%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU729^2 : 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 : 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 08:25:23 AM UTC 2026
% Result : Theorem 0.24s 0.33s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 0 equ; 0 cnn)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 440 ( 38 ~; 38 |; 6 &; 325 @)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 57 ( 0 ^; 57 !; 0 ?; 57 :)
% 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,
setminus: $i > $i > $i ).
thf(decl_27,type,
complementT_lem: $o ).
thf(decl_28,type,
subsetTI: $o ).
thf(decl_29,type,
doubleComplementI1: $o ).
thf(decl_30,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_31,type,
esk2_0: $i ).
thf(decl_32,type,
esk3_0: $i ).
thf(doubleComplementSub1,conjecture,
( complementT_lem
=> ( subsetTI
=> ( doubleComplementI1
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yrupQOUqwh/E---3.1_840898.p',doubleComplementSub1) ).
thf(complementT_lem,axiom,
( complementT_lem
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yrupQOUqwh/E---3.1_840898.p',complementT_lem) ).
thf(subsetTI,axiom,
( subsetTI
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X3 ) ) )
=> ( subset @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yrupQOUqwh/E---3.1_840898.p',subsetTI) ).
thf(doubleComplementI1,axiom,
( doubleComplementI1
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yrupQOUqwh/E---3.1_840898.p',doubleComplementI1) ).
thf(c_0_4,negated_conjecture,
~ ( complementT_lem
=> ( subsetTI
=> ( doubleComplementI1
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[doubleComplementSub1]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X16: $i,X17: $i] :
( ( in @ X17 @ ( powerset @ X16 ) )
=> ( in @ ( setminus @ X16 @ 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 ) ) ) )
=> ( ! [X22: $i,X23: $i] :
( ( in @ X23 @ ( powerset @ X22 ) )
=> ! [X24: $i] :
( ( in @ X24 @ X22 )
=> ( ( in @ X24 @ X23 )
=> ( in @ X24 @ ( setminus @ X22 @ ( setminus @ X22 @ X23 ) ) ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,complementT_lem]),subsetTI]),doubleComplementI1]) ).
thf(c_0_6,negated_conjecture,
! [X25: $i,X26: $i,X27: $i,X28: $i,X29: $i,X31: $i,X32: $i,X33: $i] :
( ( ~ ( in @ X26 @ ( powerset @ X25 ) )
| ( in @ ( setminus @ X25 @ X26 ) @ ( powerset @ X25 ) ) )
& ( ( in @ ( esk1_3 @ X27 @ X28 @ X29 ) @ X27 )
| ( subset @ X28 @ X29 )
| ~ ( in @ X29 @ ( powerset @ X27 ) )
| ~ ( in @ X28 @ ( powerset @ X27 ) ) )
& ( ( in @ ( esk1_3 @ X27 @ X28 @ X29 ) @ X28 )
| ( subset @ X28 @ X29 )
| ~ ( in @ X29 @ ( powerset @ X27 ) )
| ~ ( in @ X28 @ ( powerset @ X27 ) ) )
& ( ~ ( in @ ( esk1_3 @ X27 @ X28 @ X29 ) @ X29 )
| ( subset @ X28 @ X29 )
| ~ ( in @ X29 @ ( powerset @ X27 ) )
| ~ ( in @ X28 @ ( powerset @ X27 ) ) )
& ( ~ ( in @ X32 @ ( powerset @ X31 ) )
| ~ ( in @ X33 @ X31 )
| ~ ( in @ X33 @ X32 )
| ( in @ X33 @ ( setminus @ X31 @ ( setminus @ X31 @ X32 ) ) ) )
& ( in @ esk3_0 @ ( powerset @ esk2_0 ) )
& ~ ( subset @ esk3_0 @ ( setminus @ esk2_0 @ ( setminus @ esk2_0 @ esk3_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,
! [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_6]) ).
thf(c_0_8,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( in @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( subset @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) )
| ~ ( in @ ( esk1_3 @ X4 @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) ) @ X2 )
| ~ ( in @ ( esk1_3 @ X4 @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) ) @ X3 )
| ~ ( in @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ X1 @ ( powerset @ X4 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_10,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_6]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( subset @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) )
| ~ ( in @ ( esk1_3 @ X2 @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) ) @ X3 )
| ~ ( in @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_12,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_6]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
| ~ ( in @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( setminus @ X2 @ X1 ) @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_15,negated_conjecture,
~ ( subset @ esk3_0 @ ( setminus @ esk2_0 @ ( setminus @ esk2_0 @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
thf(c_0_17,negated_conjecture,
in @ esk3_0 @ ( powerset @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU729^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 % Computer : n019.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Sep 29 14:17:17 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running higher-order theorem proving
% 0.24/0.30 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.yrupQOUqwh/E---3.1_840898.p
% 0.24/0.33 % Version: 3.5.1-ho
% 0.24/0.33 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.24/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.33 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.24/0.33 % Starting post_as_ho8 with 300s (1) cores
% 0.24/0.33 % Starting post_as_ho3 with 300s (1) cores
% 0.24/0.33 % Starting post_as_ho2 with 300s (1) cores
% 0.24/0.33 % lpo6_lambda_fix with pid 840911 completed with status 0
% 0.24/0.33 % Result found by lpo6_lambda_fix
% 0.24/0.33 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.24/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.33 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.24/0.33 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.24/0.33 % No SInE strategy applied
% 0.24/0.33 % Search class: HGUNF-FFSF32-SFFFMFNN
% 0.24/0.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.33 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.33 % Starting lpo6_lambda_fix with 151s (1) cores
% 0.24/0.33 % Starting sh5l with 136s (1) cores
% 0.24/0.33 % Starting new_bool_1 with 136s (1) cores
% 0.24/0.33 % Starting new_bool_2 with 136s (1) cores
% 0.24/0.33 % sh5l with pid 840918 completed with status 0
% 0.24/0.33 % Result found by sh5l
% 0.24/0.33 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.24/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.33 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.24/0.33 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.24/0.33 % No SInE strategy applied
% 0.24/0.33 % Search class: HGUNF-FFSF32-SFFFMFNN
% 0.24/0.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.33 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.33 % Starting lpo6_lambda_fix with 151s (1) cores
% 0.24/0.33 % Starting sh5l with 136s (1) cores
% 0.24/0.33 % Preprocessing time : 0.001 s
% 0.24/0.33 % Presaturation interreduction done
% 0.24/0.33
% 0.24/0.33 % Proof found!
