%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU808^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:25:43 AM UTC 2026
% Result : Theorem 0.10s 0.23s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 86 ( 7 ~; 3 |; 2 &; 65 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 1 ^; 11 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
setadjoin: $i > $i > $i ).
thf(decl_25,type,
omega: $i ).
thf(decl_26,type,
omegaSAx: $o ).
thf(decl_27,type,
omegaS: $i > $i ).
thf(decl_28,type,
esk1_0: $i ).
thf(omegaSp,conjecture,
( omegaSAx
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( in @ ( omegaS @ X1 ) @ omega ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RonvusjFg9/E---3.1_808705.p',omegaSp) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RonvusjFg9/E---3.1_808705.p',omegaSAx) ).
thf(omegaS,axiom,
( omegaS
= ( ^ [X1: $i] : ( setadjoin @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RonvusjFg9/E---3.1_808705.p',omegaS) ).
thf(c_0_3,negated_conjecture,
~ ( omegaSAx
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( in @ ( omegaS @ X1 ) @ omega ) ) ),
inference(assume_negation,[status(cth)],[omegaSp]) ).
thf(c_0_4,negated_conjecture,
~ ( ! [X4: $i] :
( ( in @ X4 @ omega )
=> ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) )
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( in @ ( omegaS @ X1 ) @ omega ) ) ),
inference(apply_def,[status(thm)],[c_0_3,omegaSAx]) ).
thf(c_0_5,plain,
! [X5: $i] :
( ( omegaS @ X5 )
= ( setadjoin @ X5 @ X5 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[omegaS])]) ).
thf(c_0_6,negated_conjecture,
! [X6: $i] :
( ( ~ ( in @ X6 @ omega )
| ( in @ ( setadjoin @ X6 @ X6 ) @ omega ) )
& ( in @ esk1_0 @ omega )
& ~ ( in @ ( omegaS @ esk1_0 ) @ omega ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
thf(c_0_7,plain,
! [X8: $i] :
( ( omegaS @ X8 )
= ( setadjoin @ X8 @ X8 ) ),
inference(variable_rename,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i] :
( ( in @ ( setadjoin @ X1 @ X1 ) @ omega )
| ~ ( in @ X1 @ omega ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X1: $i] :
( ( omegaS @ X1 )
= ( setadjoin @ X1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
~ ( in @ ( omegaS @ esk1_0 ) @ omega ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i] :
( ( in @ ( omegaS @ X1 ) @ omega )
| ~ ( in @ X1 @ omega ) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,negated_conjecture,
in @ esk1_0 @ omega,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU808^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.15 % Computer : n006.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 14:32:54 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.21 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.RonvusjFg9/E---3.1_808705.p
% 0.10/0.23 % Version: 3.5.1-ho
% 0.10/0.23 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.10/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.23 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.10/0.23 % Starting post_as_ho5 with 300s (1) cores
% 0.10/0.23 % Starting sh4l with 300s (1) cores
% 0.10/0.23 % Starting ho_unfolding_2 with 300s (1) cores
% 0.10/0.23 % post_as_ho5 with pid 808719 completed with status 0
% 0.10/0.23 % Result found by post_as_ho5
% 0.10/0.23 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.10/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.23 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.10/0.23 % Starting post_as_ho5 with 300s (1) cores
% 0.10/0.23 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.10/0.23 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.10/0.23 % Search class: HHUSF-FFSF21-SSFFMFNN
% 0.10/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.23 % SubtermCWHack with pid 808725 completed with status 0
% 0.10/0.23 % Result found by SubtermCWHack
% 0.10/0.23 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.10/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.23 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.10/0.23 % Starting post_as_ho5 with 300s (1) cores
% 0.10/0.23 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.10/0.23 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.10/0.23 % Search class: HHUSF-FFSF21-SSFFMFNN
% 0.10/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.23 % Preprocessing time : 0.001 s
% 0.10/0.23
% 0.10/0.23 % Proof found!
