%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU580^2 : 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 : n019.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 08:24:35 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 0 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 151 ( 8 ~; 7 |; 3 &; 117 @)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 4 ^; 38 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
powerset: $i > $i ).
thf(decl_25,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_26,type,
dsetconstrEL: $o ).
thf(decl_27,type,
powersetI: $o ).
thf(decl_28,type,
esk1_2: $i > $i > $i ).
thf(decl_29,type,
esk2_0: $i ).
thf(decl_30,type,
epred1_0: $i > $o ).
thf(sepInPowerset,conjecture,
( dsetconstrEL
=> ( powersetI
=> ! [X1: $i,X2: $i > $o] :
( in
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
@ ( powerset @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pY2YxrXsW4/E---3.1_804500.p',sepInPowerset) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( in @ X3 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pY2YxrXsW4/E---3.1_804500.p',dsetconstrEL) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X1: $i,X5: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ X3 @ X1 ) )
=> ( in @ X5 @ ( powerset @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pY2YxrXsW4/E---3.1_804500.p',powersetI) ).
thf(c_0_3,negated_conjecture,
~ ( dsetconstrEL
=> ( powersetI
=> ! [X1: $i,X2: $i > $o] :
( in
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
@ ( powerset @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[sepInPowerset]) ).
thf(c_0_4,plain,
( dsetconstrEL
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( in @ X3 @ X1 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X14: $i,X15: $i > $o,X16: $i] :
( ( in @ X16 @ ( dsetconstr @ X14 @ X15 ) )
=> ( in @ X16 @ X14 ) )
=> ( ! [X17: $i,X18: $i] :
( ! [X19: $i] :
( ( in @ X19 @ X18 )
=> ( in @ X19 @ X17 ) )
=> ( in @ X18 @ ( powerset @ X17 ) ) )
=> ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_3]),c_0_4]),powersetI])]) ).
thf(c_0_6,negated_conjecture,
! [X20: $i,X21: $i > $o,X22: $i,X23: $i,X24: $i] :
( ( ~ ( in @ X22 @ ( dsetconstr @ X20 @ X21 ) )
| ( in @ X22 @ X20 ) )
& ( ( in @ ( esk1_2 @ X23 @ X24 ) @ X24 )
| ( in @ X24 @ ( powerset @ X23 ) ) )
& ( ~ ( in @ ( esk1_2 @ X23 @ X24 ) @ X23 )
| ( in @ X24 @ ( powerset @ X23 ) ) )
& ~ ( in @ ( dsetconstr @ esk2_0 @ epred1_0 ) @ ( powerset @ esk2_0 ) ) ),
inference(distribute,[status(thm)],[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_5])])])])])]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( in @ X1 @ X3 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X3: $i,X1: $i] :
( ( in @ ( esk1_2 @ X1 @ X3 ) @ X3 )
| ( in @ X3 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X3: $i,X1: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ ( esk1_2 @ X1 @ X3 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
! [X3: $i,X2: $i > $o,X1: $i] :
( ( in @ ( esk1_2 @ X1 @ ( dsetconstr @ X3 @ X2 ) ) @ X3 )
| ( in @ ( dsetconstr @ X3 @ X2 ) @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_11,negated_conjecture,
~ ( in @ ( dsetconstr @ esk2_0 @ epred1_0 ) @ ( powerset @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_12,negated_conjecture,
! [X2: $i > $o,X1: $i] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU580^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n019.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Sep 29 13:52:17 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.21 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.pY2YxrXsW4/E---3.1_804500.p
% 0.08/0.23 % Version: 3.5.1-ho
% 0.08/0.23 % Preprocessing class: HSSSSLSSSLMNSSN.
% 0.08/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.23 % Starting full_lambda_10 with 1500s (5) cores
% 0.08/0.23 % Starting lpo4_fix with 300s (1) cores
% 0.08/0.23 % Starting new_bool_6 with 300s (1) cores
% 0.08/0.23 % Starting lpo8_s with 300s (1) cores
% 0.08/0.23 % new_bool_6 with pid 804515 completed with status 0
% 0.08/0.23 % Result found by new_bool_6
% 0.08/0.23 % Preprocessing class: HSSSSLSSSLMNSSN.
% 0.08/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.23 % Starting full_lambda_10 with 1500s (5) cores
% 0.08/0.23 % Starting lpo4_fix with 300s (1) cores
% 0.08/0.23 % Starting new_bool_6 with 300s (1) cores
% 0.08/0.23 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.08/0.23 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.08/0.23 % Search class: HGUNF-FFSF21-SSSFMFBN
% 0.08/0.23 % partial match(2): HGUNF-FFSF21-SSSFFMBN
% 0.08/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.23 % SubtermCWHack with pid 804519 completed with status 0
% 0.08/0.23 % Result found by SubtermCWHack
% 0.08/0.23 % Preprocessing class: HSSSSLSSSLMNSSN.