% 0.24/0.33 % SZS status Theorem
% 0.24/0.33 % SZS output start CNFRefutation
% See solution above
% 0.24/0.33 % Parsed axioms : 11
% 0.24/0.33 % Removed by relevancy pruning/SinE : 0
% 0.24/0.33 % Initial clauses : 14
% 0.24/0.33 % Removed in clause preprocessing : 7
% 0.24/0.33 % Initial clauses in saturation : 7
% 0.24/0.33 % Processed clauses : 30
% 0.24/0.33 % ...of these trivial : 0
% 0.24/0.33 % ...subsumed : 1
% 0.24/0.33 % ...remaining for further processing : 29
% 0.24/0.33 % Other redundant clauses eliminated : 0
% 0.24/0.33 % Clauses deleted for lack of memory : 0
% 0.24/0.33 % Backward-subsumed : 3
% 0.24/0.33 % Backward-rewritten : 0
% 0.24/0.33 % Generated clauses : 23
% 0.24/0.33 % ...of the previous two non-redundant : 22
% 0.24/0.33 % ...aggressively subsumed : 0
% 0.24/0.33 % Contextual simplify-reflections : 2
% 0.24/0.33 % Paramodulations : 23
% 0.24/0.33 % Factorizations : 0
% 0.24/0.33 % NegExts : 0
% 0.24/0.33 % Equation resolutions : 0
% 0.24/0.33 % Disequality decompositions : 0
% 0.24/0.33 % Total rewrite steps : 1
% 0.24/0.33 % ...of those cached : 0
% 0.24/0.33 % Propositional unsat checks : 0
% 0.24/0.33 % Propositional check models : 0
% 0.24/0.33 % Propositional check unsatisfiable : 0
% 0.24/0.33 % Propositional clauses : 0
% 0.24/0.33 % Propositional clauses after purity: 0
% 0.24/0.33 % Propositional unsat core size : 0
% 0.24/0.33 % Propositional preprocessing time : 0.000
% 0.24/0.33 % Propositional encoding time : 0.000
% 0.24/0.33 % Propositional solver time : 0.000
% 0.24/0.33 % Success case prop preproc time : 0.000
% 0.24/0.33 % Success case prop encoding time : 0.000
% 0.24/0.33 % Success case prop solver time : 0.000
% 0.24/0.33 % Current number of processed clauses : 19
% 0.24/0.33 % Positive orientable unit clauses : 2
% 0.24/0.33 % Positive unorientable unit clauses: 0
% 0.24/0.33 % Negative unit clauses : 1
% 0.24/0.33 % Non-unit-clauses : 16
% 0.24/0.33 % Current number of unprocessed clauses: 6
% 0.24/0.33 % ...number of literals in the above : 42
% 0.24/0.33 % Current number of archived formulas : 0
% 0.24/0.33 % Current number of archived clauses : 10
% 0.24/0.33 % Clause-clause subsumption calls (NU) : 351
% 0.24/0.33 % Rec. Clause-clause subsumption calls : 99
% 0.24/0.33 % Non-unit clause-clause subsumptions : 6
% 0.24/0.33 % Unit Clause-clause subsumption calls : 0
% 0.24/0.33 % Rewrite failures with RHS unbound : 0
% 0.24/0.33 % BW rewrite match attempts : 0
% 0.24/0.33 % BW rewrite match successes : 0
% 0.24/0.33 % Condensation attempts : 30
% 0.24/0.33 % Condensation successes : 0
% 0.24/0.33 % Termbank termtop insertions : 5063
% 0.24/0.33 % Search garbage collected termcells : 373
% 0.24/0.33
% 0.24/0.33 % -------------------------------------------------
% 0.24/0.33 % User time : 0.010 s
% 0.24/0.33 % System time : 0.001 s
% 0.24/0.33 % Total time : 0.011 s
% 0.24/0.33 % Maximum resident set size: 3636 pages
% 0.24/0.33
% 0.24/0.33 % -------------------------------------------------
% 0.24/0.33 % User time : 0.032 s
% 0.24/0.33 % System time : 0.013 s
% 0.24/0.33 % Total time : 0.044 s
% 0.24/0.33 % Maximum resident set size: 4864 pages
% 0.24/0.33 % E exiting
%------------------------------------------------------------------------------