%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU622^2 : 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 : n026.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 08:24:46 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 9 ~; 4 |; 3 &; 83 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
setadjoin: $i > $i > $i ).
thf(decl_26,type,
powerset: $i > $i ).
thf(decl_27,type,
subset: $i > $i > $o ).
thf(decl_28,type,
powersetI1: $o ).
thf(decl_29,type,
singletonsubset: $o ).
thf(decl_30,type,
esk1_0: $i ).
thf(decl_31,type,
esk2_0: $i ).
thf(singletoninpowerset,conjecture,
( powersetI1
=> ( singletonsubset
=> ! [X1: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EoqVByTeZc/E---3.1_645557.p',singletoninpowerset) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ X1 )
=> ( in @ X2 @ ( powerset @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EoqVByTeZc/E---3.1_645557.p',powersetI1) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X1: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EoqVByTeZc/E---3.1_645557.p',singletonsubset) ).
thf(c_0_3,negated_conjecture,
~ ( powersetI1
=> ( singletonsubset
=> ! [X1: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[singletoninpowerset]) ).
thf(c_0_4,negated_conjecture,
~ ( ! [X10: $i,X11: $i] :
( ( subset @ X11 @ X10 )
=> ( in @ X11 @ ( powerset @ X10 ) ) )
=> ( ! [X12: $i,X13: $i] :
( ( in @ X13 @ X12 )
=> ( subset @ ( setadjoin @ X13 @ emptyset ) @ X12 ) )
=> ! [X1: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ X1 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,powersetI1]),singletonsubset]) ).
thf(c_0_5,negated_conjecture,
! [X14: $i,X15: $i,X16: $i,X17: $i] :
( ( ~ ( subset @ X15 @ X14 )
| ( in @ X15 @ ( powerset @ X14 ) ) )
& ( ~ ( in @ X17 @ X16 )
| ( subset @ ( setadjoin @ X17 @ emptyset ) @ X16 ) )
& ( in @ esk2_0 @ esk1_0 )
& ~ ( in @ ( setadjoin @ esk2_0 @ emptyset ) @ ( powerset @ esk1_0 ) ) ),
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,
~ ( in @ ( setadjoin @ esk2_0 @ emptyset ) @ ( powerset @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( subset @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
~ ( subset @ ( setadjoin @ esk2_0 @ emptyset ) @ esk1_0 ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X2 )
| ~ ( in @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,negated_conjecture,
in @ esk2_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU622^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n026.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 14:01:42 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 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.EoqVByTeZc/E---3.1_645557.p
% 0.10/0.25 % Version: 3.5.1-ho
% 0.10/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.10/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.10/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.10/0.25 % Starting post_as_ho2 with 300s (1) cores
% 0.10/0.25 % post_as_ho2 with pid 645573 completed with status 0
% 0.10/0.25 % Result found by post_as_ho2
% 0.10/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.10/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.10/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.10/0.25 % Starting post_as_ho2 with 300s (1) cores
% 0.10/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.25 % No SInE strategy applied
% 0.10/0.25 % Search class: HHUNF-FFSF21-SFFFMFNN
% 0.10/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.25 % SubtermCWHack with pid 645577 completed with status 0
% 0.10/0.25 % Result found by SubtermCWHack
% 0.10/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.10/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.10/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.10/0.25 % Starting post_as_ho2 with 300s (1) cores
% 0.10/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.25 % No SInE strategy applied
% 0.10/0.25 % Search class: HHUNF-FFSF21-SFFFMFNN
% 0.10/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.25 % Preprocessing time : 0.001 s
% 0.10/0.25
% 0.10/0.25 % Proof found!
