%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM409+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 01:54:55 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 60 ( 23 unt; 0 def)
% Number of atoms : 142 ( 5 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 143 ( 61 ~; 53 |; 21 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 78 ( 12 sgn 35 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( empty(X3)
& element(X2,powerset(X3))
& in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(d8_ordinal1,axiom,
! [X1,X2] :
( ( transfinite_sequence(X2)
& function(X2)
& relation(X2) )
=> ( transfinite_sequence_of(X2,X1)
<=> subset(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(dt_m1_ordinal1,axiom,
! [X1,X2] :
( transfinite_sequence_of(X2,X1)
=> ( transfinite_sequence(X2)
& function(X2)
& relation(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( in(X1,X2)
| empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(fc6_relat_1,axiom,
! [X1] :
( ( relation(X1)
& ~ empty(X1) )
=> ~ empty(relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(existence_m1_ordinal1,axiom,
! [X1] :
? [X2] : transfinite_sequence_of(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_ordinal1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(t45_ordinal1,conjecture,
! [X1] : transfinite_sequence_of(empty_set,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_ordinal1) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(fc2_ordinal1,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(c_0_13,plain,
! [X66,X67,X68] :
( ~ empty(X68)
| ~ element(X67,powerset(X68))
| ~ in(X66,X67) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])])]) ).
fof(c_0_14,plain,
! [X16,X17] :
( ( element(X16,powerset(X17))
| ~ subset(X16,X17) )
& ( subset(X16,X17)
| ~ element(X16,powerset(X17)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_15,plain,
! [X6,X7] :
( ( ~ transfinite_sequence(X7)
| ~ function(X7)
| ~ relation(X7)
| transfinite_sequence_of(X7,X6)
| ~ subset(relation_rng(X7),X6) )
& ( ~ transfinite_sequence(X7)
| ~ function(X7)
| ~ relation(X7)
| subset(relation_rng(X7),X6)
| ~ transfinite_sequence_of(X7,X6) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_ordinal1])])])]) ).
fof(c_0_16,plain,
! [X8,X9] :
( ( ~ transfinite_sequence_of(X9,X8)
| transfinite_sequence(X9) )
& ( ~ transfinite_sequence_of(X9,X8)
| function(X9) )
& ( ~ transfinite_sequence_of(X9,X8)
| relation(X9) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_ordinal1])])])]) ).
cnf(c_0_17,plain,
( ~ empty(X3)
| ~ element(X2,powerset(X3))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ transfinite_sequence_of(X1,X2)
| subset(relation_rng(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( ~ transfinite_sequence_of(X1,X2)
| function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( ~ transfinite_sequence_of(X1,X2)
| relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( ~ transfinite_sequence_of(X1,X2)
| transfinite_sequence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,plain,
! [X40,X41] :
( in(X40,X41)
| empty(X41)
| ~ element(X40,X41) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
fof(c_0_24,plain,
! [X59] : element(esk19_1(X59),X59),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_25,plain,
( ~ in(X3,X1)
| ~ empty(X2)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
( ~ transfinite_sequence_of(X1,X2)
| subset(relation_rng(X1),X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]) ).
cnf(c_0_27,plain,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
element(esk19_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_29,plain,
! [X1] :
( ( relation(X1)
& ~ empty(X1) )
=> ~ empty(relation_rng(X1)) ),
inference(fof_simplification,[status(thm)],[fc6_relat_1]) ).
cnf(c_0_30,plain,
( ~ in(X3,relation_rng(X1))
| ~ empty(X2)
| ~ transfinite_sequence_of(X1,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( in(esk19_1(X1),X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_32,plain,
! [X10] : transfinite_sequence_of(esk2_1(X10),X10),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_ordinal1])]) ).
fof(c_0_33,plain,
! [X19] :
( ~ empty(relation_rng(X19))
| ~ relation(X19)
| empty(X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
cnf(c_0_34,plain,
( ~ empty(X2)
| ~ transfinite_sequence_of(X1,X2)
| empty(relation_rng(X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
transfinite_sequence_of(esk2_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_36,plain,
! [X14] :
( X14 = empty_set
| ~ empty(X14) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])]) ).
cnf(c_0_37,plain,
( ~ empty(relation_rng(X1))
| ~ relation(X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
( ~ empty(X1)
| empty(relation_rng(esk2_1(X1))) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
relation(esk2_1(X1)),
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_40,plain,
( ~ empty(X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
( ~ empty(X1)
| empty(esk2_1(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_42,plain,
( ~ empty(X1)
| esk2_1(X1) = empty_set ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,plain,
( ~ empty(X1)
| empty(relation_rng(empty_set)) ),
inference(spm,[status(thm)],[c_0_38,c_0_42]) ).
cnf(c_0_44,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_45,plain,
transfinite_sequence(esk2_1(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_35]) ).
fof(c_0_46,negated_conjecture,
~ ! [X1] : transfinite_sequence_of(empty_set,X1),
inference(assume_negation,[status(cth)],[t45_ordinal1]) ).
cnf(c_0_47,plain,
empty(relation_rng(empty_set)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_48,plain,
! [X12] : subset(empty_set,X12),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_49,plain,
( ~ empty(X1)
| transfinite_sequence(empty_set) ),
inference(spm,[status(thm)],[c_0_45,c_0_42]) ).
