%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO311^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:42:45 AM UTC 2026
% Result : Theorem 0.25s 0.36s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 219 ( 0 equ; 0 cnn)
% Maximal formula atoms : 120 ( 18 avg)
% Number of connectives : 403 ( 120 ~; 89 |; 16 &; 174 @)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 1 usr; 2 con; 0-1 aty)
% Number of variables : 12 ( 0 ^; 10 !; 2 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
epred1_0: $o > $o ).
thf(cOMEGA_EXAMPLE2,conjecture,
( ? [X1: $o > $o > $o] :
( ( X1 @ $true @ $true )
& ~ ( X1 @ ~ $true @ ~ $true )
& ~ ( X1 @ ~ $true @ $true )
& ~ ( X1 @ $true @ ~ $true ) )
& ! [X2: $o > $o] :
( ( X2 @ $true )
<=> ( X2
@ ( $true
=> $true ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Wa7OI7mmaX/E---3.1_1543360.p',cOMEGA_EXAMPLE2) ).
thf(c_0_1,negated_conjecture,
~ ( ? [X1: $o > $o > $o] :
( ( X1 @ $true @ $true )
& ~ ( X1 @ ~ $true @ ~ $true )
& ~ ( X1 @ ~ $true @ $true )
& ~ ( X1 @ $true @ ~ $true ) )
& ! [X2: $o > $o] :
( ( X2 @ $true )
<=> ( X2
@ ( $true
=> $true ) ) ) ),
inference(assume_negation,[status(cth)],[cOMEGA_EXAMPLE2]) ).
thf(c_0_2,negated_conjecture,
! [X5: $o > $o > $o] :
( ( $true
| ~ $true
| $true
| ~ ( epred1_0 @ $true )
| ~ ( X5 @ $true @ $true )
| ( X5 @ ~ $true @ ~ $true )
| ( X5 @ ~ $true @ $true )
| ( X5 @ $true @ ~ $true ) )
& ( ~ $true
| ~ $true
| $true
| ~ ( epred1_0 @ $true )
| ~ ( X5 @ $true @ $true )
| ( X5 @ ~ $true @ ~ $true )
| ( X5 @ ~ $true @ $true )
| ( X5 @ $true @ ~ $true ) )
& ( ~ ( epred1_0 @ $false )
| ~ $true
| $true
| ~ ( epred1_0 @ $true )
| ~ ( X5 @ $true @ $true )
| ( X5 @ ~ $true @ ~ $true )
| ( X5 @ ~ $true @ $true )
| ( X5 @ $true @ ~ $true ) )
& ( $true
| ~ ( epred1_0 @ $true )
| ~ ( epred1_0 @ $true )
| ~ ( X5 @ $true @ $true )
| ( X5 @ ~ $true @ ~ $true )
| ( X5 @ ~ $true @ $true )
| ( X5 @ $true @ ~ $true ) )
& ( ~ $true
| ~ ( epred1_0 @ $true )
| ~ ( epred1_0 @ $true )
| ~ ( X5 @ $true @ $true )
| ( X5 @ ~ $true @ ~ $true )
| ( X5 @ ~ $true @ $true )
| ( X5 @ $true @ ~ $true ) )
& ( ~ ( epred1_0 @ $false )
| ~ ( epred1_0 @ $true )
| ~ ( epred1_0 @ $true )
| ~ ( X5 @ $true @ $true )
| ( X5 @ ~ $true @ ~ $true )
| ( X5 @ ~ $true @ $true )
| ( X5 @ $true @ ~ $true ) )
& ( $true
| ( epred1_0 @ $true )
| ( epred1_0 @ $true )
| ~ ( X5 @ $true @ $true )
| ( X5 @ ~ $true @ ~ $true )
| ( X5 @ ~ $true @ $true )
| ( X5 @ $true @ ~ $true ) )
& ( ~ $true
| ( epred1_0 @ $true )
| ( epred1_0 @ $true )
| ~ ( X5 @ $true @ $true )
| ( X5 @ ~ $true @ ~ $true )
| ( X5 @ ~ $true @ $true )
| ( X5 @ $true @ ~ $true ) )
& ( ~ $true
| $true
| ( epred1_0 @ $false )
| ( epred1_0 @ $true )
| ~ ( X5 @ $true @ $true )
| ( X5 @ ~ $true @ ~ $true )
| ( X5 @ ~ $true @ $true )
| ( X5 @ $true @ ~ $true ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])])])]) ).
