
% 0.13/0.47 % Backward-subsumed : 0
% 0.13/0.47 % Backward-rewritten : 2
% 0.13/0.47 % Generated clauses : 205
% 0.13/0.47 % ...of the previous two non-redundant : 178
% 0.13/0.47 % ...aggressively subsumed : 0
% 0.13/0.47 % Contextual simplify-reflections : 1
% 0.13/0.47 % Paramodulations : 203
% 0.13/0.47 % Factorizations : 0
% 0.13/0.47 % NegExts : 0
% 0.13/0.47 % Equation resolutions : 2
% 0.13/0.47 % Disequality decompositions : 0
% 0.13/0.47 % Total rewrite steps : 12
% 0.13/0.47 % ...of those cached : 3
% 0.13/0.47 % Propositional unsat checks : 0
% 0.13/0.47 % Propositional check models : 0
% 0.13/0.47 % Propositional check unsatisfiable : 0
% 0.13/0.47 % Propositional clauses : 0
% 0.13/0.47 % Propositional clauses after purity: 0
% 0.13/0.47 % Propositional unsat core size : 0
% 0.13/0.47 % Propositional preprocessing time : 0.000
% 0.13/0.47 % Propositional encoding time : 0.000
% 0.13/0.47 % Propositional solver time : 0.000
% 0.13/0.47 % Success case prop preproc time : 0.000
% 0.13/0.47 % Success case prop encoding time : 0.000
% 0.13/0.47 % Success case prop solver time : 0.000
% 0.13/0.47 % Current number of processed clauses : 103
% 0.13/0.47 % Positive orientable unit clauses : 25
% 0.13/0.47 % Positive unorientable unit clauses: 1
% 0.13/0.47 % Negative unit clauses : 1
% 0.13/0.47 % Non-unit-clauses : 76
% 0.13/0.47 % Current number of unprocessed clauses: 145
% 0.13/0.47 % ...number of literals in the above : 365
% 0.13/0.47 % Current number of archived formulas : 0
% 0.13/0.47 % Current number of archived clauses : 19
% 0.13/0.47 % Clause-clause subsumption calls (NU) : 701
% 0.13/0.47 % Rec. Clause-clause subsumption calls : 447
% 0.13/0.47 % Non-unit clause-clause subsumptions : 19
% 0.13/0.47 % Unit Clause-clause subsumption calls : 41
% 0.13/0.47 % Rewrite failures with RHS unbound : 0
% 0.13/0.47 % BW rewrite match attempts : 5
% 0.13/0.47 % BW rewrite match successes : 3
% 0.13/0.47 % Condensation attempts : 0
% 0.13/0.47 % Condensation successes : 0
% 0.13/0.47 % Termbank termtop insertions : 7341
% 0.13/0.47 % Search garbage collected termcells : 185
% 0.13/0.47
% 0.13/0.47 % -------------------------------------------------
% 0.13/0.47 % User time : 0.014 s
% 0.13/0.47 % System time : 0.005 s
% 0.13/0.47 % Total time : 0.019 s
% 0.13/0.47 % Maximum resident set size: 4000 pages
% 0.13/0.47
% 0.13/0.47 % -------------------------------------------------
% 0.13/0.47 % User time : 0.055 s
% 0.13/0.47 % System time : 0.019 s
% 0.13/0.47 % Total time : 0.075 s
% 0.13/0.47 % Maximum resident set size: 4864 pages
% 0.13/0.47 % E exiting
%------------------------------------------------------------------------------