%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM011-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 01:44:14 PM UTC 2026
% Result : Unsatisfiable 0.92s 0.59s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 47 ( 21 unt; 6 nHn; 30 RR)
% Number of literals : 82 ( 17 equ; 36 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 : 70 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(complement1,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',complement1) ).
cnf(complement2,axiom,
( ~ little_set(X1)
| member(X1,X2)
| member(X1,complement(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',complement2) ).
cnf(a2,axiom,
( ~ member(X1,X2)
| little_set(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).
cnf(empty_set,axiom,
~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',empty_set) ).
cnf(regularity1,axiom,
( member(f24(X1),X1)
| X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',regularity1) ).
cnf(intersection3,axiom,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection3) ).
cnf(successor,axiom,
successor(X1) = union(X1,singleton_set(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',successor) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(prove_zero_is_first,negated_conjecture,
empty_set = successor(f75),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_is_first) ).
cnf(union,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',union) ).
cnf(intersection2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection2) ).
cnf(a_natural_number,hypothesis,
member(f75,natural_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_natural_number) ).
cnf(non_ordered_pair2,axiom,
( X1 != X2
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair2) ).
cnf(c_0_13,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_14,plain,
( ~ little_set(X1)
| member(X1,X2)
| member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
cnf(c_0_15,plain,
( ~ member(X1,X2)
| little_set(X1) ),
inference(fof_simplification,[status(thm)],[a2]) ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_13 ).
cnf(c_0_17,plain,
( ~ little_set(X1)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_14 ).
cnf(c_0_18,plain,
( ~ member(X1,X2)
| little_set(X1) ),
c_0_15 ).
cnf(c_0_19,plain,
~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
cnf(c_0_20,plain,
( ~ member(X1,complement(complement(X2)))
| member(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_21,axiom,
( member(f24(X1),X1)
| X1 = empty_set ),
regularity1 ).
cnf(c_0_22,plain,
~ member(X1,empty_set),
c_0_19 ).
cnf(c_0_23,plain,
( member(f24(complement(complement(X1))),X1)
| complement(complement(X1)) = empty_set ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_25,plain,
complement(complement(empty_set)) = empty_set,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,axiom,
successor(X1) = union(X1,singleton_set(X1)),
successor ).
cnf(c_0_27,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_28,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_24 ).
cnf(c_0_29,plain,
( ~ little_set(X1)
| member(X1,complement(empty_set)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_25]),c_0_22]) ).
cnf(c_0_30,negated_conjecture,
empty_set = successor(f75),
prove_zero_is_first ).
cnf(c_0_31,plain,
successor(X1) = union(X1,non_ordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
union ).
cnf(c_0_33,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
cnf(c_0_34,plain,
( ~ member(X1,X2)
| member(X1,intersection(X2,complement(empty_set))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_18]) ).
cnf(c_0_35,hypothesis,
member(f75,natural_numbers),
a_natural_number ).
cnf(c_0_36,plain,
( X1 != X2
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
inference(fof_simplification,[status(thm)],[non_ordered_pair2]) ).
cnf(c_0_37,negated_conjecture,
empty_set = complement(intersection(complement(f75),complement(non_ordered_pair(f75,f75)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_38,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_33 ).
cnf(c_0_39,hypothesis,
member(f75,intersection(natural_numbers,complement(empty_set))),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
( X1 != X2
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
c_0_36 ).
cnf(c_0_41,negated_conjecture,
( ~ member(X1,complement(empty_set))
| member(X1,intersection(complement(f75),complement(non_ordered_pair(f75,f75)))) ),
inference(spm,[status(thm)],[c_0_20,c_0_37]) ).
cnf(c_0_42,hypothesis,
member(f75,complement(empty_set)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
( ~ little_set(X1)
| member(X1,non_ordered_pair(X1,X2)) ),
inference(er,[status(thm)],[c_0_40]) ).
cnf(c_0_44,negated_conjecture,
member(f75,intersection(complement(f75),complement(non_ordered_pair(f75,f75)))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
~ member(X1,complement(non_ordered_pair(X1,X2))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_43]),c_0_18]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_44]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM011-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n010.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 01:58:54 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.92/0.59 % Version: 3.5.1
% 0.92/0.59 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.92/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.92/0.59 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.92/0.59 % Starting new_bool_3 with 600s (2) cores
% 0.92/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.92/0.59 % Starting sh5l with 300s (1) cores
% 0.92/0.59 % new_bool_3 with pid 4006319 completed with status 9
% 0.92/0.59 % new_bool_1 with pid 4006320 completed with status 9
% 0.92/0.59 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 4006318 completed with status 0
% 0.92/0.59 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 0.92/0.59 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.92/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.92/0.59 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.92/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.92/0.59 % No SInE strategy applied
% 0.92/0.59 % Search class: FGHSF-FSLS31-DFFFFFNN
% 0.92/0.59 % partial match(1): FGHSF-FSLS31-SFFFFFNN
% 0.92/0.59 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 0.92/0.59 % Starting SubtermCWHack with 109s (1) cores
% 0.92/0.59 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 0.92/0.59 % Starting new_bool_3 with 245s (1) cores
% 0.92/0.59 % Starting new_bool_1 with 245s (1) cores
% 0.92/0.59 % new_bool_3 with pid 4006327 completed with status 0
% 0.92/0.59 % Result found by new_bool_3
% 0.92/0.59 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.92/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.92/0.59 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.92/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.92/0.59 % No SInE strategy applied
% 0.92/0.59 % Search class: FGHSF-FSLS31-DFFFFFNN
% 0.92/0.59 % partial match(1): FGHSF-FSLS31-SFFFFFNN
% 0.92/0.59 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 0.92/0.59 % Starting SubtermCWHack with 109s (1) cores
% 0.92/0.59 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 0.92/0.59 % Starting new_bool_3 with 245s (1) cores
% 0.92/0.59 % Preprocessing time : 0.005 s
% 0.92/0.59 % Presaturation interreduction done
% 0.92/0.59
% 0.92/0.59 % Proof found!
