%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM412+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 : n020.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 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 91 ( 36 ~; 33 |; 12 &)
% ( 1 <=>; 9 =>; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 3 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t48_ordinal1,conjecture,
! [X1,X2] :
( transfinite_sequence_of(X2,X1)
=> ! [X3] :
( ordinal(X3)
=> transfinite_sequence_of(tseq_dom_restriction(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_ordinal1) ).
fof(t47_ordinal1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> ! [X3] :
( transfinite_sequence_of(X3,X1)
=> transfinite_sequence_of(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_ordinal1) ).
fof(dt_k2_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X2)
& transfinite_sequence(X1)
& function(X1)
& relation(X1) )
=> transfinite_sequence_of(tseq_dom_restriction(X1,X2),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_ordinal1) ).
fof(c_0_5,plain,
! [X12,X13] :
( ( ~ transfinite_sequence(X13)
| ~ function(X13)
| ~ relation(X13)
| transfinite_sequence_of(X13,X12)
| ~ subset(relation_rng(X13),X12) )
& ( ~ transfinite_sequence(X13)
| ~ function(X13)
| ~ relation(X13)
| subset(relation_rng(X13),X12)
| ~ transfinite_sequence_of(X13,X12) ) ),
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,
! [X18,X19] :
( ( ~ transfinite_sequence_of(X19,X18)
| transfinite_sequence(X19) )
& ( ~ transfinite_sequence_of(X19,X18)
| function(X19) )
& ( ~ transfinite_sequence_of(X19,X18)
| relation(X19) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_ordinal1])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( transfinite_sequence_of(X2,X1)
=> ! [X3] :
( ordinal(X3)
=> transfinite_sequence_of(tseq_dom_restriction(X2,X3),X1) ) ),
inference(assume_negation,[status(cth)],[t48_ordinal1]) ).
cnf(c_0_8,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_5]) ).
cnf(c_0_9,plain,
( ~ transfinite_sequence_of(X1,X2)
| function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ transfinite_sequence_of(X1,X2)
| relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( ~ transfinite_sequence_of(X1,X2)
| transfinite_sequence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,negated_conjecture,
( ~ transfinite_sequence_of(tseq_dom_restriction(esk18_0,esk19_0),esk17_0)
& ordinal(esk19_0)
& transfinite_sequence_of(esk18_0,esk17_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_13,plain,
! [X54,X55,X56] :
( transfinite_sequence_of(X56,X55)
| ~ transfinite_sequence_of(X56,X54)
| ~ subset(X54,X55) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_ordinal1])])])]) ).
cnf(c_0_14,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_8,c_0_9]),c_0_10]),c_0_11]) ).
cnf(c_0_15,negated_conjecture,
transfinite_sequence_of(esk18_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( ~ transfinite_sequence_of(X3,X1)
| ~ subset(X1,X2)
| transfinite_sequence_of(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
subset(relation_rng(esk18_0),esk17_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_18,plain,
! [X14,X15] :
( transfinite_sequence_of(tseq_dom_restriction(X14,X15),relation_rng(X14))
| ~ ordinal(X15)
| ~ transfinite_sequence(X14)
| ~ function(X14)
| ~ relation(X14) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_ordinal1])])]) ).
cnf(c_0_19,negated_conjecture,
( ~ transfinite_sequence_of(X1,relation_rng(esk18_0))
| transfinite_sequence_of(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( ~ ordinal(X2)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| transfinite_sequence_of(tseq_dom_restriction(X1,X2),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,negated_conjecture,
transfinite_sequence(esk18_0),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_22,negated_conjecture,
relation(esk18_0),
inference(spm,[status(thm)],[c_0_10,c_0_15]) ).
cnf(c_0_23,negated_conjecture,
function(esk18_0),
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_24,negated_conjecture,
~ transfinite_sequence_of(tseq_dom_restriction(esk18_0,esk19_0),esk17_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,negated_conjecture,
( ~ ordinal(X1)
| transfinite_sequence_of(tseq_dom_restriction(esk18_0,X1),esk17_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
ordinal(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM412+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 02:28:17 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.45 % Version: 3.5.1
% 0.14/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.45 % Starting sh5l with 300s (1) cores
% 0.14/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1794084 completed with status 0
% 0.14/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.45 % No SInE strategy applied
% 0.14/0.45 % Search class: FGHSS-FFMM21-SFFFFFNN
% 0.14/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.45 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.14/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.45 % G-E--_208_B07_F1_SE_CS_SP_PS_S4d with pid 1794092 completed with status 0
% 0.14/0.45 % Result found by G-E--_208_B07_F1_SE_CS_SP_PS_S4d
% 0.14/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.45 % No SInE strategy applied
% 0.14/0.45 % Search class: FGHSS-FFMM21-SFFFFFNN
% 0.14/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.45 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.14/0.45 % Preprocessing time : 0.003 s
% 0.14/0.45 % Presaturation interreduction done
% 0.14/0.45
% 0.14/0.45 % Proof found!
