%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU540^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 0.26s 0.27s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 4 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 189 ( 18 ~; 14 |; 7 &; 128 @)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 42 ( 9 ^; 33 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
powerset: $i > $i ).
thf(decl_26,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_27,type,
dsetconstrI: $o ).
thf(decl_28,type,
prop2set: $o > $i ).
thf(decl_29,type,
powersetI: $o ).
thf(decl_30,type,
esk1_2: $i > $i > $i ).
thf(decl_31,type,
epred1_0: $o ).
thf(prop2setI,conjecture,
( dsetconstrI
=> ( powersetI
=> ! [X7: $o] :
( X7
=> ( in @ emptyset @ ( prop2set @ X7 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1bK0XY1U8d/E---3.1_1081979.p',prop2setI) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1bK0XY1U8d/E---3.1_1081979.p',dsetconstrI) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X1: $i,X6: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X6 )
=> ( in @ X3 @ X1 ) )
=> ( in @ X6 @ ( powerset @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1bK0XY1U8d/E---3.1_1081979.p',powersetI) ).
thf(prop2set,axiom,
( prop2set
= ( ^ [X5: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X3: $i] : X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1bK0XY1U8d/E---3.1_1081979.p',prop2set) ).
thf(c_0_4,negated_conjecture,
~ ( dsetconstrI
=> ( powersetI
=> ! [X7: $o] :
( X7
=> ( in @ emptyset @ ( prop2set @ X7 ) ) ) ) ),
inference(assume_negation,[status(cth)],[prop2setI]) ).
thf(c_0_5,plain,
( dsetconstrI
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrI]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X15: $i,X16: $i > $o,X17: $i] :
( ( in @ X17 @ X15 )
=> ( ( X16 @ X17 )
=> ( in @ X17 @ ( dsetconstr @ X15 @ X16 ) ) ) )
=> ( ! [X18: $i,X19: $i] :
( ! [X20: $i] :
( ( in @ X20 @ X19 )
=> ( in @ X20 @ X18 ) )
=> ( in @ X19 @ ( powerset @ X18 ) ) )
=> ! [X7: $o] :
( X7
=> ( in @ emptyset @ ( prop2set @ X7 ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_5]),powersetI])]) ).
thf(c_0_7,plain,
( prop2set
= ( ^ [Z0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(fof_simplification,[status(thm)],[prop2set]) ).
thf(c_0_8,negated_conjecture,
! [X21: $i,X22: $i > $o,X23: $i,X24: $i,X25: $i] :
( ( ~ ( in @ X23 @ X21 )
| ~ ( X22 @ X23 )
| ( in @ X23 @ ( dsetconstr @ X21 @ X22 ) ) )
& ( ( in @ ( esk1_2 @ X24 @ X25 ) @ X25 )
| ( in @ X25 @ ( powerset @ X24 ) ) )
& ( ~ ( in @ ( esk1_2 @ X24 @ X25 ) @ X24 )
| ( in @ X25 @ ( powerset @ X24 ) ) )
& 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_6])])])])])])]) ).
thf(c_0_9,plain,
( prop2set
= ( ^ [Z0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X3: $i,X2: $i > $o,X1: $i] :
( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
| ~ ( in @ X1 @ X3 )
| ~ ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,plain,
! [X5: $o] :
( ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X5 )
= ( prop2set @ X5 ) ),
inference(arg_cong,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X3: $i,X1: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ ( esk1_2 @ X1 @ X3 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,negated_conjecture,
! [X3: $i,X1: $i] :
( ( in @ ( esk1_2 @ X1 @ X3 ) @ X3 )
| ( in @ X3 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,negated_conjecture,
( ~ epred1_0
| ~ ( in @ emptyset @ ( prop2set @ $true ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_15,negated_conjecture,
epred1_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ ( prop2set @ $true ) )
| ~ ( in @ X1 @ ( powerset @ emptyset ) ) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11])]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_18,negated_conjecture,
~ ( in @ emptyset @ ( prop2set @ $true ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU540^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:49:49 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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.1bK0XY1U8d/E---3.1_1081979.p
% 0.26/0.26 % Version: 3.5.1-ho
% 0.26/0.26 % Preprocessing class: HSSSSLSSSLMNSFA.
% 0.26/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.26/0.26 % Starting full_lambda_3 with 300s (1) cores
% 0.26/0.26 % Starting ho_unfolding_6 with 300s (1) cores
% 0.26/0.26 % Starting sh4l with 300s (1) cores
% 0.26/0.26 % sh4l with pid 1081999 completed with status 0
% 0.26/0.26 % Result found by sh4l
% 0.26/0.26 % Preprocessing class: HSSSSLSSSLMNSFA.
% 0.26/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.26/0.26 % Starting full_lambda_3 with 300s (1) cores
% 0.26/0.26 % Starting ho_unfolding_6 with 300s (1) cores
% 0.26/0.26 % Starting sh4l with 300s (1) cores
% 0.26/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.26 % No SInE strategy applied
% 0.26/0.26 % Search class: HGHSF-FFSF21-MSFFMSBN
% 0.26/0.26 % partial match(2): HGHSF-FFSF22-SSFFMSBN
% 0.26/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.26/0.26 % SubtermCWHack with pid 1082000 completed with status 0
% 0.26/0.26 % Result found by SubtermCWHack
% 0.26/0.26 % Preprocessing class: HSSSSLSSSLMNSFA.