% 0.08/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.23 % Starting full_lambda_10 with 1500s (5) cores
% 0.08/0.23 % Starting lpo4_fix with 300s (1) cores
% 0.08/0.23 % Starting new_bool_6 with 300s (1) cores
% 0.08/0.23 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.08/0.23 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.08/0.23 % Search class: HGUNF-FFSF21-SSSFMFBN
% 0.08/0.23 % partial match(2): HGUNF-FFSF21-SSSFFMBN
% 0.08/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.23 % Preprocessing time : 0.001 s
% 0.08/0.23
% 0.08/0.23 % Proof found!
% 0.08/0.23 % SZS status Theorem
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23 % Parsed axioms : 8
% 0.08/0.23 % Removed by relevancy pruning/SinE : 5
% 0.08/0.23 % Initial clauses : 4
% 0.08/0.23 % Removed in clause preprocessing : 0
% 0.08/0.23 % Initial clauses in saturation : 4
% 0.08/0.23 % Processed clauses : 7
% 0.08/0.23 % ...of these trivial : 0
% 0.08/0.23 % ...subsumed : 0
% 0.08/0.23 % ...remaining for further processing : 7
% 0.08/0.23 % Other redundant clauses eliminated : 0
% 0.08/0.23 % Clauses deleted for lack of memory : 0
% 0.08/0.23 % Backward-subsumed : 0
% 0.08/0.23 % Backward-rewritten : 1
% 0.08/0.23 % Generated clauses : 4
% 0.08/0.23 % ...of the previous two non-redundant : 4
% 0.08/0.23 % ...aggressively subsumed : 0
% 0.08/0.23 % Contextual simplify-reflections : 0
% 0.08/0.23 % Paramodulations : 4
% 0.08/0.23 % Factorizations : 0
% 0.08/0.23 % NegExts : 0
% 0.08/0.23 % Equation resolutions : 0
% 0.08/0.23 % Disequality decompositions : 0
% 0.08/0.23 % Total rewrite steps : 1
% 0.08/0.23 % ...of those cached : 0
% 0.08/0.23 % Propositional unsat checks : 0
% 0.08/0.23 % Propositional check models : 0
% 0.08/0.23 % Propositional check unsatisfiable : 0
% 0.08/0.23 % Propositional clauses : 0
% 0.08/0.23 % Propositional clauses after purity: 0
% 0.08/0.23 % Propositional unsat core size : 0
% 0.08/0.23 % Propositional preprocessing time : 0.000
% 0.08/0.23 % Propositional encoding time : 0.000
% 0.08/0.23 % Propositional solver time : 0.000
% 0.08/0.23 % Success case prop preproc time : 0.000
% 0.08/0.23 % Success case prop encoding time : 0.000
% 0.08/0.23 % Success case prop solver time : 0.000
% 0.08/0.23 % Current number of processed clauses : 6
% 0.08/0.23 % Positive orientable unit clauses : 2
% 0.08/0.23 % Positive unorientable unit clauses: 0
% 0.08/0.23 % Negative unit clauses : 0
% 0.08/0.23 % Non-unit-clauses : 4
% 0.08/0.23 % Current number of unprocessed clauses: 1
% 0.08/0.23 % ...number of literals in the above : 2
% 0.08/0.23 % Current number of archived formulas : 0
% 0.08/0.23 % Current number of archived clauses : 1
% 0.08/0.23 % Clause-clause subsumption calls (NU) : 6
% 0.08/0.23 % Rec. Clause-clause subsumption calls : 5
% 0.08/0.23 % Non-unit clause-clause subsumptions : 0
% 0.08/0.23 % Unit Clause-clause subsumption calls : 5
% 0.08/0.23 % Rewrite failures with RHS unbound : 0
% 0.08/0.23 % BW rewrite match attempts : 5
% 0.08/0.23 % BW rewrite match successes : 1
% 0.08/0.23 % Condensation attempts : 0
% 0.08/0.23 % Condensation successes : 0
% 0.08/0.23 % Termbank termtop insertions : 657
% 0.08/0.23 % Search garbage collected termcells : 227
% 0.08/0.23
% 0.08/0.23 % -------------------------------------------------
% 0.08/0.23 % User time : 0.002 s
% 0.08/0.23 % System time : 0.003 s
% 0.08/0.23 % Total time : 0.004 s
% 0.08/0.23 % Maximum resident set size: 3636 pages
% 0.08/0.23
% 0.08/0.23 % -------------------------------------------------
% 0.08/0.23 % User time : 0.003 s
% 0.08/0.23 % System time : 0.007 s
% 0.08/0.23 % Total time : 0.010 s
% 0.08/0.23 % Maximum resident set size: 4864 pages
% 0.08/0.23 % E exiting
%------------------------------------------------------------------------------