% 0.10/0.25 % SZS status Theorem
% 0.10/0.25 % SZS output start CNFRefutation
% See solution above
% 0.10/0.25 % Parsed axioms : 10
% 0.10/0.25 % Removed by relevancy pruning/SinE : 0
% 0.10/0.25 % Initial clauses : 11
% 0.10/0.25 % Removed in clause preprocessing : 7
% 0.10/0.25 % Initial clauses in saturation : 4
% 0.10/0.25 % Processed clauses : 5
% 0.10/0.25 % ...of these trivial : 0
% 0.10/0.25 % ...subsumed : 0
% 0.10/0.25 % ...remaining for further processing : 5
% 0.10/0.25 % Other redundant clauses eliminated : 0
% 0.10/0.25 % Clauses deleted for lack of memory : 0
% 0.10/0.25 % Backward-subsumed : 0
% 0.10/0.25 % Backward-rewritten : 0
% 0.10/0.25 % Generated clauses : 2
% 0.10/0.25 % ...of the previous two non-redundant : 1
% 0.10/0.25 % ...aggressively subsumed : 0
% 0.10/0.25 % Contextual simplify-reflections : 0
% 0.10/0.25 % Paramodulations : 2
% 0.10/0.25 % Factorizations : 0
% 0.10/0.25 % NegExts : 0
% 0.10/0.25 % Equation resolutions : 0
% 0.10/0.25 % Disequality decompositions : 0
% 0.10/0.25 % Total rewrite steps : 1
% 0.10/0.25 % ...of those cached : 0
% 0.10/0.25 % Propositional unsat checks : 0
% 0.10/0.25 % Propositional check models : 0
% 0.10/0.25 % Propositional check unsatisfiable : 0
% 0.10/0.25 % Propositional clauses : 0
% 0.10/0.25 % Propositional clauses after purity: 0
% 0.10/0.25 % Propositional unsat core size : 0
% 0.10/0.25 % Propositional preprocessing time : 0.000
% 0.10/0.25 % Propositional encoding time : 0.000
% 0.10/0.25 % Propositional solver time : 0.000
% 0.10/0.25 % Success case prop preproc time : 0.000
% 0.10/0.25 % Success case prop encoding time : 0.000
% 0.10/0.25 % Success case prop solver time : 0.000
% 0.10/0.25 % Current number of processed clauses : 5
% 0.10/0.25 % Positive orientable unit clauses : 1
% 0.10/0.25 % Positive unorientable unit clauses: 0
% 0.10/0.25 % Negative unit clauses : 2
% 0.10/0.25 % Non-unit-clauses : 2
% 0.10/0.25 % Current number of unprocessed clauses: 0
% 0.10/0.25 % ...number of literals in the above : 0
% 0.10/0.25 % Current number of archived formulas : 0
% 0.10/0.25 % Current number of archived clauses : 0
% 0.10/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.10/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.10/0.25 % Non-unit clause-clause subsumptions : 0
% 0.10/0.25 % Unit Clause-clause subsumption calls : 0
% 0.10/0.25 % Rewrite failures with RHS unbound : 0
% 0.10/0.25 % BW rewrite match attempts : 0
% 0.10/0.25 % BW rewrite match successes : 0
% 0.10/0.25 % Condensation attempts : 0
% 0.10/0.25 % Condensation successes : 0
% 0.10/0.25 % Termbank termtop insertions : 524
% 0.10/0.25 % Search garbage collected termcells : 151
% 0.10/0.25
% 0.10/0.25 % -------------------------------------------------
% 0.10/0.25 % User time : 0.003 s
% 0.10/0.25 % System time : 0.002 s
% 0.10/0.25 % Total time : 0.005 s
% 0.10/0.25 % Maximum resident set size: 3888 pages
% 0.10/0.25
% 0.10/0.25 % -------------------------------------------------
% 0.10/0.25 % User time : 0.004 s
% 0.10/0.25 % System time : 0.005 s
% 0.10/0.25 % Total time : 0.010 s
% 0.10/0.25 % Maximum resident set size: 4864 pages
% 0.10/0.25 % E exiting
%------------------------------------------------------------------------------