% 0.26/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.26/0.27 % Starting full_lambda_3 with 300s (1) cores
% 0.26/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.26/0.27 % Starting sh4l with 300s (1) cores
% 0.26/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.27 % No SInE strategy applied
% 0.26/0.27 % Search class: HGHSF-FFSF21-MSFFMSBN
% 0.26/0.27 % partial match(2): HGHSF-FFSF22-SSFFMSBN
% 0.26/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.26/0.27 % Preprocessing time : 0.001 s
% 0.26/0.27
% 0.26/0.27 % Proof found!
% 0.26/0.27 % SZS status Theorem
% 0.26/0.27 % SZS output start CNFRefutation
% See solution above
% 0.26/0.27 % Parsed axioms : 11
% 0.26/0.27 % Removed by relevancy pruning/SinE : 0
% 0.26/0.27 % Initial clauses : 16
% 0.26/0.27 % Removed in clause preprocessing : 8
% 0.26/0.27 % Initial clauses in saturation : 8
% 0.26/0.27 % Processed clauses : 12
% 0.26/0.27 % ...of these trivial : 1
% 0.26/0.27 % ...subsumed : 1
% 0.26/0.27 % ...remaining for further processing : 10
% 0.26/0.27 % Other redundant clauses eliminated : 2
% 0.26/0.27 % Clauses deleted for lack of memory : 0
% 0.26/0.27 % Backward-subsumed : 0
% 0.26/0.27 % Backward-rewritten : 0
% 0.26/0.27 % Generated clauses : 11
% 0.26/0.27 % ...of the previous two non-redundant : 8
% 0.26/0.27 % ...aggressively subsumed : 0
% 0.26/0.27 % Contextual simplify-reflections : 0
% 0.26/0.27 % Paramodulations : 8
% 0.26/0.27 % Factorizations : 0
% 0.26/0.27 % NegExts : 0
% 0.26/0.27 % Equation resolutions : 2
% 0.26/0.27 % Disequality decompositions : 0
% 0.26/0.27 % Total rewrite steps : 2
% 0.26/0.27 % ...of those cached : 1
% 0.26/0.27 % Propositional unsat checks : 0
% 0.26/0.27 % Propositional check models : 0
% 0.26/0.27 % Propositional check unsatisfiable : 0
% 0.26/0.27 % Propositional clauses : 0
% 0.26/0.27 % Propositional clauses after purity: 0
% 0.26/0.27 % Propositional unsat core size : 0
% 0.26/0.27 % Propositional preprocessing time : 0.000
% 0.26/0.27 % Propositional encoding time : 0.000
% 0.26/0.27 % Propositional solver time : 0.000
% 0.26/0.27 % Success case prop preproc time : 0.000
% 0.26/0.27 % Success case prop encoding time : 0.000
% 0.26/0.27 % Success case prop solver time : 0.000
% 0.26/0.27 % Current number of processed clauses : 10
% 0.26/0.27 % Positive orientable unit clauses : 4
% 0.26/0.27 % Positive unorientable unit clauses: 0
% 0.26/0.27 % Negative unit clauses : 1
% 0.26/0.27 % Non-unit-clauses : 5
% 0.26/0.27 % Current number of unprocessed clauses: 3
% 0.26/0.27 % ...number of literals in the above : 8
% 0.26/0.27 % Current number of archived formulas : 0
% 0.26/0.27 % Current number of archived clauses : 0
% 0.26/0.27 % Clause-clause subsumption calls (NU) : 5
% 0.26/0.27 % Rec. Clause-clause subsumption calls : 5
% 0.26/0.27 % Non-unit clause-clause subsumptions : 0
% 0.26/0.27 % Unit Clause-clause subsumption calls : 2
% 0.26/0.27 % Rewrite failures with RHS unbound : 0
% 0.26/0.27 % BW rewrite match attempts : 2
% 0.26/0.27 % BW rewrite match successes : 0
% 0.26/0.27 % Condensation attempts : 0
% 0.26/0.27 % Condensation successes : 0
% 0.26/0.27 % Termbank termtop insertions : 1055
% 0.26/0.27 % Search garbage collected termcells : 283
% 0.26/0.27
% 0.26/0.27 % -------------------------------------------------
% 0.26/0.27 % User time : 0.003 s
% 0.26/0.27 % System time : 0.002 s
% 0.26/0.27 % Total time : 0.005 s
% 0.26/0.27 % Maximum resident set size: 3640 pages
% 0.26/0.27
% 0.26/0.27 % -------------------------------------------------
% 0.26/0.27 % User time : 0.004 s
% 0.26/0.27 % System time : 0.006 s
% 0.26/0.27 % Total time : 0.011 s
% 0.26/0.27 % Maximum resident set size: 4608 pages
% 0.26/0.27 % E exiting
%------------------------------------------------------------------------------