%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM412+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 : n019.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 01:54:56 PM UTC 2026
% Result : Theorem 0.15s 0.51s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 95 ( 38 ~; 35 |; 12 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 45 ( 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(t47_ordinal1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> ! [X3] :
( transfinite_sequence_of(X3,X1)
=> transfinite_sequence_of(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_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/sandbox2/benchmark/theBenchmark.p',t48_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/sandbox2/benchmark/theBenchmark.p',dt_k2_ordinal1) ).
fof(c_0_5,plain,
! [X7,X8] :
( ( ~ transfinite_sequence(X8)
| ~ function(X8)
| ~ relation(X8)
| transfinite_sequence_of(X8,X7)
| ~ subset(relation_rng(X8),X7) )
& ( ~ transfinite_sequence(X8)
| ~ function(X8)
| ~ relation(X8)
| subset(relation_rng(X8),X7)
| ~ transfinite_sequence_of(X8,X7) ) ),
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,
! [X9,X10] :
( ( ~ transfinite_sequence_of(X10,X9)
| transfinite_sequence(X10) )
& ( ~ transfinite_sequence_of(X10,X9)
| function(X10) )
& ( ~ transfinite_sequence_of(X10,X9)
| relation(X10) ) ),
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,plain,
! [X13,X14,X15] :
( transfinite_sequence_of(X15,X14)
| ~ transfinite_sequence_of(X15,X13)
| ~ subset(X13,X14) ),
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_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,
~ ! [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_13,plain,
( ~ transfinite_sequence_of(X3,X1)
| ~ subset(X1,X2)
| transfinite_sequence_of(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
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]) ).
fof(c_0_15,plain,
! [X16,X17] :
( transfinite_sequence_of(tseq_dom_restriction(X16,X17),relation_rng(X16))
| ~ ordinal(X17)
| ~ transfinite_sequence(X16)
| ~ function(X16)
| ~ relation(X16) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_ordinal1])])]) ).
fof(c_0_16,negated_conjecture,
( ~ transfinite_sequence_of(tseq_dom_restriction(esk2_0,esk3_0),esk1_0)
& ordinal(esk3_0)
& transfinite_sequence_of(esk2_0,esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_17,plain,
( ~ transfinite_sequence_of(X3,X2)
| ~ transfinite_sequence_of(X1,relation_rng(X3))
| transfinite_sequence_of(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,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_15]) ).
cnf(c_0_19,negated_conjecture,
~ transfinite_sequence_of(tseq_dom_restriction(esk2_0,esk3_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( ~ ordinal(X2)
| ~ transfinite_sequence_of(X1,X3)
| transfinite_sequence_of(tseq_dom_restriction(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_9]),c_0_10]),c_0_11]) ).
cnf(c_0_21,negated_conjecture,
transfinite_sequence_of(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
ordinal(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[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])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM412+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:28:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 0.15/0.51 % Version: 3.5.1
% 0.15/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.51 % Starting sh5l with 300s (1) cores
% 0.15/0.51 % new_bool_3 with pid 1491491 completed with status 0
% 0.15/0.51 % Result found by new_bool_3
% 0.15/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.51 % Search class: FGHSS-FFMM21-SFFFFFNN
% 0.15/0.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.51 % SubtermCWHack with pid 1491499 completed with status 0
% 0.15/0.51 % Result found by SubtermCWHack
% 0.15/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.51 % Search class: FGHSS-FFMM21-SFFFFFNN
% 0.15/0.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.51 % Preprocessing time : 0.001 s
% 0.15/0.51
% 0.15/0.51 % Proof found!
