%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM172-1 : 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 : n026.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 01:44:27 PM UTC 2026
% Result : Unsatisfiable 1.55s 0.91s
% Output : CNFRefutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of clauses : 55 ( 19 unt; 15 nHn; 33 RR)
% Number of literals : 108 ( 34 equ; 41 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; 3 con; 0-2 aty)
% Number of variables : 85 ( 10 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(successor,axiom,
union(X1,singleton(X1)) = successor(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',successor) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
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(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_successor_is_different_2,negated_conjecture,
successor(x) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_successor_is_different_2) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
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(intersection2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(regularity2,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
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_successor_is_different_1,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_successor_is_different_1) ).
cnf(c_0_15,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_17,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_15 ).
cnf(c_0_18,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_19,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_16 ).
cnf(c_0_20,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_21,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,axiom,
union(X1,singleton(X1)) = successor(X1),
successor ).
cnf(c_0_23,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_24,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_26,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_27,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
cnf(c_0_28,negated_conjecture,
successor(x) = x,
prove_successor_is_different_2 ).
cnf(c_0_29,plain,
union(X1,unordered_pair(X1,X1)) = successor(X1),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_31,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_32,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_26 ).
cnf(c_0_34,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
cnf(c_0_35,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_27 ).
cnf(c_0_36,negated_conjecture,
complement(intersection(complement(x),complement(unordered_pair(x,x)))) = x,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_37,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_31 ).
cnf(c_0_38,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
regularity2 ).
cnf(c_0_39,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_32]),c_0_21]) ).
cnf(c_0_40,plain,
( unordered_pair(X1,X2) = null_class
| regular(unordered_pair(X1,X2)) = X2
| regular(unordered_pair(X1,X2)) = X1 ),
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
cnf(c_0_41,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_34 ).
cnf(c_0_42,negated_conjecture,
( ~ member(X1,universal_class)
| member(X1,x)
| member(X1,intersection(complement(x),complement(unordered_pair(x,x)))) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
( ~ member(X2,X1)
| ~ member(X2,regular(X1))
| X1 = null_class ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_44,plain,
( unordered_pair(X1,X1) = null_class
| regular(unordered_pair(X1,X1)) = X1 ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_40])]) ).
cnf(c_0_45,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[unordered_pair2]) ).
cnf(c_0_46,negated_conjecture,
( ~ member(X1,universal_class)
| member(X1,x)
| member(X1,complement(unordered_pair(x,x))) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
( ~ member(X2,X1)
| ~ member(X2,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
c_0_45 ).
cnf(c_0_49,negated_conjecture,
( ~ member(X1,unordered_pair(x,x))
| member(X1,x) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_46]),c_0_21]) ).
cnf(c_0_50,negated_conjecture,
member(x,universal_class),
prove_successor_is_different_1 ).
cnf(c_0_51,plain,
( ~ member(X1,X1)
| unordered_pair(X1,X1) = null_class ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_21]) ).
cnf(c_0_52,negated_conjecture,
member(x,x),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_48]),c_0_50])]) ).
cnf(c_0_53,negated_conjecture,
unordered_pair(x,x) = null_class,
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_53]),c_0_50])]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM172-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.47 % Computer : n026.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Mon Sep 21 02:12:38 UTC 2026
% 0.20/0.48 % CPUTime :
% 0.20/0.48 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.53 Running first-order theorem proving
% 0.25/0.53 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
% 1.55/0.91 % Version: 3.5.1
% 1.55/0.91 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.55/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.55/0.91 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.55/0.91 % Starting new_bool_3 with 300s (1) cores
% 1.55/0.91 % Starting new_bool_1 with 300s (1) cores
% 1.55/0.91 % Starting sh5l with 300s (1) cores
% 1.55/0.91 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1145408 completed with status 0
% 1.55/0.91 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.55/0.91 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.55/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.55/0.91 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.55/0.91 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.55/0.91 % No SInE strategy applied
% 1.55/0.91 % Search class: FGHSM-FFLM31-DFFFFFNN
% 1.55/0.91 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.55/0.91 % Starting SubtermCWHack with 136s (1) cores
% 1.55/0.91 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.55/0.91 % Starting new_bool_3 with 311s (1) cores
% 1.55/0.91 % Starting new_bool_1 with 308s (1) cores
% 1.55/0.91 % Starting sh5l with 304s (1) cores
% 1.55/0.91 % sh5l with pid 1145418 completed with status 0
% 1.55/0.91 % Result found by sh5l
% 1.55/0.91 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.55/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.55/0.91 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.55/0.91 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.55/0.91 % No SInE strategy applied
% 1.55/0.91 % Search class: FGHSM-FFLM31-DFFFFFNN
% 1.55/0.91 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.55/0.91 % Starting SubtermCWHack with 136s (1) cores
% 1.55/0.91 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.55/0.91 % Starting new_bool_3 with 311s (1) cores
% 1.55/0.91 % Starting new_bool_1 with 308s (1) cores
% 1.55/0.91 % Starting sh5l with 304s (1) cores
% 1.55/0.91 % Preprocessing time : 0.003 s
% 1.55/0.91 % Presaturation interreduction done
% 1.55/0.91
% 1.55/0.91 % Proof found!