% 0.10/0.23 % SZS status Theorem
% 0.10/0.23 % SZS output start CNFRefutation
% See solution above
% 0.10/0.23 % Parsed axioms : 8
% 0.10/0.23 % Removed by relevancy pruning/SinE : 5
% 0.10/0.23 % Initial clauses : 4
% 0.10/0.23 % Removed in clause preprocessing : 0
% 0.10/0.23 % Initial clauses in saturation : 4
% 0.10/0.23 % Processed clauses : 4
% 0.10/0.23 % ...of these trivial : 0
% 0.10/0.23 % ...subsumed : 0
% 0.10/0.23 % ...remaining for further processing : 4
% 0.10/0.23 % Other redundant clauses eliminated : 0
% 0.10/0.23 % Clauses deleted for lack of memory : 0
% 0.10/0.23 % Backward-subsumed : 0
% 0.10/0.23 % Backward-rewritten : 0
% 0.10/0.23 % Generated clauses : 1
% 0.10/0.23 % ...of the previous two non-redundant : 0
% 0.10/0.23 % ...aggressively subsumed : 0
% 0.10/0.23 % Contextual simplify-reflections : 0
% 0.10/0.23 % Paramodulations : 1
% 0.10/0.23 % Factorizations : 0
% 0.10/0.23 % NegExts : 0
% 0.10/0.23 % Equation resolutions : 0
% 0.10/0.23 % Disequality decompositions : 0
% 0.10/0.23 % Total rewrite steps : 2
% 0.10/0.23 % ...of those cached : 0
% 0.10/0.23 % Propositional unsat checks : 0
% 0.10/0.23 % Propositional check models : 0
% 0.10/0.23 % Propositional check unsatisfiable : 0
% 0.10/0.23 % Propositional clauses : 0
% 0.10/0.23 % Propositional clauses after purity: 0
% 0.10/0.23 % Propositional unsat core size : 0
% 0.10/0.23 % Propositional preprocessing time : 0.000
% 0.10/0.23 % Propositional encoding time : 0.000
% 0.10/0.23 % Propositional solver time : 0.000
% 0.10/0.23 % Success case prop preproc time : 0.000
% 0.10/0.23 % Success case prop encoding time : 0.000
% 0.10/0.23 % Success case prop solver time : 0.000
% 0.10/0.23 % Current number of processed clauses : 4
% 0.10/0.23 % Positive orientable unit clauses : 2
% 0.10/0.23 % Positive unorientable unit clauses: 0
% 0.10/0.23 % Negative unit clauses : 1
% 0.10/0.23 % Non-unit-clauses : 1
% 0.10/0.23 % Current number of unprocessed clauses: 0
% 0.10/0.23 % ...number of literals in the above : 0
% 0.10/0.23 % Current number of archived formulas : 0
% 0.10/0.23 % Current number of archived clauses : 0
% 0.10/0.23 % Clause-clause subsumption calls (NU) : 0
% 0.10/0.23 % Rec. Clause-clause subsumption calls : 0
% 0.10/0.23 % Non-unit clause-clause subsumptions : 0
% 0.10/0.23 % Unit Clause-clause subsumption calls : 0
% 0.10/0.23 % Rewrite failures with RHS unbound : 0
% 0.10/0.23 % BW rewrite match attempts : 0
% 0.10/0.23 % BW rewrite match successes : 0
% 0.10/0.23 % Condensation attempts : 0
% 0.10/0.23 % Condensation successes : 0
% 0.10/0.23 % Termbank termtop insertions : 308
% 0.10/0.23 % Search garbage collected termcells : 84
% 0.10/0.23
% 0.10/0.23 % -------------------------------------------------
% 0.10/0.23 % User time : 0.003 s
% 0.10/0.23 % System time : 0.000 s
% 0.10/0.23 % Total time : 0.004 s
% 0.10/0.23 % Maximum resident set size: 3628 pages
% 0.10/0.23
% 0.10/0.23 % -------------------------------------------------
% 0.10/0.23 % User time : 0.005 s
% 0.10/0.23 % System time : 0.004 s
% 0.10/0.23 % Total time : 0.009 s
% 0.10/0.23 % Maximum resident set size: 4864 pages
% 0.10/0.23 % E exiting
%------------------------------------------------------------------------------