%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU717^2 : 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 : n010.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 08:25:20 AM UTC 2026
% Result : Theorem 0.11s 0.24s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 0 equ; 0 cnn)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 337 ( 30 ~; 31 |; 7 &; 234 @)
% ( 2 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 45 ( 0 ^; 45 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
powerset: $i > $i ).
thf(decl_25,type,
subset: $i > $i > $o ).
thf(decl_26,type,
powersetI1: $o ).
thf(decl_27,type,
subsetTI: $o ).
thf(decl_28,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_29,type,
esk2_0: $i ).
thf(decl_30,type,
esk3_0: $i ).
thf(decl_31,type,
esk4_0: $i ).
thf(powersetTI1,conjecture,
( powersetI1
=> ( subsetTI
=> ! [X1: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ X5 @ X3 )
=> ( in @ X5 @ X4 ) ) )
=> ( in @ X3 @ ( powerset @ X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HWmnCbeqAJ/E---3.1_2920648.p',powersetTI1) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ X1 )
=> ( in @ X2 @ ( powerset @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HWmnCbeqAJ/E---3.1_2920648.p',powersetI1) ).
thf(subsetTI,axiom,
( subsetTI
<=> ! [X1: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ X5 @ X3 )
=> ( in @ X5 @ X4 ) ) )
=> ( subset @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HWmnCbeqAJ/E---3.1_2920648.p',subsetTI) ).
thf(c_0_3,negated_conjecture,
~ ( powersetI1
=> ( subsetTI
=> ! [X1: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ X5 @ X3 )
=> ( in @ X5 @ X4 ) ) )
=> ( in @ X3 @ ( powerset @ X4 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[powersetTI1]) ).
thf(c_0_4,negated_conjecture,
~ ( ! [X16: $i,X17: $i] :
( ( subset @ X17 @ X16 )
=> ( in @ X17 @ ( powerset @ X16 ) ) )
=> ( ! [X18: $i,X19: $i] :
( ( in @ X19 @ ( powerset @ X18 ) )
=> ! [X20: $i] :
( ( in @ X20 @ ( powerset @ X18 ) )
=> ( ! [X21: $i] :
( ( in @ X21 @ X18 )
=> ( ( in @ X21 @ X19 )
=> ( in @ X21 @ X20 ) ) )
=> ( subset @ X19 @ X20 ) ) ) )
=> ! [X1: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ X5 @ X3 )
=> ( in @ X5 @ X4 ) ) )
=> ( in @ X3 @ ( powerset @ X4 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,powersetI1]),subsetTI]) ).
thf(c_0_5,negated_conjecture,
! [X22: $i,X23: $i,X24: $i,X25: $i,X26: $i,X31: $i] :
( ( ~ ( subset @ X23 @ X22 )
| ( in @ X23 @ ( powerset @ X22 ) ) )
& ( ( in @ ( esk1_3 @ X24 @ X25 @ X26 ) @ X24 )
| ( subset @ X25 @ X26 )
| ~ ( in @ X26 @ ( powerset @ X24 ) )
| ~ ( in @ X25 @ ( powerset @ X24 ) ) )
& ( ( in @ ( esk1_3 @ X24 @ X25 @ X26 ) @ X25 )
| ( subset @ X25 @ X26 )
| ~ ( in @ X26 @ ( powerset @ X24 ) )
| ~ ( in @ X25 @ ( powerset @ X24 ) ) )
& ( ~ ( in @ ( esk1_3 @ X24 @ X25 @ X26 ) @ X26 )
| ( subset @ X25 @ X26 )
| ~ ( in @ X26 @ ( powerset @ X24 ) )
| ~ ( in @ X25 @ ( powerset @ X24 ) ) )
& ( in @ esk3_0 @ ( powerset @ esk2_0 ) )
& ( in @ esk4_0 @ ( powerset @ esk2_0 ) )
& ( ~ ( in @ X31 @ esk2_0 )
| ~ ( in @ X31 @ esk3_0 )
| ( in @ X31 @ esk4_0 ) )
& ~ ( in @ esk3_0 @ ( powerset @ esk4_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_4])])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ esk4_0 )
| ~ ( in @ X1 @ esk2_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X2 )
| ( subset @ X2 @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
! [X2: $i,X1: $i] :
( ( in @ ( esk1_3 @ X1 @ esk3_0 @ X2 ) @ esk4_0 )
| ( subset @ esk3_0 @ X2 )
| ~ ( in @ ( esk1_3 @ X1 @ esk3_0 @ X2 ) @ esk2_0 )
| ~ ( in @ esk3_0 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i] :
( ( subset @ esk3_0 @ esk4_0 )
| ~ ( in @ ( esk1_3 @ X1 @ esk3_0 @ esk4_0 ) @ esk2_0 )
| ~ ( in @ esk4_0 @ ( powerset @ X1 ) )
| ~ ( in @ esk3_0 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
| ( subset @ X2 @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,negated_conjecture,
in @ esk4_0 @ ( powerset @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_13,negated_conjecture,
in @ esk3_0 @ ( powerset @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( subset @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_15,negated_conjecture,
subset @ esk3_0 @ esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]) ).
