%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO559^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 : Wed Sep 30 08:43:25 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 1 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 87 ( 17 ~; 9 |; 3 &; 52 @)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 15 ( 2 ^; 11 !; 2 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
epso: ( $o > $o ) > $o ).
thf(decl_24,type,
epsoo: ( ( $o > $o ) > $o ) > $o > $o ).
thf(c,conjecture,
( ( epsoo @ epso @ ~ $true )
=> ( epsoo @ epso @ $true ) ),
file('/export/starexec/sandbox/tmp/tmp.00hojnuOmf/E---3.1_3455027.p',c) ).
thf(choiceaxo,axiom,
! [X1: $o > $o] :
( ? [X2: $o] : ( X1 @ X2 )
=> ( X1 @ ( epso @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.00hojnuOmf/E---3.1_3455027.p',choiceaxo) ).
thf(choiceaxoo,axiom,
! [X3: ( $o > $o ) > $o] :
( ? [X4: $o > $o] : ( X3 @ X4 )
=> ( X3 @ ( epsoo @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.00hojnuOmf/E---3.1_3455027.p',choiceaxoo) ).
thf(c_0_3,negated_conjecture,
~ ( ( epsoo @ epso @ ~ $true )
=> ( epsoo @ epso @ $true ) ),
inference(assume_negation,[status(cth)],[c]) ).
thf(c_0_4,negated_conjecture,
~ ( ( ( ~ ~ $true
| ( epsoo @ epso @ $true ) )
& ( ~ $true
| ( epsoo @ epso @ $false ) ) )
=> ( epsoo @ epso @ $true ) ),
inference(fool_unroll,[status(thm)],[c_0_3]) ).
thf(c_0_5,plain,
! [X9: $o > $o,X10: $o] :
( ~ ( X9 @ X10 )
| ( X9 @ ( epso @ X9 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceaxo])])])]) ).
thf(c_0_6,negated_conjecture,
( ( $true
| ( epsoo @ epso @ $true ) )
& ( ~ $true
| ( epsoo @ epso @ $false ) )
& ~ ( epsoo @ epso @ $true ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).
thf(c_0_7,plain,
! [X1: $o > $o,X2: $o] :
( ( X1 @ ( epso @ X1 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
( ( epsoo @ epso @ ~ $true )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X11: ( $o > $o ) > $o,X12: $o > $o] :
( ~ ( X11 @ X12 )
| ( X11 @ ( epsoo @ X11 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceaxoo])])])]) ).
thf(c_0_10,plain,
! [X2: $o] :
( ( epso
@ ^ [Z0: $o] : ( Z0 = X2 ) )
<=> X2 ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_7]) ).
thf(c_0_11,negated_conjecture,
epsoo @ epso @ ~ $true,
inference(cn,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X3: ( $o > $o ) > $o,X1: $o > $o] :
( ( X3 @ ( epsoo @ X3 ) )
| ~ ( X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
( epso
@ ^ [Z0: $o] : Z0 ),
inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_10])]) ).
thf(c_0_14,negated_conjecture,
epsoo @ epso @ ( epso @ ( epsoo @ epso ) ),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
thf(c_0_15,plain,
epso @ ( epsoo @ epso ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
~ ( epsoo @ epso @ $true ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO559^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n008.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 17:15:54 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.00hojnuOmf/E---3.1_3455027.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSCHHA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.08/0.25 % Starting ehoh_best_sine with 300s (1) cores
% 0.08/0.25 % Starting ehoh_best_nonlift with 300s (1) cores
% 0.08/0.25 % Starting lpo4_lambdas_fix with 300s (1) cores
% 0.08/0.25 % ho_unfolding_6 with pid 3455040 completed with status 0
% 0.08/0.25 % Result found by ho_unfolding_6
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSCHHA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HHUNF-FFSF00-SHHFFMBC
% 0.08/0.25 % partial match(2): HGUNF-FFSF00-SHHFFMBN
% 0.08/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.25 % Starting ho_unfolding_6 with 151s (1) cores
% 0.08/0.25 % Starting ehoh_best_sine with 136s (1) cores
% 0.08/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 136s (1) cores
% 0.08/0.25 % Starting sh2lt with 136s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 3455044 completed with status 10
% 0.08/0.25 % Starting sh2l with 136s (1) cores
% 0.08/0.25 % sh2l with pid 3455052 completed with status 0
% 0.08/0.25 % Result found by sh2l
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSCHHA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HHUNF-FFSF00-SHHFFMBC
% 0.08/0.25 % partial match(2): HGUNF-FFSF00-SHHFFMBN
% 0.08/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.25 % Starting ho_unfolding_6 with 151s (1) cores
% 0.08/0.25 % Starting ehoh_best_sine with 136s (1) cores
% 0.08/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 136s (1) cores
% 0.08/0.25 % Starting sh2lt with 136s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 3455044 completed with status 10
% 0.08/0.25 % Starting sh2l with 136s (1) cores
% 0.08/0.25 % Preprocessing time : 0.001 s
% 0.08/0.25 % Presaturation interreduction done
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25 % Parsed axioms : 5
% 0.08/0.25 % Removed by relevancy pruning/SinE : 0
% 0.08/0.25 % Initial clauses : 7
% 0.08/0.25 % Removed in clause preprocessing : 3
% 0.08/0.25 % Initial clauses in saturation : 4
% 0.08/0.25 % Processed clauses : 19
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 3
% 0.08/0.25 % ...remaining for further processing : 16
% 0.08/0.25 % Other redundant clauses eliminated : 0
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 1
% 0.08/0.25 % Backward-rewritten : 1
% 0.08/0.25 % Generated clauses : 23
% 0.08/0.25 % ...of the previous two non-redundant : 16
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 6
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 0
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 2
% 0.08/0.25 % ...of those cached : 0
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 9
% 0.08/0.25 % Positive orientable unit clauses : 3
% 0.08/0.25 % Positive unorientable unit clauses: 1
% 0.08/0.25 % Negative unit clauses : 2
% 0.08/0.25 % Non-unit-clauses : 3
% 0.08/0.25 % Current number of unprocessed clauses: 5
% 0.08/0.25 % ...number of literals in the above : 8
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 7
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 4
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 4
% 0.08/0.25 % Non-unit clause-clause subsumptions : 3
% 0.08/0.25 % Unit Clause-clause subsumption calls : 4
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 18
% 0.08/0.25 % BW rewrite match successes : 3
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 1340
% 0.08/0.25 % Search garbage collected termcells : 94
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.006 s
% 0.08/0.25 % System time : 0.001 s
% 0.08/0.25 % Total time : 0.007 s
% 0.08/0.25 % Maximum resident set size: 3632 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.016 s
% 0.08/0.25 % System time : 0.008 s
% 0.08/0.25 % Total time : 0.024 s
% 0.08/0.25 % Maximum resident set size: 4864 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------