%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU579^2 : 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 : n018.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 0.16s 0.31s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 0 equ; 0 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 299 ( 18 ~; 24 |; 7 &; 215 @)
% ( 4 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 64 ( 0 ^; 64 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
powerset: $i > $i ).
thf(decl_25,type,
powersetI: $o ).
thf(decl_26,type,
powersetE: $o ).
thf(decl_27,type,
subset: $i > $i > $o ).
thf(decl_28,type,
subsetI2: $o ).
thf(decl_29,type,
subsetE: $o ).
thf(decl_30,type,
esk1_2: $i > $i > $i ).
thf(decl_31,type,
esk2_2: $i > $i > $i ).
thf(decl_32,type,
esk3_0: $i ).
thf(decl_33,type,
esk4_0: $i ).
thf(powersetsubset,conjecture,
( powersetI
=> ( powersetE
=> ( subsetI2
=> ( subsetE
=> ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.p33oSvgEZV/E---3.1_109867.p',powersetsubset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( in @ X2 @ ( powerset @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.p33oSvgEZV/E---3.1_109867.p',powersetI) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.p33oSvgEZV/E---3.1_109867.p',powersetE) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.p33oSvgEZV/E---3.1_109867.p',subsetI2) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.p33oSvgEZV/E---3.1_109867.p',subsetE) ).
thf(c_0_5,negated_conjecture,
~ ( powersetI
=> ( powersetE
=> ( subsetI2
=> ( subsetE
=> ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[powersetsubset]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X18: $i,X19: $i] :
( ! [X20: $i] :
( ( in @ X20 @ X19 )
=> ( in @ X20 @ X18 ) )
=> ( in @ X19 @ ( powerset @ X18 ) ) )
=> ( ! [X21: $i,X22: $i,X23: $i] :
( ( in @ X22 @ ( powerset @ X21 ) )
=> ( ( in @ X23 @ X22 )
=> ( in @ X23 @ X21 ) ) )
=> ( ! [X24: $i,X25: $i] :
( ! [X26: $i] :
( ( in @ X26 @ X24 )
=> ( in @ X26 @ X25 ) )
=> ( subset @ X24 @ X25 ) )
=> ( ! [X27: $i,X28: $i,X29: $i] :
( ( subset @ X27 @ X28 )
=> ( ( in @ X29 @ X27 )
=> ( in @ X29 @ X28 ) ) )
=> ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,powersetI]),powersetE]),subsetI2]),subsetE]) ).
thf(c_0_7,negated_conjecture,
! [X30: $i,X31: $i,X33: $i,X34: $i,X35: $i,X36: $i,X37: $i,X39: $i,X40: $i,X41: $i] :
( ( ( in @ ( esk1_2 @ X30 @ X31 ) @ X31 )
| ( in @ X31 @ ( powerset @ X30 ) ) )
& ( ~ ( in @ ( esk1_2 @ X30 @ X31 ) @ X30 )
| ( in @ X31 @ ( powerset @ X30 ) ) )
& ( ~ ( in @ X34 @ ( powerset @ X33 ) )
| ~ ( in @ X35 @ X34 )
| ( in @ X35 @ X33 ) )
& ( ( in @ ( esk2_2 @ X36 @ X37 ) @ X36 )
| ( subset @ X36 @ X37 ) )
& ( ~ ( in @ ( esk2_2 @ X36 @ X37 ) @ X37 )
| ( subset @ X36 @ X37 ) )
& ( ~ ( subset @ X39 @ X40 )
| ~ ( in @ X41 @ X39 )
| ( in @ X41 @ X40 ) )
& ( subset @ esk3_0 @ esk4_0 )
& ~ ( subset @ ( powerset @ 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_6])])])])])]) ).