% 0.14/0.45 % SZS status Theorem
% 0.14/0.45 % SZS output start CNFRefutation
% See solution above
% 0.14/0.45 % Parsed axioms : 48
% 0.14/0.45 % Removed by relevancy pruning/SinE : 0
% 0.14/0.45 % Initial clauses : 97
% 0.14/0.45 % Removed in clause preprocessing : 2
% 0.14/0.45 % Initial clauses in saturation : 95
% 0.14/0.45 % Processed clauses : 290
% 0.14/0.45 % ...of these trivial : 9
% 0.14/0.45 % ...subsumed : 68
% 0.14/0.45 % ...remaining for further processing : 213
% 0.14/0.45 % Other redundant clauses eliminated : 0
% 0.14/0.45 % Clauses deleted for lack of memory : 0
% 0.14/0.45 % Backward-subsumed : 0
% 0.14/0.45 % Backward-rewritten : 14
% 0.14/0.45 % Generated clauses : 315
% 0.14/0.45 % ...of the previous two non-redundant : 289
% 0.14/0.45 % ...aggressively subsumed : 0
% 0.14/0.45 % Contextual simplify-reflections : 5
% 0.14/0.45 % Paramodulations : 315
% 0.14/0.45 % Factorizations : 0
% 0.14/0.45 % NegExts : 0
% 0.14/0.45 % Equation resolutions : 0
% 0.14/0.45 % Disequality decompositions : 0
% 0.14/0.45 % Total rewrite steps : 109
% 0.14/0.45 % ...of those cached : 83
% 0.14/0.45 % Propositional unsat checks : 0
% 0.14/0.45 % Propositional check models : 0
% 0.14/0.45 % Propositional check unsatisfiable : 0
% 0.14/0.45 % Propositional clauses : 0
% 0.14/0.45 % Propositional clauses after purity: 0
% 0.14/0.45 % Propositional unsat core size : 0
% 0.14/0.45 % Propositional preprocessing time : 0.000
% 0.14/0.45 % Propositional encoding time : 0.000
% 0.14/0.45 % Propositional solver time : 0.000
% 0.14/0.45 % Success case prop preproc time : 0.000
% 0.14/0.45 % Success case prop encoding time : 0.000
% 0.14/0.45 % Success case prop solver time : 0.000
% 0.14/0.45 % Current number of processed clauses : 112
% 0.14/0.45 % Positive orientable unit clauses : 47
% 0.14/0.45 % Positive unorientable unit clauses: 0
% 0.14/0.45 % Negative unit clauses : 5
% 0.14/0.45 % Non-unit-clauses : 60
% 0.14/0.45 % Current number of unprocessed clauses: 171
% 0.14/0.45 % ...number of literals in the above : 655
% 0.14/0.45 % Current number of archived formulas : 0
% 0.14/0.45 % Current number of archived clauses : 101
% 0.14/0.45 % Clause-clause subsumption calls (NU) : 1672
% 0.14/0.45 % Rec. Clause-clause subsumption calls : 853
% 0.14/0.45 % Non-unit clause-clause subsumptions : 67
% 0.14/0.45 % Unit Clause-clause subsumption calls : 55
% 0.14/0.45 % Rewrite failures with RHS unbound : 0
% 0.14/0.45 % BW rewrite match attempts : 4
% 0.14/0.45 % BW rewrite match successes : 4
% 0.14/0.45 % Condensation attempts : 0
% 0.14/0.45 % Condensation successes : 0
% 0.14/0.45 % Termbank termtop insertions : 7002
% 0.14/0.45 % Search garbage collected termcells : 658
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.022 s
% 0.14/0.45 % System time : 0.008 s
% 0.14/0.45 % Total time : 0.030 s
% 0.14/0.45 % Maximum resident set size: 3672 pages
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.076 s
% 0.14/0.45 % System time : 0.025 s
% 0.14/0.45 % Total time : 0.101 s
% 0.14/0.45 % Maximum resident set size: 4864 pages
% 0.14/0.45 % E exiting
%------------------------------------------------------------------------------