%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM409+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 01:48:59 PM UTC 2026
% Result : Theorem 0.24s 0.62s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 11 unt; 0 def)
% Number of atoms : 108 ( 5 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 117 ( 49 ~; 45 |; 13 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 39 ( 3 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(fc8_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( relation(relation_rng(X1))
& empty(relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(fc7_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( relation(relation_dom(X1))
& empty(relation_dom(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
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/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(d7_ordinal1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ( transfinite_sequence(X1)
<=> ordinal(relation_dom(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_ordinal1) ).
fof(t45_ordinal1,conjecture,
! [X1] : transfinite_sequence_of(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_ordinal1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(cc3_ordinal1,axiom,
! [X1] :
( empty(X1)
=> ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(c_0_11,plain,
! [X12] :
( X12 = empty_set
| ~ empty(X12) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])]) ).
fof(c_0_12,plain,
! [X18] :
( ( ~ empty(X18)
| relation(relation_rng(X18)) )
& ( ~ empty(X18)
| empty(relation_rng(X18)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc8_relat_1])])])]) ).
fof(c_0_13,plain,
! [X45] :
( ( ~ empty(X45)
| relation(relation_dom(X45)) )
& ( ~ empty(X45)
| empty(relation_dom(X45)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])])]) ).
fof(c_0_14,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])])])]) ).
cnf(c_0_15,plain,
( ~ empty(X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ empty(X1)
| empty(relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X14] : subset(empty_set,X14),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(c_0_18,plain,
! [X22] :
( function(X22)
| ~ empty(X22) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])])]) ).
fof(c_0_19,plain,
! [X25] :
( relation(X25)
| ~ empty(X25) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])])]) ).
fof(c_0_20,plain,
! [X20] :
( ( ~ function(X20)
| ~ relation(X20)
| transfinite_sequence(X20)
| ~ ordinal(relation_dom(X20)) )
& ( ~ function(X20)
| ~ relation(X20)
| ordinal(relation_dom(X20))
| ~ transfinite_sequence(X20) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_ordinal1])])])]) ).
cnf(c_0_21,plain,
( ~ empty(X1)
| empty(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_22,negated_conjecture,
~ ! [X1] : transfinite_sequence_of(empty_set,X1),
inference(assume_negation,[status(cth)],[t45_ordinal1]) ).
cnf(c_0_23,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_14]) ).
cnf(c_0_24,plain,
( ~ empty(X1)
| relation_rng(X1) = empty_set ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_25,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( ~ empty(X1)
| function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
( ~ empty(X1)
| relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ ordinal(relation_dom(X1))
| transfinite_sequence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( ~ empty(X1)
| relation_dom(X1) = empty_set ),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
fof(c_0_30,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_22])])])]) ).
cnf(c_0_31,plain,
( ~ empty(X1)
| ~ transfinite_sequence(X1)
| transfinite_sequence_of(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),c_0_26]),c_0_27]) ).
cnf(c_0_32,plain,
( ~ empty(X1)
| ~ ordinal(empty_set)
| transfinite_sequence(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26]),c_0_27]) ).
cnf(c_0_33,negated_conjecture,
~ transfinite_sequence_of(empty_set,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
( ~ empty(X1)
| ~ ordinal(empty_set)
| transfinite_sequence_of(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
fof(c_0_36,plain,
! [X48] :
( ( ~ empty(X48)
| ordinal(X48) )
& ( ~ empty(X48)
| epsilon_connected(X48) )
& ( ~ empty(X48)
| epsilon_transitive(X48) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_ordinal1])])])]) ).
cnf(c_0_37,negated_conjecture,
~ ordinal(empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_38,plain,
( ~ empty(X1)
| ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM409+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n002.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 02:30:01 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.55 Running first-order theorem proving
% 0.24/0.55 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
% 0.24/0.62 % Version: 3.5.1
% 0.24/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.62 % Starting sh5l with 300s (1) cores
% 0.24/0.62 % new_bool_3 with pid 2233534 completed with status 0
% 0.24/0.62 % Result found by new_bool_3
% 0.24/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.62 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.62 % Search class: FGHSM-FFMM11-SFFFFFNN
% 0.24/0.62 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.62 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.62 % SubtermCWHack with pid 2233537 completed with status 0
% 0.24/0.62 % Result found by SubtermCWHack
% 0.24/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.62 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.62 % Search class: FGHSM-FFMM11-SFFFFFNN
% 0.24/0.62 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.62 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.62 % Preprocessing time : 0.002 s
% 0.24/0.62
% 0.24/0.62 % Proof found!
