%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET068-7 : 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 : n001.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 02:13:24 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 45 ( 19 unt; 13 nHn; 24 RR)
% Number of literals : 80 ( 20 equ; 28 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; 5 con; 0-2 aty)
% Number of variables : 66 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(unordered_pair_member,axiom,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(choice2,axiom,
( ~ member(X1,universal_class)
| member(apply(choice,X1),X1)
| X1 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',choice2) ).
cnf(unordered_pairs_in_universal,axiom,
member(unordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
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(prove_singleton_in_unordered_pair2_1,negated_conjecture,
~ subclass(singleton(y),unordered_pair(x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair2_1) ).
cnf(not_subclass_members2,axiom,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(not_subclass_members1,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(commutativity_of_unordered_pair,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
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(null_class_is_subclass,axiom,
subclass(null_class,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_subclass) ).
cnf(c_0_12,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_13,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_12 ).
cnf(c_0_14,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_15,plain,
( ~ member(X1,universal_class)
| member(apply(choice,X1),X1)
| X1 = null_class ),
inference(fof_simplification,[status(thm)],[choice2]) ).
cnf(c_0_16,axiom,
member(unordered_pair(X1,X2),universal_class),
unordered_pairs_in_universal ).
cnf(c_0_17,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_18,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
( ~ member(X1,universal_class)
| member(apply(choice,X1),X1)
| X1 = null_class ),
c_0_15 ).
cnf(c_0_20,plain,
member(singleton(X1),universal_class),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_21,negated_conjecture,
~ subclass(singleton(y),unordered_pair(x,y)),
inference(fof_simplification,[status(thm)],[prove_singleton_in_unordered_pair2_1]) ).
cnf(c_0_22,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).
cnf(c_0_23,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
not_subclass_members1 ).
cnf(c_0_24,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_17 ).
cnf(c_0_25,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_26,plain,
( singleton(X1) = null_class
| apply(choice,singleton(X1)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_27,negated_conjecture,
~ subclass(singleton(y),unordered_pair(x,y)),
c_0_21 ).
cnf(c_0_28,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
c_0_22 ).
cnf(c_0_29,plain,
( subclass(singleton(X1),X2)
| not_subclass_element(singleton(X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_30,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( member(X1,singleton(X1))
| singleton(X1) = null_class ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_26]),c_0_20])]) ).
cnf(c_0_32,negated_conjecture,
~ subclass(unordered_pair(y,y),unordered_pair(x,y)),
inference(rw,[status(thm)],[c_0_27,c_0_14]) ).
cnf(c_0_33,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
commutativity_of_unordered_pair ).
cnf(c_0_34,plain,
( ~ member(X1,X2)
| subclass(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
( member(X1,universal_class)
| singleton(X1) = null_class ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
~ subclass(unordered_pair(y,y),unordered_pair(y,x)),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
( ~ member(X1,X2)
| subclass(unordered_pair(X1,X1),X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_14]) ).
cnf(c_0_38,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[unordered_pair2]) ).
cnf(c_0_39,plain,
( member(X1,universal_class)
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_14,c_0_35]) ).
cnf(c_0_40,axiom,
subclass(null_class,X1),
null_class_is_subclass ).
cnf(c_0_41,negated_conjecture,
~ member(y,unordered_pair(y,x)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
c_0_38 ).
cnf(c_0_43,negated_conjecture,
member(y,universal_class),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_39]),c_0_40])]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET068-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:54:59 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.45 % Version: 3.5.1
% 0.10/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.45 % Starting sh5l with 300s (1) cores
% 0.10/0.45 % sh5l with pid 2227462 completed with status 0
% 0.10/0.45 % Result found by sh5l
% 0.10/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.45 % Starting sh5l with 300s (1) cores
% 0.10/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.45 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.10/0.45 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.45 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.45 % SubtermCWHack with pid 2227465 completed with status 0
% 0.10/0.45 % Result found by SubtermCWHack
% 0.10/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.45 % Starting sh5l with 300s (1) cores
% 0.10/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.45 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.10/0.45 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.45 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.45 % Preprocessing time : 0.001 s
% 0.10/0.45
% 0.10/0.45 % Proof found!