thf(c_0_3,negated_conjecture,
! [X1: $o > $o > $o] :
( ( X1 @ ~ $true @ ~ $true )
| ( X1 @ ~ $true @ $true )
| ( X1 @ $true @ ~ $true )
| ~ $true
| ~ ( epred1_0 @ $true )
| ~ ( epred1_0 @ $true )
| ~ ( X1 @ $true @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
! [X1: $o > $o > $o] :
( ( epred1_0 @ $true )
| ( epred1_0 @ $true )
| ( X1 @ ~ $true @ ~ $true )
| ( X1 @ ~ $true @ $true )
| ( X1 @ $true @ ~ $true )
| ~ $true
| ~ ( X1 @ $true @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,negated_conjecture,
! [X1: $o > $o > $o] :
( ( X1 @ $true @ ~ $true )
| ( X1 @ ~ $true @ $true )
| ( X1 @ ~ $true @ ~ $true )
| ~ ( epred1_0 @ $true )
| ~ ( X1 @ $true @ $true ) ),
inference(cn,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X1: $o > $o > $o] :
( ( epred1_0 @ $true )
| ( X1 @ $true @ ~ $true )
| ( X1 @ ~ $true @ $true )
| ( X1 @ ~ $true @ ~ $true )
| ~ ( X1 @ $true @ $true ) ),
inference(cn,[status(thm)],[c_0_4]) ).
thf(c_0_7,negated_conjecture,
! [X1: $o > $o > $o] :
( ( X1 @ ~ $true @ ~ $true )
| ( X1 @ ~ $true @ $true )
| ( X1 @ $true @ ~ $true )
| ~ ( X1 @ $true @ $true )
| ~ ( epred1_0 @ $true ) ),
inference(cn,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X1: $o > $o > $o] :
( ( X1 @ ~ $true @ ~ $true )
| ( X1 @ ~ $true @ $true )
| ( X1 @ $true @ ~ $true )
| ( epred1_0 @ $true )
| ~ ( X1 @ $true @ $true ) ),
inference(cn,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
~ ( epred1_0 @ $true ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(primitive_enumeration,[status(thm)],[c_0_7])])]) ).
thf(c_0_10,negated_conjecture,
! [X1: $o > $o > $o] :
( ( X1 @ $true @ ~ $true )
| ( X1 @ ~ $true @ $true )
| ( X1 @ ~ $true @ ~ $true )
| ~ ( X1 @ $true @ $true ) ),
inference(sr,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(primitive_enumeration,[status(thm)],[c_0_10])])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO311^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n004.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 16:44:52 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running higher-order theorem proving
% 0.25/0.32 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.Wa7OI7mmaX/E---3.1_1543360.p
% 0.25/0.36 % Version: 3.5.1-ho
% 0.25/0.36 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.25/0.36 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.36 % Starting post_as_ho12 with 300s (1) cores
% 0.25/0.36 % Starting new_bool_9 with 300s (1) cores
% 0.25/0.36 % Starting post_as_ho1 with 300s (1) cores
% 0.25/0.36 % Starting post_as_ho4 with 300s (1) cores
% 0.25/0.36 % Starting post_as_ho2 with 300s (1) cores
% 0.25/0.36 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.25/0.36 % Starting full_lambda_10 with 300s (1) cores
% 0.25/0.36 % Starting new_ho_8 with 300s (1) cores
% 0.25/0.36 % post_as_ho2 with pid 1543377 completed with status 0
% 0.25/0.36 % Result found by post_as_ho2
% 0.25/0.36 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.25/0.36 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.36 % Starting post_as_ho12 with 300s (1) cores
% 0.25/0.36 % Starting new_bool_9 with 300s (1) cores
% 0.25/0.36 % Starting post_as_ho1 with 300s (1) cores
% 0.25/0.36 % Starting post_as_ho4 with 300s (1) cores
% 0.25/0.36 % Starting post_as_ho2 with 300s (1) cores
% 0.25/0.36 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.36 % No SInE strategy applied
% 0.25/0.36 % Search class: HGUNF-FFSF00-SSSFFMBN
% 0.25/0.36 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.36 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.36 % SubtermCWHack with pid 1543384 completed with status 10
% 0.25/0.36 % Starting post_as_ho2 with 31s (1) cores
% 0.25/0.36 % post_as_ho2 with pid 1543391 completed with status 10
% 0.25/0.36 % Starting sh2lt with 28s (1) cores
% 0.25/0.36 % sh2lt with pid 1543399 completed with status 0
% 0.25/0.36 % Result found by sh2lt
% 0.25/0.36 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.25/0.36 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.36 % Starting post_as_ho12 with 300s (1) cores
% 0.25/0.36 % Starting new_bool_9 with 300s (1) cores
% 0.25/0.36 % Starting post_as_ho1 with 300s (1) cores
% 0.25/0.36 % Starting post_as_ho4 with 300s (1) cores
% 0.25/0.36 % Starting post_as_ho2 with 300s (1) cores
% 0.25/0.36 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.36 % No SInE strategy applied
% 0.25/0.36 % Search class: HGUNF-FFSF00-SSSFFMBN
% 0.25/0.36 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.36 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.36 % SubtermCWHack with pid 1543384 completed with status 10
% 0.25/0.36 % Starting post_as_ho2 with 31s (1) cores
% 0.25/0.36 % post_as_ho2 with pid 1543391 completed with status 10
% 0.25/0.36 % Starting sh2lt with 28s (1) cores
% 0.25/0.36 % Preprocessing time : 0.001 s
% 0.25/0.36 % Presaturation interreduction done
% 0.25/0.36
% 0.25/0.36 % Proof found!