% 0.92/0.59 % SZS status Unsatisfiable
% 0.92/0.59 % SZS output start CNFRefutation
% See solution above
% 0.92/0.59 % Parsed axioms : 221
% 0.92/0.59 % Removed by relevancy pruning/SinE : 0
% 0.92/0.59 % Initial clauses : 221
% 0.92/0.59 % Removed in clause preprocessing : 6
% 0.92/0.59 % Initial clauses in saturation : 215
% 0.92/0.59 % Processed clauses : 1039
% 0.92/0.59 % ...of these trivial : 21
% 0.92/0.59 % ...subsumed : 148
% 0.92/0.59 % ...remaining for further processing : 870
% 0.92/0.59 % Other redundant clauses eliminated : 19
% 0.92/0.59 % Clauses deleted for lack of memory : 0
% 0.92/0.59 % Backward-subsumed : 27
% 0.92/0.59 % Backward-rewritten : 9
% 0.92/0.59 % Generated clauses : 3046
% 0.92/0.59 % ...of the previous two non-redundant : 2689
% 0.92/0.59 % ...aggressively subsumed : 0
% 0.92/0.59 % Contextual simplify-reflections : 13
% 0.92/0.59 % Paramodulations : 3025
% 0.92/0.59 % Factorizations : 2
% 0.92/0.59 % NegExts : 0
% 0.92/0.59 % Equation resolutions : 19
% 0.92/0.59 % Disequality decompositions : 0
% 0.92/0.59 % Total rewrite steps : 502
% 0.92/0.59 % ...of those cached : 382
% 0.92/0.59 % Propositional unsat checks : 0
% 0.92/0.59 % Propositional check models : 0
% 0.92/0.59 % Propositional check unsatisfiable : 0
% 0.92/0.59 % Propositional clauses : 0
% 0.92/0.59 % Propositional clauses after purity: 0
% 0.92/0.59 % Propositional unsat core size : 0
% 0.92/0.59 % Propositional preprocessing time : 0.000
% 0.92/0.59 % Propositional encoding time : 0.000
% 0.92/0.59 % Propositional solver time : 0.000
% 0.92/0.59 % Success case prop preproc time : 0.000
% 0.92/0.59 % Success case prop encoding time : 0.000
% 0.92/0.59 % Success case prop solver time : 0.000
% 0.92/0.59 % Current number of processed clauses : 600
% 0.92/0.59 % Positive orientable unit clauses : 106
% 0.92/0.59 % Positive unorientable unit clauses: 0
% 0.92/0.59 % Negative unit clauses : 114
% 0.92/0.59 % Non-unit-clauses : 380
% 0.92/0.59 % Current number of unprocessed clauses: 2060
% 0.92/0.59 % ...number of literals in the above : 5021
% 0.92/0.59 % Current number of archived formulas : 0
% 0.92/0.59 % Current number of archived clauses : 257
% 0.92/0.59 % Clause-clause subsumption calls (NU) : 43170
% 0.92/0.59 % Rec. Clause-clause subsumption calls : 21445
% 0.92/0.59 % Non-unit clause-clause subsumptions : 93
% 0.92/0.59 % Unit Clause-clause subsumption calls : 3092
% 0.92/0.59 % Rewrite failures with RHS unbound : 0
% 0.92/0.59 % BW rewrite match attempts : 102
% 0.92/0.59 % BW rewrite match successes : 8
% 0.92/0.59 % Condensation attempts : 0
% 0.92/0.59 % Condensation successes : 0
% 0.92/0.59 % Termbank termtop insertions : 54654
% 0.92/0.59 % Search garbage collected termcells : 536
% 0.92/0.59
% 0.92/0.59 % -------------------------------------------------
% 0.92/0.59 % User time : 0.105 s
% 0.92/0.59 % System time : 0.011 s
% 0.92/0.59 % Total time : 0.116 s
% 0.92/0.59 % Maximum resident set size: 4104 pages
% 0.92/0.59
% 0.92/0.59 % -------------------------------------------------
% 0.92/0.59 % User time : 0.518 s
% 0.92/0.59 % System time : 0.081 s
% 0.92/0.59 % Total time : 0.599 s
% 0.92/0.59 % Maximum resident set size: 5120 pages
% 0.92/0.59 % E exiting
%------------------------------------------------------------------------------