% 0.10/0.45 % SZS status Unsatisfiable
% 0.10/0.45 % SZS output start CNFRefutation
% See solution above
% 0.10/0.45 % Parsed axioms : 109
% 0.10/0.45 % Removed by relevancy pruning/SinE : 9
% 0.10/0.45 % Initial clauses : 100
% 0.10/0.45 % Removed in clause preprocessing : 0
% 0.10/0.45 % Initial clauses in saturation : 100
% 0.10/0.45 % Processed clauses : 394
% 0.10/0.45 % ...of these trivial : 5
% 0.10/0.45 % ...subsumed : 157
% 0.10/0.45 % ...remaining for further processing : 232
% 0.10/0.45 % Other redundant clauses eliminated : 3
% 0.10/0.45 % Clauses deleted for lack of memory : 0
% 0.10/0.45 % Backward-subsumed : 0
% 0.10/0.45 % Backward-rewritten : 3
% 0.10/0.45 % Generated clauses : 975
% 0.10/0.45 % ...of the previous two non-redundant : 802
% 0.10/0.45 % ...aggressively subsumed : 0
% 0.10/0.45 % Contextual simplify-reflections : 0
% 0.10/0.45 % Paramodulations : 970
% 0.10/0.45 % Factorizations : 2
% 0.10/0.45 % NegExts : 0
% 0.10/0.45 % Equation resolutions : 3
% 0.10/0.45 % Disequality decompositions : 0
% 0.10/0.45 % Total rewrite steps : 204
% 0.10/0.45 % ...of those cached : 135
% 0.10/0.45 % Propositional unsat checks : 0
% 0.10/0.45 % Propositional check models : 0
% 0.10/0.45 % Propositional check unsatisfiable : 0
% 0.10/0.45 % Propositional clauses : 0
% 0.10/0.45 % Propositional clauses after purity: 0
% 0.10/0.45 % Propositional unsat core size : 0
% 0.10/0.45 % Propositional preprocessing time : 0.000
% 0.10/0.45 % Propositional encoding time : 0.000
% 0.10/0.45 % Propositional solver time : 0.000
% 0.10/0.45 % Success case prop preproc time : 0.000
% 0.10/0.45 % Success case prop encoding time : 0.000
% 0.10/0.45 % Success case prop solver time : 0.000
% 0.10/0.45 % Current number of processed clauses : 226
% 0.10/0.45 % Positive orientable unit clauses : 55
% 0.10/0.45 % Positive unorientable unit clauses: 3
% 0.10/0.45 % Negative unit clauses : 5
% 0.10/0.45 % Non-unit-clauses : 163
% 0.10/0.45 % Current number of unprocessed clauses: 508
% 0.10/0.45 % ...number of literals in the above : 1319
% 0.10/0.45 % Current number of archived formulas : 0
% 0.10/0.45 % Current number of archived clauses : 3
% 0.10/0.45 % Clause-clause subsumption calls (NU) : 4419
% 0.10/0.45 % Rec. Clause-clause subsumption calls : 4079
% 0.10/0.45 % Non-unit clause-clause subsumptions : 131
% 0.10/0.45 % Unit Clause-clause subsumption calls : 358
% 0.10/0.45 % Rewrite failures with RHS unbound : 0
% 0.10/0.45 % BW rewrite match attempts : 15
% 0.10/0.45 % BW rewrite match successes : 12
% 0.10/0.45 % Condensation attempts : 0
% 0.10/0.45 % Condensation successes : 0
% 0.10/0.45 % Termbank termtop insertions : 13019
% 0.10/0.45 % Search garbage collected termcells : 214
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.019 s
% 0.10/0.45 % System time : 0.001 s
% 0.10/0.45 % Total time : 0.020 s
% 0.10/0.45 % Maximum resident set size: 3724 pages
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.022 s
% 0.10/0.45 % System time : 0.005 s
% 0.10/0.45 % Total time : 0.028 s
% 0.10/0.45 % Maximum resident set size: 4608 pages
% 0.10/0.45 % E exiting
%------------------------------------------------------------------------------