%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM410+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 : n007.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 0.16s 0.50s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 69 ( 27 ~; 24 |; 10 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 16 ( 1 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t46_ordinal1,conjecture,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ordinal(relation_dom(X1))
=> transfinite_sequence_of(X1,relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_ordinal1) ).
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(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
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(c_0_4,negated_conjecture,
~ ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ordinal(relation_dom(X1))
=> transfinite_sequence_of(X1,relation_rng(X1)) ) ),
inference(assume_negation,[status(cth)],[t46_ordinal1]) ).
fof(c_0_5,plain,
! [X5,X6] :
( ( ~ transfinite_sequence(X6)
| ~ function(X6)
| ~ relation(X6)
| transfinite_sequence_of(X6,X5)
| ~ subset(relation_rng(X6),X5) )
& ( ~ transfinite_sequence(X6)
| ~ function(X6)
| ~ relation(X6)
| subset(relation_rng(X6),X5)
| ~ transfinite_sequence_of(X6,X5) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_ordinal1])])])]) ).
fof(c_0_6,plain,
! [X27] : subset(X27,X27),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_7,plain,
! [X18] :
( ( ~ function(X18)
| ~ relation(X18)
| transfinite_sequence(X18)
| ~ ordinal(relation_dom(X18)) )
& ( ~ function(X18)
| ~ relation(X18)
| ordinal(relation_dom(X18))
| ~ transfinite_sequence(X18) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_ordinal1])])])]) ).
fof(c_0_8,negated_conjecture,
( ~ transfinite_sequence_of(esk1_0,relation_rng(esk1_0))
& ordinal(relation_dom(esk1_0))
& function(esk1_0)
& relation(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
cnf(c_0_9,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_5]) ).
cnf(c_0_10,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ ordinal(relation_dom(X1))
| transfinite_sequence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
ordinal(relation_dom(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
relation(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
function(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
~ transfinite_sequence_of(esk1_0,relation_rng(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ transfinite_sequence(X1)
| transfinite_sequence_of(X1,relation_rng(X1)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_17,negated_conjecture,
transfinite_sequence(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM410+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 02:25:20 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.45 Running first-order theorem proving
% 0.16/0.46 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
% 0.16/0.50 % Version: 3.5.1
% 0.16/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.50 % Starting sh5l with 300s (1) cores
% 0.16/0.50 % new_bool_3 with pid 4164732 completed with status 0
% 0.16/0.50 % Result found by new_bool_3
% 0.16/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.50 % Search class: FGHSS-FFMM11-SFFFFFNN
% 0.16/0.50 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.50 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.50 % SubtermCWHack with pid 4164735 completed with status 0
% 0.16/0.50 % Result found by SubtermCWHack
% 0.16/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.50 % Search class: FGHSS-FFMM11-SFFFFFNN
% 0.16/0.50 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.50 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.50 % Preprocessing time : 0.002 s
% 0.16/0.50
% 0.16/0.50 % Proof found!
% 0.16/0.50 % SZS status Theorem
% 0.16/0.50 % SZS output start CNFRefutation
% See solution above
% 0.16/0.50 % Parsed axioms : 45
% 0.16/0.50 % Removed by relevancy pruning/SinE : 14
% 0.16/0.50 % Initial clauses : 56
% 0.16/0.50 % Removed in clause preprocessing : 0
% 0.16/0.50 % Initial clauses in saturation : 56
% 0.16/0.50 % Processed clauses : 159
% 0.16/0.50 % ...of these trivial : 0
% 0.16/0.50 % ...subsumed : 50
% 0.16/0.50 % ...remaining for further processing : 109
% 0.16/0.50 % Other redundant clauses eliminated : 0
% 0.16/0.50 % Clauses deleted for lack of memory : 0
% 0.16/0.50 % Backward-subsumed : 11
% 0.16/0.50 % Backward-rewritten : 7
% 0.16/0.50 % Generated clauses : 203
% 0.16/0.50 % ...of the previous two non-redundant : 168
% 0.16/0.50 % ...aggressively subsumed : 0
% 0.16/0.50 % Contextual simplify-reflections : 12
% 0.16/0.50 % Paramodulations : 203
% 0.16/0.50 % Factorizations : 0
% 0.16/0.50 % NegExts : 0
% 0.16/0.50 % Equation resolutions : 0
% 0.16/0.50 % Disequality decompositions : 0
% 0.16/0.50 % Total rewrite steps : 32
% 0.16/0.50 % ...of those cached : 19
% 0.16/0.50 % Propositional unsat checks : 0
% 0.16/0.50 % Propositional check models : 0
% 0.16/0.50 % Propositional check unsatisfiable : 0
% 0.16/0.50 % Propositional clauses : 0
% 0.16/0.50 % Propositional clauses after purity: 0
% 0.16/0.50 % Propositional unsat core size : 0
% 0.16/0.50 % Propositional preprocessing time : 0.000
% 0.16/0.50 % Propositional encoding time : 0.000
% 0.16/0.50 % Propositional solver time : 0.000
% 0.16/0.50 % Success case prop preproc time : 0.000
% 0.16/0.50 % Success case prop encoding time : 0.000
% 0.16/0.50 % Success case prop solver time : 0.000
% 0.16/0.50 % Current number of processed clauses : 91
% 0.16/0.50 % Positive orientable unit clauses : 29
% 0.16/0.50 % Positive unorientable unit clauses: 0
% 0.16/0.50 % Negative unit clauses : 4
% 0.16/0.50 % Non-unit-clauses : 58
% 0.16/0.50 % Current number of unprocessed clauses: 47
% 0.16/0.50 % ...number of literals in the above : 210
% 0.16/0.50 % Current number of archived formulas : 0
% 0.16/0.50 % Current number of archived clauses : 18
% 0.16/0.50 % Clause-clause subsumption calls (NU) : 1283
% 0.16/0.50 % Rec. Clause-clause subsumption calls : 981
% 0.16/0.50 % Non-unit clause-clause subsumptions : 73
% 0.16/0.50 % Unit Clause-clause subsumption calls : 23
% 0.16/0.50 % Rewrite failures with RHS unbound : 0
% 0.16/0.50 % BW rewrite match attempts : 3
% 0.16/0.50 % BW rewrite match successes : 3
% 0.16/0.50 % Condensation attempts : 0
% 0.16/0.50 % Condensation successes : 0
% 0.16/0.50 % Termbank termtop insertions : 4804
% 0.16/0.50 % Search garbage collected termcells : 507
% 0.16/0.50
% 0.16/0.50 % -------------------------------------------------
% 0.16/0.50 % User time : 0.018 s
% 0.16/0.50 % System time : 0.006 s
% 0.16/0.50 % Total time : 0.024 s
% 0.16/0.50 % Maximum resident set size: 3664 pages
% 0.16/0.50
% 0.16/0.50 % -------------------------------------------------
% 0.16/0.50 % User time : 0.021 s
% 0.16/0.50 % System time : 0.013 s
% 0.16/0.50 % Total time : 0.033 s
% 0.16/0.50 % Maximum resident set size: 4608 pages
% 0.16/0.50 % E exiting
%------------------------------------------------------------------------------