% 0.15/0.51 % SZS status Theorem
% 0.15/0.51 % SZS output start CNFRefutation
% See solution above
% 0.15/0.51 % Parsed axioms : 48
% 0.15/0.51 % Removed by relevancy pruning/SinE : 10
% 0.15/0.51 % Initial clauses : 74
% 0.15/0.51 % Removed in clause preprocessing : 0
% 0.15/0.51 % Initial clauses in saturation : 74
% 0.15/0.51 % Processed clauses : 462
% 0.15/0.51 % ...of these trivial : 10
% 0.15/0.51 % ...subsumed : 205
% 0.15/0.51 % ...remaining for further processing : 247
% 0.15/0.51 % Other redundant clauses eliminated : 0
% 0.15/0.51 % Clauses deleted for lack of memory : 0
% 0.15/0.51 % Backward-subsumed : 19
% 0.15/0.51 % Backward-rewritten : 30
% 0.15/0.51 % Generated clauses : 1379
% 0.15/0.51 % ...of the previous two non-redundant : 1078
% 0.15/0.51 % ...aggressively subsumed : 0
% 0.15/0.51 % Contextual simplify-reflections : 14
% 0.15/0.51 % Paramodulations : 1379
% 0.15/0.51 % Factorizations : 0
% 0.15/0.51 % NegExts : 0
% 0.15/0.51 % Equation resolutions : 0
% 0.15/0.51 % Disequality decompositions : 0
% 0.15/0.51 % Total rewrite steps : 698
% 0.15/0.51 % ...of those cached : 616
% 0.15/0.51 % Propositional unsat checks : 0
% 0.15/0.51 % Propositional check models : 0
% 0.15/0.51 % Propositional check unsatisfiable : 0
% 0.15/0.51 % Propositional clauses : 0
% 0.15/0.51 % Propositional clauses after purity: 0
% 0.15/0.51 % Propositional unsat core size : 0
% 0.15/0.51 % Propositional preprocessing time : 0.000
% 0.15/0.51 % Propositional encoding time : 0.000
% 0.15/0.51 % Propositional solver time : 0.000
% 0.15/0.51 % Success case prop preproc time : 0.000
% 0.15/0.51 % Success case prop encoding time : 0.000
% 0.15/0.51 % Success case prop solver time : 0.000
% 0.15/0.51 % Current number of processed clauses : 198
% 0.15/0.51 % Positive orientable unit clauses : 56
% 0.15/0.51 % Positive unorientable unit clauses: 0
% 0.15/0.51 % Negative unit clauses : 7
% 0.15/0.51 % Non-unit-clauses : 135
% 0.15/0.51 % Current number of unprocessed clauses: 654
% 0.15/0.51 % ...number of literals in the above : 2390
% 0.15/0.51 % Current number of archived formulas : 0
% 0.15/0.51 % Current number of archived clauses : 49
% 0.15/0.51 % Clause-clause subsumption calls (NU) : 6321
% 0.15/0.51 % Rec. Clause-clause subsumption calls : 4500
% 0.15/0.51 % Non-unit clause-clause subsumptions : 223
% 0.15/0.51 % Unit Clause-clause subsumption calls : 279
% 0.15/0.51 % Rewrite failures with RHS unbound : 0
% 0.15/0.51 % BW rewrite match attempts : 35
% 0.15/0.51 % BW rewrite match successes : 9
% 0.15/0.51 % Condensation attempts : 0
% 0.15/0.51 % Condensation successes : 0
% 0.15/0.51 % Termbank termtop insertions : 18031
% 0.15/0.51 % Search garbage collected termcells : 554
% 0.15/0.51
% 0.15/0.51 % -------------------------------------------------
% 0.15/0.51 % User time : 0.030 s
% 0.15/0.51 % System time : 0.003 s
% 0.15/0.51 % Total time : 0.032 s
% 0.15/0.51 % Maximum resident set size: 3672 pages
% 0.15/0.51
% 0.15/0.51 % -------------------------------------------------
% 0.15/0.51 % User time : 0.032 s
% 0.15/0.51 % System time : 0.007 s
% 0.15/0.51 % Total time : 0.039 s
% 0.15/0.51 % Maximum resident set size: 4864 pages
% 0.15/0.51 % E exiting
%------------------------------------------------------------------------------