%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET096-7 : 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 : n005.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 02:13:34 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 12 unt; 2 nHn; 26 RR)
% Number of literals : 50 ( 16 equ; 28 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 0 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(only_member_in_singleton,axiom,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
cnf(prove_two_subsets_of_singleton_1,negated_conjecture,
subclass(x,singleton(y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_two_subsets_of_singleton_1) ).
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(prove_two_subsets_of_singleton_3,negated_conjecture,
singleton(y) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_two_subsets_of_singleton_3) ).
cnf(prove_two_subsets_of_singleton_2,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_two_subsets_of_singleton_2) ).
cnf(property_of_singletons2,axiom,
( ~ member(X1,X2)
| subclass(singleton(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_singletons2) ).
cnf(null_class_is_unique,axiom,
( member(not_subclass_element(X1,null_class),X1)
| X1 = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_unique) ).
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,singleton(X2))
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[only_member_in_singleton]) ).
cnf(c_0_10,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_8 ).
cnf(c_0_11,negated_conjecture,
subclass(x,singleton(y)),
prove_two_subsets_of_singleton_1 ).
cnf(c_0_12,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[subclass_implies_equal]) ).
cnf(c_0_13,negated_conjecture,
singleton(y) != x,
inference(fof_simplification,[status(thm)],[prove_two_subsets_of_singleton_3]) ).
cnf(c_0_14,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
c_0_9 ).
cnf(c_0_15,negated_conjecture,
( ~ member(X1,x)
| member(X1,singleton(y)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
x != null_class,
inference(fof_simplification,[status(thm)],[prove_two_subsets_of_singleton_2]) ).
cnf(c_0_17,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
c_0_12 ).
cnf(c_0_18,negated_conjecture,
singleton(y) != x,
c_0_13 ).
cnf(c_0_19,plain,
( ~ member(X1,X2)
| subclass(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[property_of_singletons2]) ).
cnf(c_0_20,negated_conjecture,
( ~ member(X1,x)
| X1 = y ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,axiom,
( member(not_subclass_element(X1,null_class),X1)
| X1 = null_class ),
null_class_is_unique ).
cnf(c_0_22,negated_conjecture,
x != null_class,
c_0_16 ).
cnf(c_0_23,negated_conjecture,
~ subclass(singleton(y),x),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_11]),c_0_18]) ).
cnf(c_0_24,plain,
( ~ member(X1,X2)
| subclass(singleton(X1),X2) ),
c_0_19 ).
cnf(c_0_25,negated_conjecture,
not_subclass_element(x,null_class) = y,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_26,negated_conjecture,
~ member(y,x),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_25]),c_0_22]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET096-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:51:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.43 % Version: 3.5.1
% 0.09/0.43 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.09/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.43 % Starting sh5l with 300s (1) cores
% 0.09/0.43 % sh5l with pid 2592995 completed with status 0
% 0.09/0.43 % Result found by sh5l
% 0.09/0.43 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.09/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.43 % Starting sh5l with 300s (1) cores
% 0.09/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.09/0.43 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.09/0.43 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.09/0.43 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.43 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.43 % SubtermCWHack with pid 2592999 completed with status 0
% 0.09/0.43 % Result found by SubtermCWHack
% 0.09/0.43 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.09/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.43 % Starting sh5l with 300s (1) cores
% 0.09/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.09/0.43 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.09/0.43 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.09/0.43 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.43 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.43 % Preprocessing time : 0.003 s
% 0.09/0.43
% 0.09/0.43 % Proof found!