fof(c_0_50,negated_conjecture,
~ transfinite_sequence_of(empty_set,esk1_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])]) ).
cnf(c_0_51,plain,
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_rng(X1),X2)
| transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_52,plain,
relation_rng(empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_40,c_0_47]) ).
cnf(c_0_53,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,plain,
transfinite_sequence(empty_set),
inference(spm,[status(thm)],[c_0_49,c_0_44]) ).
cnf(c_0_55,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_56,plain,
function(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]) ).
cnf(c_0_57,negated_conjecture,
~ transfinite_sequence_of(empty_set,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_58,plain,
transfinite_sequence_of(empty_set,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54]),c_0_55]),c_0_56])]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM409+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:27:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.45 % Version: 3.5.1
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % Starting sh5l with 300s (1) cores
% 0.11/0.45 % sh5l with pid 1804953 completed with status 0
% 0.11/0.45 % Result found by sh5l
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % Starting sh5l with 300s (1) cores
% 0.11/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.11/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.11/0.45 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.11/0.45 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.45 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.45 % SubtermCWHack with pid 1804954 completed with status 0
% 0.11/0.45 % Result found by SubtermCWHack
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % Starting sh5l with 300s (1) cores
% 0.11/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.11/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.11/0.45 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.11/0.45 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.45 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.45 % Preprocessing time : 0.002 s
% 0.11/0.45
% 0.11/0.45 % Proof found!
% 0.11/0.45 % SZS status Theorem
% 0.11/0.45 % SZS output start CNFRefutation
% See solution above
% 0.11/0.45 % Parsed axioms : 51
% 0.11/0.45 % Removed by relevancy pruning/SinE : 0
% 0.11/0.45 % Initial clauses : 102
% 0.11/0.45 % Removed in clause preprocessing : 2
% 0.11/0.45 % Initial clauses in saturation : 100
% 0.11/0.45 % Processed clauses : 175
% 0.11/0.45 % ...of these trivial : 6
% 0.11/0.45 % ...subsumed : 34
% 0.11/0.45 % ...remaining for further processing : 135
% 0.11/0.45 % Other redundant clauses eliminated : 1
% 0.11/0.45 % Clauses deleted for lack of memory : 0
% 0.11/0.45 % Backward-subsumed : 1
% 0.11/0.45 % Backward-rewritten : 17
% 0.11/0.45 % Generated clauses : 235
% 0.11/0.45 % ...of the previous two non-redundant : 176
% 0.11/0.45 % ...aggressively subsumed : 0
% 0.11/0.45 % Contextual simplify-reflections : 7
% 0.11/0.45 % Paramodulations : 234
% 0.11/0.45 % Factorizations : 0
% 0.11/0.45 % NegExts : 0
% 0.11/0.45 % Equation resolutions : 1
% 0.11/0.45 % Disequality decompositions : 0
% 0.11/0.45 % Total rewrite steps : 101
% 0.11/0.45 % ...of those cached : 76
% 0.11/0.45 % Propositional unsat checks : 0
% 0.11/0.45 % Propositional check models : 0
% 0.11/0.45 % Propositional check unsatisfiable : 0
% 0.11/0.45 % Propositional clauses : 0
% 0.11/0.45 % Propositional clauses after purity: 0
% 0.11/0.45 % Propositional unsat core size : 0
% 0.11/0.45 % Propositional preprocessing time : 0.000
% 0.11/0.45 % Propositional encoding time : 0.000
% 0.11/0.45 % Propositional solver time : 0.000
% 0.11/0.45 % Success case prop preproc time : 0.000
% 0.11/0.45 % Success case prop encoding time : 0.000
% 0.11/0.45 % Success case prop solver time : 0.000
% 0.11/0.45 % Current number of processed clauses : 116
% 0.11/0.45 % Positive orientable unit clauses : 47
% 0.11/0.45 % Positive unorientable unit clauses: 1
% 0.11/0.45 % Negative unit clauses : 5
% 0.11/0.45 % Non-unit-clauses : 63
% 0.11/0.45 % Current number of unprocessed clauses: 96
% 0.11/0.45 % ...number of literals in the above : 349
% 0.11/0.45 % Current number of archived formulas : 0
% 0.11/0.45 % Current number of archived clauses : 18
% 0.11/0.45 % Clause-clause subsumption calls (NU) : 958
% 0.11/0.45 % Rec. Clause-clause subsumption calls : 855
% 0.11/0.45 % Non-unit clause-clause subsumptions : 41
% 0.11/0.45 % Unit Clause-clause subsumption calls : 71
% 0.11/0.45 % Rewrite failures with RHS unbound : 0
% 0.11/0.45 % BW rewrite match attempts : 10
% 0.11/0.45 % BW rewrite match successes : 9
% 0.11/0.45 % Condensation attempts : 0
% 0.11/0.45 % Condensation successes : 0
% 0.11/0.45 % Termbank termtop insertions : 6401
% 0.11/0.45 % Search garbage collected termcells : 726
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.011 s
% 0.11/0.45 % System time : 0.003 s
% 0.11/0.45 % Total time : 0.013 s
% 0.11/0.45 % Maximum resident set size: 3672 pages
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.012 s
% 0.11/0.45 % System time : 0.008 s
% 0.11/0.45 % Total time : 0.020 s
% 0.11/0.45 % Maximum resident set size: 4864 pages
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------