%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU541^2 : 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 08:24:26 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 2 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 69 ( 11 ~; 6 |; 5 &; 38 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 8 ( 2 ^; 6 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
prop2set: $o > $i ).
thf(decl_26,type,
prop2setI: $o ).
thf(decl_27,type,
set2prop: $i > $o ).
thf(decl_28,type,
epred1_0: $o ).
thf(prop2set2propI,conjecture,
( prop2setI
=> ! [X1: $o] :
( X1
=> ( set2prop @ ( prop2set @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YqWycMXJI9/E---3.1_747028.p',prop2set2propI) ).
thf(set2prop,axiom,
( set2prop
= ( ^ [X2: $i] : ( in @ emptyset @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YqWycMXJI9/E---3.1_747028.p',set2prop) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X1: $o] :
( X1
=> ( in @ emptyset @ ( prop2set @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YqWycMXJI9/E---3.1_747028.p',prop2setI) ).
thf(c_0_3,negated_conjecture,
~ ( prop2setI
=> ! [X1: $o] :
( X1
=> ( set2prop @ ( prop2set @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[prop2set2propI]) ).
thf(c_0_4,plain,
( set2prop
= ( ^ [Z0: $i] : ( in @ emptyset @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[set2prop]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X5: $o] :
( X5
=> ( in @ emptyset @ ( prop2set @ X5 ) ) )
=> ! [X1: $o] :
( X1
=> ( in @ emptyset @ ( prop2set @ X1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,prop2setI]),c_0_4]) ).
thf(c_0_6,negated_conjecture,
! [X6: $o] :
( ( ~ X6
| ( in @ emptyset @ ( prop2set @ X6 ) ) )
& epred1_0
& ( ~ epred1_0
| epred1_0 )
& ( ~ ( in @ emptyset @ ( prop2set @ $false ) )
| epred1_0 )
& ( ~ epred1_0
| ~ ( in @ emptyset @ ( prop2set @ $true ) ) )
& ( ~ ( in @ emptyset @ ( prop2set @ $false ) )
| ~ ( in @ emptyset @ ( prop2set @ $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_5])])])])])])]) ).
thf(c_0_7,negated_conjecture,
( ~ epred1_0
| ~ ( in @ emptyset @ ( prop2set @ $true ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
epred1_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
in @ emptyset @ ( prop2set @ $true ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_6])])]) ).
thf(c_0_10,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_9])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU541^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n006.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:48:54 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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.YqWycMXJI9/E---3.1_747028.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.07/0.25 % Starting post_as_ho5 with 300s (1) cores
% 0.07/0.25 % Starting sh4l with 300s (1) cores
% 0.07/0.25 % Starting ho_unfolding_2 with 300s (1) cores
% 0.07/0.25 % post_as_ho5 with pid 747042 completed with status 0
% 0.07/0.25 % Result found by post_as_ho5
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.07/0.25 % Starting post_as_ho5 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.07/0.25 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.07/0.25 % Search class: HHHNF-FFSF11-SSFFMFNN
% 0.07/0.25 % partial match(1): HHUNF-FFSF11-SSFFMFNN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 747045 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.07/0.25 % Starting post_as_ho5 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.07/0.25 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.07/0.25 % Search class: HHHNF-FFSF11-SSFFMFNN
% 0.07/0.25 % partial match(1): HHUNF-FFSF11-SSFFMFNN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 8
% 0.07/0.25 % Removed by relevancy pruning/SinE : 5
% 0.07/0.25 % Initial clauses : 6
% 0.07/0.25 % Removed in clause preprocessing : 1
% 0.07/0.25 % Initial clauses in saturation : 5
% 0.07/0.25 % Processed clauses : 4
% 0.07/0.25 % ...of these trivial : 1
% 0.07/0.25 % ...subsumed : 0
% 0.07/0.25 % ...remaining for further processing : 2
% 0.07/0.25 % Other redundant clauses eliminated : 0
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 0
% 0.07/0.25 % Backward-rewritten : 0
% 0.07/0.25 % Generated clauses : 0
% 0.07/0.25 % ...of the previous two non-redundant : 0
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 0
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 0
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 3
% 0.07/0.25 % ...of those cached : 1
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 2
% 0.07/0.25 % Positive orientable unit clauses : 2
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 0
% 0.07/0.25 % Non-unit-clauses : 0
% 0.07/0.25 % Current number of unprocessed clauses: 1
% 0.07/0.25 % ...number of literals in the above : 2
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 0
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.25 % Non-unit clause-clause subsumptions : 0
% 0.07/0.25 % Unit Clause-clause subsumption calls : 0
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 0
% 0.07/0.25 % BW rewrite match successes : 0
% 0.07/0.25 % Condensation attempts : 0
% 0.07/0.25 % Condensation successes : 0
% 0.07/0.25 % Termbank termtop insertions : 369
% 0.07/0.25 % Search garbage collected termcells : 115
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.004 s
% 0.07/0.25 % System time : 0.000 s
% 0.07/0.25 % Total time : 0.004 s
% 0.07/0.25 % Maximum resident set size: 3632 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.005 s
% 0.07/0.25 % System time : 0.005 s
% 0.07/0.25 % Total time : 0.010 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------