thf(c_0_16,negated_conjecture,
~ ( in @ esk3_0 @ ( powerset @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU717^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n010.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 14:15:18 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.22 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.HWmnCbeqAJ/E---3.1_2920648.p
% 0.11/0.24 % Version: 3.5.1-ho
% 0.11/0.24 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.11/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.24 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.11/0.24 % Starting post_as_ho8 with 300s (1) cores
% 0.11/0.24 % Starting post_as_ho3 with 300s (1) cores
% 0.11/0.24 % Starting post_as_ho2 with 300s (1) cores
% 0.11/0.24 % post_as_ho8 with pid 2920662 completed with status 0
% 0.11/0.24 % Result found by post_as_ho8
% 0.11/0.24 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.11/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.24 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.11/0.24 % Starting post_as_ho8 with 300s (1) cores
% 0.11/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.11/0.24 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.11/0.24 % Search class: HGUNF-FFSF32-SFFFMFNN
% 0.11/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.24 % SubtermCWHack with pid 2920665 completed with status 0
% 0.11/0.24 % Result found by SubtermCWHack
% 0.11/0.24 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.11/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.24 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.11/0.24 % Starting post_as_ho8 with 300s (1) cores
% 0.11/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.11/0.24 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.11/0.24 % Search class: HGUNF-FFSF32-SFFFMFNN
% 0.11/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.24 % Preprocessing time : 0.001 s
% 0.11/0.24
% 0.11/0.24 % Proof found!
% 0.11/0.24 % SZS status Theorem
% 0.11/0.24 % SZS output start CNFRefutation
% See solution above
% 0.11/0.24 % Parsed axioms : 8
% 0.11/0.24 % Removed by relevancy pruning/SinE : 5
% 0.11/0.24 % Initial clauses : 8
% 0.11/0.24 % Removed in clause preprocessing : 0
% 0.11/0.24 % Initial clauses in saturation : 8
% 0.11/0.24 % Processed clauses : 19
% 0.11/0.24 % ...of these trivial : 0
% 0.11/0.24 % ...subsumed : 0
% 0.11/0.24 % ...remaining for further processing : 19
% 0.11/0.24 % Other redundant clauses eliminated : 0
% 0.11/0.24 % Clauses deleted for lack of memory : 0
% 0.11/0.24 % Backward-subsumed : 0
% 0.11/0.24 % Backward-rewritten : 1
% 0.11/0.24 % Generated clauses : 19
% 0.11/0.24 % ...of the previous two non-redundant : 14
% 0.11/0.24 % ...aggressively subsumed : 0
% 0.11/0.24 % Contextual simplify-reflections : 0
% 0.11/0.24 % Paramodulations : 19
% 0.11/0.24 % Factorizations : 0
% 0.11/0.24 % NegExts : 0
% 0.11/0.24 % Equation resolutions : 0
% 0.11/0.24 % Disequality decompositions : 0
% 0.11/0.24 % Total rewrite steps : 5
% 0.11/0.24 % ...of those cached : 0
% 0.11/0.24 % Propositional unsat checks : 0
% 0.11/0.24 % Propositional check models : 0
% 0.11/0.24 % Propositional check unsatisfiable : 0
% 0.11/0.24 % Propositional clauses : 0
% 0.11/0.24 % Propositional clauses after purity: 0
% 0.11/0.24 % Propositional unsat core size : 0
% 0.11/0.24 % Propositional preprocessing time : 0.000
% 0.11/0.24 % Propositional encoding time : 0.000
% 0.11/0.24 % Propositional solver time : 0.000
% 0.11/0.24 % Success case prop preproc time : 0.000
% 0.11/0.24 % Success case prop encoding time : 0.000
% 0.11/0.24 % Success case prop solver time : 0.000
% 0.11/0.24 % Current number of processed clauses : 18
% 0.11/0.24 % Positive orientable unit clauses : 7
% 0.11/0.24 % Positive unorientable unit clauses: 0
% 0.11/0.24 % Negative unit clauses : 1
% 0.11/0.24 % Non-unit-clauses : 10
% 0.11/0.24 % Current number of unprocessed clauses: 3
% 0.11/0.24 % ...number of literals in the above : 13
% 0.11/0.24 % Current number of archived formulas : 0
% 0.11/0.24 % Current number of archived clauses : 1
% 0.11/0.24 % Clause-clause subsumption calls (NU) : 53
% 0.11/0.24 % Rec. Clause-clause subsumption calls : 27
% 0.11/0.24 % Non-unit clause-clause subsumptions : 0
% 0.11/0.24 % Unit Clause-clause subsumption calls : 2
% 0.11/0.24 % Rewrite failures with RHS unbound : 0
% 0.11/0.24 % BW rewrite match attempts : 1
% 0.11/0.24 % BW rewrite match successes : 1
% 0.11/0.24 % Condensation attempts : 0
% 0.11/0.24 % Condensation successes : 0
% 0.11/0.24 % Termbank termtop insertions : 1356
% 0.11/0.24 % Search garbage collected termcells : 359
% 0.11/0.24
% 0.11/0.24 % -------------------------------------------------
% 0.11/0.24 % User time : 0.003 s
% 0.11/0.24 % System time : 0.002 s
% 0.11/0.24 % Total time : 0.005 s
% 0.11/0.24 % Maximum resident set size: 3632 pages
% 0.11/0.24
% 0.11/0.24 % -------------------------------------------------
% 0.11/0.24 % User time : 0.005 s
% 0.11/0.24 % System time : 0.006 s
% 0.11/0.24 % Total time : 0.011 s
% 0.11/0.24 % Maximum resident set size: 4608 pages
% 0.11/0.24 % E exiting
%------------------------------------------------------------------------------