%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET123-6 : 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 : n006.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 02:13:40 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 40 ( 22 unt; 6 nHn; 28 RR)
% Number of literals : 70 ( 16 equ; 35 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(definition_of_set_builder,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_set_builder) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(complement1,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(prove_set_builder_alternate_defn1_1,negated_conjecture,
member(x,set_builder(y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_1) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
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(intersection3,axiom,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(complement2,axiom,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(prove_set_builder_alternate_defn1_3,negated_conjecture,
~ member(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_3) ).
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(prove_set_builder_alternate_defn1_2,negated_conjecture,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_2) ).
cnf(c_0_12,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
definition_of_set_builder ).
cnf(c_0_13,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_14,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_15,negated_conjecture,
member(x,set_builder(y,z)),
prove_set_builder_alternate_defn1_1 ).
cnf(c_0_16,plain,
union(unordered_pair(X1,X1),X2) = set_builder(X1,X2),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_18,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_19,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_14 ).
cnf(c_0_20,negated_conjecture,
member(x,complement(intersection(complement(unordered_pair(y,y)),complement(z)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_22,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_18 ).
cnf(c_0_23,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_24,negated_conjecture,
~ member(x,intersection(complement(unordered_pair(y,y)),complement(z))),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_21 ).
cnf(c_0_26,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
cnf(c_0_27,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( ~ member(x,complement(z))
| ~ member(x,complement(unordered_pair(y,y))) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_26 ).
cnf(c_0_30,negated_conjecture,
member(x,universal_class),
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_31,negated_conjecture,
~ member(x,z),
inference(fof_simplification,[status(thm)],[prove_set_builder_alternate_defn1_3]) ).
cnf(c_0_32,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_33,negated_conjecture,
( ~ member(x,complement(z))
| member(x,unordered_pair(y,y)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_34,negated_conjecture,
~ member(x,z),
c_0_31 ).
cnf(c_0_35,negated_conjecture,
x != y,
inference(fof_simplification,[status(thm)],[prove_set_builder_alternate_defn1_2]) ).
cnf(c_0_36,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_32 ).
cnf(c_0_37,negated_conjecture,
member(x,unordered_pair(y,y)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_29]),c_0_30])]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
x != y,
c_0_35 ).
cnf(c_0_39,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET123-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:54:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 0.15/0.45 % Version: 3.5.1
% 0.15/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.45 % Starting sh5l with 300s (1) cores
% 0.15/0.45 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2045798 completed with status 0
% 0.15/0.45 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.15/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.45 % No SInE strategy applied
% 0.15/0.45 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.15/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.15/0.45 % Starting new_bool_3 with 311s (1) cores
% 0.15/0.45 % Starting new_bool_1 with 308s (1) cores
% 0.15/0.45 % Starting sh5l with 304s (1) cores
% 0.15/0.45 % SubtermCWHack with pid 2045805 completed with status 0
% 0.15/0.45 % Result found by SubtermCWHack
% 0.15/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.45 % No SInE strategy applied
% 0.15/0.45 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.15/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.45 % Preprocessing time : 0.003 s
% 0.15/0.45
% 0.15/0.45 % Proof found!
% 0.15/0.45 % SZS status Unsatisfiable
% 0.15/0.45 % SZS output start CNFRefutation
% See solution above
% 0.15/0.45 % Parsed axioms : 95
% 0.15/0.45 % Removed by relevancy pruning/SinE : 0
% 0.15/0.45 % Initial clauses : 95
% 0.15/0.45 % Removed in clause preprocessing : 16
% 0.15/0.45 % Initial clauses in saturation : 79
% 0.15/0.45 % Processed clauses : 96
% 0.15/0.45 % ...of these trivial : 0
% 0.15/0.45 % ...subsumed : 13
% 0.15/0.45 % ...remaining for further processing : 83
% 0.15/0.45 % Other redundant clauses eliminated : 2
% 0.15/0.45 % Clauses deleted for lack of memory : 0
% 0.15/0.45 % Backward-subsumed : 0
% 0.15/0.45 % Backward-rewritten : 2
% 0.15/0.45 % Generated clauses : 124
% 0.15/0.45 % ...of the previous two non-redundant : 103
% 0.15/0.45 % ...aggressively subsumed : 0
% 0.15/0.45 % Contextual simplify-reflections : 1
% 0.15/0.45 % Paramodulations : 122
% 0.15/0.45 % Factorizations : 0
% 0.15/0.45 % NegExts : 0
% 0.15/0.45 % Equation resolutions : 2
% 0.15/0.45 % Disequality decompositions : 0
% 0.15/0.45 % Total rewrite steps : 16
% 0.15/0.45 % ...of those cached : 6
% 0.15/0.45 % Propositional unsat checks : 0
% 0.15/0.45 % Propositional check models : 0
% 0.15/0.45 % Propositional check unsatisfiable : 0
% 0.15/0.45 % Propositional clauses : 0
% 0.15/0.45 % Propositional clauses after purity: 0
% 0.15/0.45 % Propositional unsat core size : 0
% 0.15/0.45 % Propositional preprocessing time : 0.000
% 0.15/0.45 % Propositional encoding time : 0.000
% 0.15/0.45 % Propositional solver time : 0.000
% 0.15/0.45 % Success case prop preproc time : 0.000
% 0.15/0.45 % Success case prop encoding time : 0.000
% 0.15/0.45 % Success case prop solver time : 0.000
% 0.15/0.45 % Current number of processed clauses : 79
% 0.15/0.45 % Positive orientable unit clauses : 20
% 0.15/0.45 % Positive unorientable unit clauses: 1
% 0.15/0.45 % Negative unit clauses : 4
% 0.15/0.45 % Non-unit-clauses : 54
% 0.15/0.45 % Current number of unprocessed clauses: 85
% 0.15/0.45 % ...number of literals in the above : 217
% 0.15/0.45 % Current number of archived formulas : 0
% 0.15/0.45 % Current number of archived clauses : 18
% 0.15/0.45 % Clause-clause subsumption calls (NU) : 500
% 0.15/0.45 % Rec. Clause-clause subsumption calls : 341
% 0.15/0.45 % Non-unit clause-clause subsumptions : 11
% 0.15/0.45 % Unit Clause-clause subsumption calls : 76
% 0.15/0.45 % Rewrite failures with RHS unbound : 0
% 0.15/0.45 % BW rewrite match attempts : 4
% 0.15/0.45 % BW rewrite match successes : 2
% 0.15/0.45 % Condensation attempts : 0
% 0.15/0.45 % Condensation successes : 0
% 0.15/0.45 % Termbank termtop insertions : 5374
% 0.15/0.45 % Search garbage collected termcells : 158
% 0.15/0.45
% 0.15/0.45 % -------------------------------------------------
% 0.15/0.45 % User time : 0.013 s
% 0.15/0.45 % System time : 0.002 s
% 0.15/0.45 % Total time : 0.016 s
% 0.15/0.45 % Maximum resident set size: 3412 pages
% 0.15/0.45
% 0.15/0.45 % -------------------------------------------------
% 0.15/0.45 % User time : 0.042 s
% 0.15/0.45 % System time : 0.021 s
% 0.15/0.45 % Total time : 0.063 s
% 0.15/0.45 % Maximum resident set size: 4608 pages
% 0.15/0.45 % E exiting
%------------------------------------------------------------------------------