%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU713^2 : 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 : n004.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 08:27:30 AM UTC 2026
% Result : Theorem 0.24s 0.27s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 0 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 237 ( 13 ~; 13 |; 6 &; 177 @)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% 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,
setminus: $i > $i > $i ).
thf(decl_28,type,
setminusEL: $o ).
thf(decl_29,type,
esk1_2: $i > $i > $i ).
thf(decl_30,type,
esk2_0: $i ).
thf(decl_31,type,
esk3_0: $i ).
thf(decl_32,type,
esk4_0: $i ).
thf(setminusT_lem,conjecture,
( powersetI
=> ( powersetE
=> ( setminusEL
=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X4 @ X5 ) @ ( powerset @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iygzZzX98G/E---3.1_1347696.p',setminusT_lem) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( in @ X2 @ ( powerset @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iygzZzX98G/E---3.1_1347696.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/sandbox/tmp/tmp.iygzZzX98G/E---3.1_1347696.p',powersetE) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iygzZzX98G/E---3.1_1347696.p',setminusEL) ).
thf(c_0_4,negated_conjecture,
~ ( powersetI
=> ( powersetE
=> ( setminusEL
=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X4 @ X5 ) @ ( powerset @ X1 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[setminusT_lem]) ).
thf(c_0_5,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 @ ( setminus @ X24 @ X25 ) )
=> ( in @ X26 @ X24 ) )
=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X4 @ X5 ) @ ( powerset @ X1 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,powersetI]),powersetE]),setminusEL]) ).
thf(c_0_6,negated_conjecture,
! [X27: $i,X28: $i,X30: $i,X31: $i,X32: $i,X33: $i,X34: $i,X35: $i] :
( ( ( in @ ( esk1_2 @ X27 @ X28 ) @ X28 )
| ( in @ X28 @ ( powerset @ X27 ) ) )
& ( ~ ( in @ ( esk1_2 @ X27 @ X28 ) @ X27 )
| ( in @ X28 @ ( powerset @ X27 ) ) )
& ( ~ ( in @ X31 @ ( powerset @ X30 ) )
| ~ ( in @ X32 @ X31 )
| ( in @ X32 @ X30 ) )
& ( ~ ( in @ X35 @ ( setminus @ X33 @ X34 ) )
| ( in @ X35 @ X33 ) )
& ( in @ esk3_0 @ ( powerset @ esk2_0 ) )
& ( in @ esk4_0 @ ( powerset @ esk2_0 ) )
& ~ ( in @ ( setminus @ esk3_0 @ esk4_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,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ X3 @ X2 )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
in @ esk3_0 @ ( powerset @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X1 @ X2 )
| ~ ( in @ X1 @ ( setminus @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
! [X2: $i,X1: $i] :
( ( in @ ( esk1_2 @ X1 @ X2 ) @ X2 )
| ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ esk2_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_12,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk1_2 @ X1 @ ( setminus @ X2 @ X3 ) ) @ X2 )
| ( in @ ( setminus @ X2 @ X3 ) @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X2: $i,X1: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
| ~ ( in @ ( esk1_2 @ X1 @ X2 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_14,negated_conjecture,
! [X2: $i,X1: $i] :
( ( in @ ( esk1_2 @ X1 @ ( setminus @ esk3_0 @ X2 ) ) @ esk2_0 )
| ( in @ ( setminus @ esk3_0 @ X2 ) @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_15,negated_conjecture,
~ ( in @ ( setminus @ esk3_0 @ esk4_0 ) @ ( powerset @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] : ( in @ ( setminus @ esk3_0 @ X1 ) @ ( powerset @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU713^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:13:36 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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.iygzZzX98G/E---3.1_1347696.p
% 0.24/0.27 % Version: 3.5.1-ho
% 0.24/0.27 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.24/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.27 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.24/0.27 % Starting post_as_ho8 with 300s (1) cores
% 0.24/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.24/0.27 % Starting post_as_ho2 with 300s (1) cores
% 0.24/0.27 % lpo6_lambda_fix with pid 1347727 completed with status 0
% 0.24/0.27 % Result found by lpo6_lambda_fix
% 0.24/0.27 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.24/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.27 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.24/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.24/0.27 % No SInE strategy applied
% 0.24/0.27 % Search class: HGUNF-FFSF21-SFFFMFNN
% 0.24/0.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.27 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.27 % Starting lpo6_lambda_fix with 151s (1) cores
% 0.24/0.27 % Starting sh5l with 136s (1) cores
% 0.24/0.27 % Starting new_bool_1 with 136s (1) cores
% 0.24/0.27 % Starting new_bool_2 with 136s (1) cores
% 0.24/0.27 % sh5l with pid 1347734 completed with status 0
% 0.24/0.27 % Result found by sh5l
% 0.24/0.27 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.24/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.27 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.24/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.24/0.27 % No SInE strategy applied
% 0.24/0.27 % Search class: HGUNF-FFSF21-SFFFMFNN
% 0.24/0.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.27 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.27 % Starting lpo6_lambda_fix with 151s (1) cores
% 0.24/0.27 % Starting sh5l with 136s (1) cores
% 0.24/0.27 % Preprocessing time : 0.001 s
% 0.24/0.27 % Presaturation interreduction done
% 0.24/0.27
% 0.24/0.27 % Proof found!