thf(c_0_8,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ X3 @ X2 )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk2_2 @ X1 @ X2 ) @ X1 )
| ( subset @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ X3 @ X2 )
| ~ ( subset @ X1 @ X2 )
| ~ ( in @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
subset @ esk3_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( subset @ ( powerset @ X1 ) @ X2 )
| ( in @ X3 @ X1 )
| ~ ( in @ X3 @ ( esk2_2 @ ( powerset @ X1 ) @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_13,negated_conjecture,
! [X2: $i,X1: $i] :
( ( in @ ( esk1_2 @ X1 @ X2 ) @ X2 )
| ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ esk4_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ ( esk1_2 @ X1 @ ( esk2_2 @ ( powerset @ X2 ) @ X3 ) ) @ X2 )
| ( in @ ( esk2_2 @ ( powerset @ X2 ) @ X3 ) @ ( powerset @ X1 ) )
| ( subset @ ( powerset @ X2 ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X2: $i,X1: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
| ~ ( in @ ( esk1_2 @ X1 @ X2 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_2 @ X1 @ ( esk2_2 @ ( powerset @ esk3_0 ) @ X2 ) ) @ esk4_0 )
| ( in @ ( esk2_2 @ ( powerset @ esk3_0 ) @ X2 ) @ ( powerset @ X1 ) )
| ( subset @ ( powerset @ esk3_0 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
| ~ ( in @ ( esk2_2 @ X1 @ X2 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk2_2 @ ( powerset @ esk3_0 ) @ X1 ) @ ( powerset @ esk4_0 ) )
| ( subset @ ( powerset @ esk3_0 ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_20,negated_conjecture,
~ ( subset @ ( powerset @ esk3_0 ) @ ( powerset @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU579^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 % Computer : n018.cluster.edu
% 0.08/0.24 % Model : x86_64 x86_64
% 0.08/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.24 % Memory : 8046.5625MB
% 0.08/0.24 % OS : Linux 6.8.0-71-generic
% 0.08/0.24 % CPULimit : 300
% 0.08/0.24 % WCLimit : 300
% 0.08/0.24 % DateTime : Tue Sep 29 13:54:11 UTC 2026
% 0.08/0.24 % CPUTime :
% 0.08/0.24 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.28 Running higher-order theorem proving
% 0.16/0.29 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.p33oSvgEZV/E---3.1_109867.p
% 0.16/0.31 % Version: 3.5.1-ho
% 0.16/0.31 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.16/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.31 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.16/0.31 % Starting post_as_ho8 with 300s (1) cores
% 0.16/0.31 % Starting post_as_ho3 with 300s (1) cores
% 0.16/0.31 % Starting post_as_ho2 with 300s (1) cores
% 0.16/0.31 % lpo6_lambda_fix with pid 109890 completed with status 0
% 0.16/0.31 % Result found by lpo6_lambda_fix
% 0.16/0.31 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.16/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.31 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.16/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.16/0.31 % No SInE strategy applied
% 0.16/0.31 % Search class: HGUNF-FFSF21-SFFFMFNN
% 0.16/0.31 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.31 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.31 % Starting lpo6_lambda_fix with 151s (1) cores
% 0.16/0.31 % Starting sh5l with 136s (1) cores
% 0.16/0.31 % Starting new_bool_1 with 136s (1) cores
% 0.16/0.31 % Starting new_bool_2 with 136s (1) cores
% 0.16/0.31 % SubtermCWHack with pid 109894 completed with status 0
% 0.16/0.31 % Result found by SubtermCWHack
% 0.16/0.31 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.16/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.31 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.16/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.16/0.31 % No SInE strategy applied
% 0.16/0.31 % Search class: HGUNF-FFSF21-SFFFMFNN
% 0.16/0.31 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.31 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.31 % Preprocessing time : 0.001 s
% 0.16/0.31
% 0.16/0.31 % Proof found!