% 0.24/0.62 % SZS status Theorem
% 0.24/0.62 % SZS output start CNFRefutation
% See solution above
% 0.24/0.62 % Parsed axioms : 51
% 0.24/0.62 % Removed by relevancy pruning/SinE : 15
% 0.24/0.62 % Initial clauses : 60
% 0.24/0.62 % Removed in clause preprocessing : 0
% 0.24/0.62 % Initial clauses in saturation : 60
% 0.24/0.62 % Processed clauses : 189
% 0.24/0.62 % ...of these trivial : 1
% 0.24/0.62 % ...subsumed : 76
% 0.24/0.62 % ...remaining for further processing : 112
% 0.24/0.62 % Other redundant clauses eliminated : 0
% 0.24/0.62 % Clauses deleted for lack of memory : 0
% 0.24/0.62 % Backward-subsumed : 4
% 0.24/0.62 % Backward-rewritten : 6
% 0.24/0.62 % Generated clauses : 289
% 0.24/0.62 % ...of the previous two non-redundant : 233
% 0.24/0.62 % ...aggressively subsumed : 0
% 0.24/0.62 % Contextual simplify-reflections : 9
% 0.24/0.62 % Paramodulations : 289
% 0.24/0.62 % Factorizations : 0
% 0.24/0.62 % NegExts : 0
% 0.24/0.62 % Equation resolutions : 0
% 0.24/0.62 % Disequality decompositions : 0
% 0.24/0.62 % Total rewrite steps : 48
% 0.24/0.62 % ...of those cached : 31
% 0.24/0.62 % Propositional unsat checks : 0
% 0.24/0.62 % Propositional check models : 0
% 0.24/0.62 % Propositional check unsatisfiable : 0
% 0.24/0.62 % Propositional clauses : 0
% 0.24/0.62 % Propositional clauses after purity: 0
% 0.24/0.62 % Propositional unsat core size : 0
% 0.24/0.62 % Propositional preprocessing time : 0.000
% 0.24/0.62 % Propositional encoding time : 0.000
% 0.24/0.62 % Propositional solver time : 0.000
% 0.24/0.62 % Success case prop preproc time : 0.000
% 0.24/0.62 % Success case prop encoding time : 0.000
% 0.24/0.62 % Success case prop solver time : 0.000
% 0.24/0.62 % Current number of processed clauses : 102
% 0.24/0.62 % Positive orientable unit clauses : 26
% 0.24/0.62 % Positive unorientable unit clauses: 0
% 0.24/0.62 % Negative unit clauses : 5
% 0.24/0.62 % Non-unit-clauses : 71
% 0.24/0.62 % Current number of unprocessed clauses: 101
% 0.24/0.62 % ...number of literals in the above : 461
% 0.24/0.62 % Current number of archived formulas : 0
% 0.24/0.62 % Current number of archived clauses : 10
% 0.24/0.62 % Clause-clause subsumption calls (NU) : 1337
% 0.24/0.62 % Rec. Clause-clause subsumption calls : 1060
% 0.24/0.62 % Non-unit clause-clause subsumptions : 87
% 0.24/0.62 % Unit Clause-clause subsumption calls : 24
% 0.24/0.62 % Rewrite failures with RHS unbound : 0
% 0.24/0.62 % BW rewrite match attempts : 4
% 0.24/0.62 % BW rewrite match successes : 3
% 0.24/0.62 % Condensation attempts : 0
% 0.24/0.62 % Condensation successes : 0
% 0.24/0.62 % Termbank termtop insertions : 5806
% 0.24/0.62 % Search garbage collected termcells : 527
% 0.24/0.62
% 0.24/0.62 % -------------------------------------------------
% 0.24/0.62 % User time : 0.022 s
% 0.24/0.62 % System time : 0.004 s
% 0.24/0.62 % Total time : 0.026 s
% 0.24/0.62 % Maximum resident set size: 3620 pages
% 0.24/0.63
% 0.24/0.63 % -------------------------------------------------
% 0.24/0.63 % User time : 0.024 s
% 0.24/0.63 % System time : 0.012 s
% 0.24/0.63 % Total time : 0.036 s
% 0.24/0.63 % Maximum resident set size: 4608 pages
% 0.24/0.63 % E exiting
%------------------------------------------------------------------------------