% 0.24/0.27 % SZS status Theorem
% 0.24/0.27 % SZS output start CNFRefutation
% See solution above
% 0.24/0.27 % Parsed axioms : 10
% 0.24/0.27 % Removed by relevancy pruning/SinE : 0
% 0.24/0.27 % Initial clauses : 13
% 0.24/0.27 % Removed in clause preprocessing : 6
% 0.24/0.27 % Initial clauses in saturation : 7
% 0.24/0.27 % Processed clauses : 29
% 0.24/0.27 % ...of these trivial : 0
% 0.24/0.27 % ...subsumed : 1
% 0.24/0.27 % ...remaining for further processing : 28
% 0.24/0.27 % Other redundant clauses eliminated : 0
% 0.24/0.27 % Clauses deleted for lack of memory : 0
% 0.24/0.27 % Backward-subsumed : 0
% 0.24/0.27 % Backward-rewritten : 1
% 0.24/0.27 % Generated clauses : 31
% 0.24/0.27 % ...of the previous two non-redundant : 27
% 0.24/0.27 % ...aggressively subsumed : 0
% 0.24/0.27 % Contextual simplify-reflections : 0
% 0.24/0.27 % Paramodulations : 31
% 0.24/0.27 % Factorizations : 0
% 0.24/0.27 % NegExts : 0
% 0.24/0.27 % Equation resolutions : 0
% 0.24/0.27 % Disequality decompositions : 0
% 0.24/0.27 % Total rewrite steps : 3
% 0.24/0.27 % ...of those cached : 0
% 0.24/0.27 % Propositional unsat checks : 0
% 0.24/0.27 % Propositional check models : 0
% 0.24/0.27 % Propositional check unsatisfiable : 0
% 0.24/0.27 % Propositional clauses : 0
% 0.24/0.27 % Propositional clauses after purity: 0
% 0.24/0.27 % Propositional unsat core size : 0
% 0.24/0.27 % Propositional preprocessing time : 0.000
% 0.24/0.27 % Propositional encoding time : 0.000
% 0.24/0.27 % Propositional solver time : 0.000
% 0.24/0.27 % Success case prop preproc time : 0.000
% 0.24/0.27 % Success case prop encoding time : 0.000
% 0.24/0.27 % Success case prop solver time : 0.000
% 0.24/0.27 % Current number of processed clauses : 20
% 0.24/0.27 % Positive orientable unit clauses : 6
% 0.24/0.27 % Positive unorientable unit clauses: 0
% 0.24/0.27 % Negative unit clauses : 0
% 0.24/0.27 % Non-unit-clauses : 14
% 0.24/0.27 % Current number of unprocessed clauses: 12
% 0.24/0.27 % ...number of literals in the above : 28
% 0.24/0.27 % Current number of archived formulas : 0
% 0.24/0.27 % Current number of archived clauses : 8
% 0.24/0.27 % Clause-clause subsumption calls (NU) : 54
% 0.24/0.27 % Rec. Clause-clause subsumption calls : 40
% 0.24/0.27 % Non-unit clause-clause subsumptions : 1
% 0.24/0.27 % Unit Clause-clause subsumption calls : 9
% 0.24/0.27 % Rewrite failures with RHS unbound : 0
% 0.24/0.27 % BW rewrite match attempts : 8
% 0.24/0.27 % BW rewrite match successes : 1
% 0.24/0.27 % Condensation attempts : 29
% 0.24/0.27 % Condensation successes : 0
% 0.24/0.27 % Termbank termtop insertions : 1837
% 0.24/0.27 % Search garbage collected termcells : 302
% 0.24/0.27
% 0.24/0.27 % -------------------------------------------------
% 0.24/0.27 % User time : 0.004 s
% 0.24/0.27 % System time : 0.002 s
% 0.24/0.27 % Total time : 0.006 s
% 0.24/0.27 % Maximum resident set size: 3636 pages
% 0.24/0.27
% 0.24/0.27 % -------------------------------------------------
% 0.24/0.27 % User time : 0.011 s
% 0.24/0.27 % System time : 0.010 s
% 0.24/0.27 % Total time : 0.021 s
% 0.24/0.27 % Maximum resident set size: 4608 pages
% 0.24/0.27 % E exiting
%------------------------------------------------------------------------------