% 1.55/0.91 % SZS status Unsatisfiable
% 1.55/0.91 % SZS output start CNFRefutation
% See solution above
% 1.55/0.91 % Parsed axioms : 160
% 1.55/0.91 % Removed by relevancy pruning/SinE : 0
% 1.55/0.91 % Initial clauses : 160
% 1.55/0.91 % Removed in clause preprocessing : 19
% 1.55/0.91 % Initial clauses in saturation : 141
% 1.55/0.91 % Processed clauses : 979
% 1.55/0.91 % ...of these trivial : 3
% 1.55/0.91 % ...subsumed : 339
% 1.55/0.91 % ...remaining for further processing : 637
% 1.55/0.91 % Other redundant clauses eliminated : 8
% 1.55/0.91 % Clauses deleted for lack of memory : 0
% 1.55/0.91 % Backward-subsumed : 18
% 1.55/0.91 % Backward-rewritten : 29
% 1.55/0.91 % Generated clauses : 2410
% 1.55/0.91 % ...of the previous two non-redundant : 2000
% 1.55/0.91 % ...aggressively subsumed : 0
% 1.55/0.91 % Contextual simplify-reflections : 18
% 1.55/0.91 % Paramodulations : 2400
% 1.55/0.91 % Factorizations : 2
% 1.55/0.91 % NegExts : 0
% 1.55/0.91 % Equation resolutions : 8
% 1.55/0.91 % Disequality decompositions : 0
% 1.55/0.91 % Total rewrite steps : 899
% 1.55/0.91 % ...of those cached : 785
% 1.55/0.91 % Propositional unsat checks : 0
% 1.55/0.91 % Propositional check models : 0
% 1.55/0.91 % Propositional check unsatisfiable : 0
% 1.55/0.91 % Propositional clauses : 0
% 1.55/0.91 % Propositional clauses after purity: 0
% 1.55/0.91 % Propositional unsat core size : 0
% 1.55/0.91 % Propositional preprocessing time : 0.000
% 1.55/0.91 % Propositional encoding time : 0.000
% 1.55/0.91 % Propositional solver time : 0.000
% 1.55/0.91 % Success case prop preproc time : 0.000
% 1.55/0.91 % Success case prop encoding time : 0.000
% 1.55/0.91 % Success case prop solver time : 0.000
% 1.55/0.91 % Current number of processed clauses : 444
% 1.55/0.91 % Positive orientable unit clauses : 53
% 1.55/0.91 % Positive unorientable unit clauses: 3
% 1.55/0.91 % Negative unit clauses : 1
% 1.55/0.91 % Non-unit-clauses : 387
% 1.55/0.91 % Current number of unprocessed clauses: 1267
% 1.55/0.91 % ...number of literals in the above : 4200
% 1.55/0.91 % Current number of archived formulas : 0
% 1.55/0.91 % Current number of archived clauses : 206
% 1.55/0.91 % Clause-clause subsumption calls (NU) : 18016
% 1.55/0.91 % Rec. Clause-clause subsumption calls : 13208
% 1.55/0.91 % Non-unit clause-clause subsumptions : 336
% 1.55/0.91 % Unit Clause-clause subsumption calls : 715
% 1.55/0.91 % Rewrite failures with RHS unbound : 16
% 1.55/0.91 % BW rewrite match attempts : 30
% 1.55/0.91 % BW rewrite match successes : 14
% 1.55/0.91 % Condensation attempts : 979
% 1.55/0.91 % Condensation successes : 32
% 1.55/0.91 % Termbank termtop insertions : 84154
% 1.55/0.91 % Search garbage collected termcells : 285
% 1.55/0.91
% 1.55/0.91 % -------------------------------------------------
% 1.55/0.91 % User time : 0.118 s
% 1.55/0.91 % System time : 0.010 s
% 1.55/0.91 % Total time : 0.128 s
% 1.55/0.91 % Maximum resident set size: 3496 pages
% 1.55/0.91
% 1.55/0.91 % -------------------------------------------------
% 1.55/0.91 % User time : 0.884 s
% 1.55/0.91 % System time : 0.070 s
% 1.55/0.91 % Total time : 0.954 s
% 1.55/0.91 % Maximum resident set size: 4864 pages
% 1.55/0.91 % E exiting
%------------------------------------------------------------------------------