% 0.16/0.31 % SZS status Theorem
% 0.16/0.31 % SZS output start CNFRefutation
% See solution above
% 0.16/0.31 % Parsed axioms : 12
% 0.16/0.31 % Removed by relevancy pruning/SinE : 0
% 0.16/0.31 % Initial clauses : 15
% 0.16/0.31 % Removed in clause preprocessing : 7
% 0.16/0.31 % Initial clauses in saturation : 8
% 0.16/0.31 % Processed clauses : 31
% 0.16/0.31 % ...of these trivial : 0
% 0.16/0.31 % ...subsumed : 5
% 0.16/0.31 % ...remaining for further processing : 26
% 0.16/0.31 % Other redundant clauses eliminated : 0
% 0.16/0.31 % Clauses deleted for lack of memory : 0
% 0.16/0.31 % Backward-subsumed : 0
% 0.16/0.31 % Backward-rewritten : 0
% 0.16/0.31 % Generated clauses : 43
% 0.16/0.31 % ...of the previous two non-redundant : 39
% 0.16/0.31 % ...aggressively subsumed : 0
% 0.16/0.31 % Contextual simplify-reflections : 0
% 0.16/0.31 % Paramodulations : 43
% 0.16/0.31 % Factorizations : 0
% 0.16/0.31 % NegExts : 0
% 0.16/0.31 % Equation resolutions : 0
% 0.16/0.31 % Disequality decompositions : 0
% 0.16/0.31 % Total rewrite steps : 1
% 0.16/0.31 % ...of those cached : 0
% 0.16/0.31 % Propositional unsat checks : 0
% 0.16/0.31 % Propositional check models : 0
% 0.16/0.31 % Propositional check unsatisfiable : 0
% 0.16/0.31 % Propositional clauses : 0
% 0.16/0.31 % Propositional clauses after purity: 0
% 0.16/0.31 % Propositional unsat core size : 0
% 0.16/0.31 % Propositional preprocessing time : 0.000
% 0.16/0.31 % Propositional encoding time : 0.000
% 0.16/0.31 % Propositional solver time : 0.000
% 0.16/0.31 % Success case prop preproc time : 0.000
% 0.16/0.31 % Success case prop encoding time : 0.000
% 0.16/0.31 % Success case prop solver time : 0.000
% 0.16/0.31 % Current number of processed clauses : 26
% 0.16/0.31 % Positive orientable unit clauses : 4
% 0.16/0.31 % Positive unorientable unit clauses: 0
% 0.16/0.31 % Negative unit clauses : 1
% 0.16/0.31 % Non-unit-clauses : 21
% 0.16/0.31 % Current number of unprocessed clauses: 15
% 0.16/0.31 % ...number of literals in the above : 57
% 0.16/0.31 % Current number of archived formulas : 0
% 0.16/0.31 % Current number of archived clauses : 0
% 0.16/0.31 % Clause-clause subsumption calls (NU) : 95
% 0.16/0.31 % Rec. Clause-clause subsumption calls : 65
% 0.16/0.31 % Non-unit clause-clause subsumptions : 5
% 0.16/0.31 % Unit Clause-clause subsumption calls : 5
% 0.16/0.31 % Rewrite failures with RHS unbound : 0
% 0.16/0.31 % BW rewrite match attempts : 6
% 0.16/0.31 % BW rewrite match successes : 0
% 0.16/0.31 % Condensation attempts : 0
% 0.16/0.31 % Condensation successes : 0
% 0.16/0.31 % Termbank termtop insertions : 2004
% 0.16/0.31 % Search garbage collected termcells : 387
% 0.16/0.31
% 0.16/0.31 % -------------------------------------------------
% 0.16/0.31 % User time : 0.005 s
% 0.16/0.31 % System time : 0.001 s
% 0.16/0.31 % Total time : 0.007 s
% 0.16/0.31 % Maximum resident set size: 3584 pages
% 0.16/0.31
% 0.16/0.31 % -------------------------------------------------
% 0.16/0.31 % User time : 0.012 s
% 0.16/0.31 % System time : 0.008 s
% 0.16/0.31 % Total time : 0.020 s
% 0.16/0.31 % Maximum resident set size: 4864 pages
% 0.16/0.31 % E exiting
%------------------------------------------------------------------------------