% 0.25/0.36 % SZS status Theorem
% 0.25/0.36 % SZS output start CNFRefutation
% See solution above
% 0.25/0.36 % Parsed axioms : 1
% 0.25/0.36 % Removed by relevancy pruning/SinE : 0
% 0.25/0.36 % Initial clauses : 9
% 0.25/0.36 % Removed in clause preprocessing : 6
% 0.25/0.36 % Initial clauses in saturation : 3
% 0.25/0.36 % Processed clauses : 6
% 0.25/0.36 % ...of these trivial : 0
% 0.25/0.36 % ...subsumed : 0
% 0.25/0.36 % ...remaining for further processing : 6
% 0.25/0.36 % Other redundant clauses eliminated : 0
% 0.25/0.36 % Clauses deleted for lack of memory : 0
% 0.25/0.36 % Backward-subsumed : 1
% 0.25/0.36 % Backward-rewritten : 0
% 0.25/0.36 % Generated clauses : 42
% 0.25/0.36 % ...of the previous two non-redundant : 8
% 0.25/0.36 % ...aggressively subsumed : 0
% 0.25/0.36 % Contextual simplify-reflections : 0
% 0.25/0.36 % Paramodulations : 0
% 0.25/0.36 % Factorizations : 0
% 0.25/0.36 % NegExts : 0
% 0.25/0.36 % Equation resolutions : 0
% 0.25/0.36 % Disequality decompositions : 0
% 0.25/0.36 % Total rewrite steps : 0
% 0.25/0.36 % ...of those cached : 0
% 0.25/0.36 % Propositional unsat checks : 0
% 0.25/0.36 % Propositional check models : 0
% 0.25/0.36 % Propositional check unsatisfiable : 0
% 0.25/0.36 % Propositional clauses : 0
% 0.25/0.36 % Propositional clauses after purity: 0
% 0.25/0.36 % Propositional unsat core size : 0
% 0.25/0.36 % Propositional preprocessing time : 0.000
% 0.25/0.36 % Propositional encoding time : 0.000
% 0.25/0.36 % Propositional solver time : 0.000
% 0.25/0.36 % Success case prop preproc time : 0.000
% 0.25/0.36 % Success case prop encoding time : 0.000
% 0.25/0.36 % Success case prop solver time : 0.000
% 0.25/0.36 % Current number of processed clauses : 2
% 0.25/0.36 % Positive orientable unit clauses : 0
% 0.25/0.36 % Positive unorientable unit clauses: 0
% 0.25/0.36 % Negative unit clauses : 1
% 0.25/0.36 % Non-unit-clauses : 1
% 0.25/0.36 % Current number of unprocessed clauses: 5
% 0.25/0.36 % ...number of literals in the above : 22
% 0.25/0.36 % Current number of archived formulas : 0
% 0.25/0.36 % Current number of archived clauses : 4
% 0.25/0.36 % Clause-clause subsumption calls (NU) : 4
% 0.25/0.36 % Rec. Clause-clause subsumption calls : 0
% 0.25/0.36 % Non-unit clause-clause subsumptions : 0
% 0.25/0.36 % Unit Clause-clause subsumption calls : 1
% 0.25/0.36 % Rewrite failures with RHS unbound : 0
% 0.25/0.36 % BW rewrite match attempts : 0
% 0.25/0.36 % BW rewrite match successes : 0
% 0.25/0.36 % Condensation attempts : 0
% 0.25/0.36 % Condensation successes : 0
% 0.25/0.36 % Termbank termtop insertions : 1816
% 0.25/0.36 % Search garbage collected termcells : 180
% 0.25/0.36
% 0.25/0.36 % -------------------------------------------------
% 0.25/0.36 % User time : 0.009 s
% 0.25/0.36 % System time : 0.006 s
% 0.25/0.36 % Total time : 0.015 s
% 0.25/0.36 % Maximum resident set size: 3576 pages
% 0.25/0.36
% 0.25/0.36 % -------------------------------------------------
% 0.25/0.36 % User time : 0.011 s
% 0.25/0.36 % System time : 0.012 s
% 0.25/0.36 % Total time : 0.023 s
% 0.25/0.36 % Maximum resident set size: 4864 pages
% 0.25/0.36 % E exiting
%------------------------------------------------------------------------------