% 0.09/0.43 % SZS status Unsatisfiable
% 0.09/0.43 % SZS output start CNFRefutation
% See solution above
% 0.09/0.43 % Parsed axioms : 142
% 0.09/0.43 % Removed by relevancy pruning/SinE : 9
% 0.09/0.43 % Initial clauses : 133
% 0.09/0.43 % Removed in clause preprocessing : 0
% 0.09/0.43 % Initial clauses in saturation : 133
% 0.09/0.43 % Processed clauses : 170
% 0.09/0.43 % ...of these trivial : 2
% 0.09/0.43 % ...subsumed : 41
% 0.09/0.43 % ...remaining for further processing : 127
% 0.09/0.43 % Other redundant clauses eliminated : 13
% 0.09/0.43 % Clauses deleted for lack of memory : 0
% 0.09/0.43 % Backward-subsumed : 0
% 0.09/0.43 % Backward-rewritten : 2
% 0.09/0.43 % Generated clauses : 405
% 0.09/0.43 % ...of the previous two non-redundant : 269
% 0.09/0.43 % ...aggressively subsumed : 0
% 0.09/0.43 % Contextual simplify-reflections : 1
% 0.09/0.43 % Paramodulations : 391
% 0.09/0.43 % Factorizations : 0
% 0.09/0.43 % NegExts : 0
% 0.09/0.43 % Equation resolutions : 14
% 0.09/0.43 % Disequality decompositions : 0
% 0.09/0.43 % Total rewrite steps : 107
% 0.09/0.43 % ...of those cached : 76
% 0.09/0.43 % Propositional unsat checks : 0
% 0.09/0.43 % Propositional check models : 0
% 0.09/0.43 % Propositional check unsatisfiable : 0
% 0.09/0.43 % Propositional clauses : 0
% 0.09/0.43 % Propositional clauses after purity: 0
% 0.09/0.43 % Propositional unsat core size : 0
% 0.09/0.43 % Propositional preprocessing time : 0.000
% 0.09/0.43 % Propositional encoding time : 0.000
% 0.09/0.43 % Propositional solver time : 0.000
% 0.09/0.43 % Success case prop preproc time : 0.000
% 0.09/0.43 % Success case prop encoding time : 0.000
% 0.09/0.43 % Success case prop solver time : 0.000
% 0.09/0.43 % Current number of processed clauses : 123
% 0.09/0.43 % Positive orientable unit clauses : 36
% 0.09/0.43 % Positive unorientable unit clauses: 1
% 0.09/0.43 % Negative unit clauses : 5
% 0.09/0.43 % Non-unit-clauses : 81
% 0.09/0.43 % Current number of unprocessed clauses: 230
% 0.09/0.43 % ...number of literals in the above : 604
% 0.09/0.43 % Current number of archived formulas : 0
% 0.09/0.43 % Current number of archived clauses : 2
% 0.09/0.43 % Clause-clause subsumption calls (NU) : 1072
% 0.09/0.43 % Rec. Clause-clause subsumption calls : 968
% 0.09/0.43 % Non-unit clause-clause subsumptions : 35
% 0.09/0.43 % Unit Clause-clause subsumption calls : 132
% 0.09/0.43 % Rewrite failures with RHS unbound : 0
% 0.09/0.43 % BW rewrite match attempts : 12
% 0.09/0.43 % BW rewrite match successes : 8
% 0.09/0.43 % Condensation attempts : 0
% 0.09/0.43 % Condensation successes : 0
% 0.09/0.43 % Termbank termtop insertions : 6737
% 0.09/0.43 % Search garbage collected termcells : 262
% 0.09/0.43
% 0.09/0.43 % -------------------------------------------------
% 0.09/0.43 % User time : 0.012 s
% 0.09/0.43 % System time : 0.007 s
% 0.09/0.43 % Total time : 0.019 s
% 0.09/0.43 % Maximum resident set size: 4000 pages
% 0.09/0.43
% 0.09/0.43 % -------------------------------------------------
% 0.09/0.43 % User time : 0.016 s
% 0.09/0.43 % System time : 0.012 s
% 0.09/0.43 % Total time : 0.028 s
% 0.09/0.43 % Maximum resident set size: 4864 pages
% 0.09/0.43 % E exiting
%------------------------------------------------------------------------------