%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU728^2 : 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 : 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 08:25:23 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 0 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 171 ( 15 ~; 6 |; 5 &; 122 @)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 33 ( 0 ^; 33 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
powerset: $i > $i ).
thf(decl_25,type,
setminus: $i > $i > $i ).
thf(decl_26,type,
setminusI: $o ).
thf(decl_27,type,
setminusER: $o ).
thf(decl_28,type,
esk1_0: $i ).
thf(decl_29,type,
esk2_0: $i ).
thf(decl_30,type,
esk3_0: $i ).
thf(doubleComplementE1,conjecture,
( setminusI
=> ( setminusER
=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( setminus @ X1 @ X4 ) ) )
=> ( in @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aAKPvgJ13Z/E---3.1_145855.p',doubleComplementE1) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aAKPvgJ13Z/E---3.1_145855.p',setminusI) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aAKPvgJ13Z/E---3.1_145855.p',setminusER) ).
thf(c_0_3,negated_conjecture,
~ ( setminusI
=> ( setminusER
=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( setminus @ X1 @ X4 ) ) )
=> ( in @ X3 @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[doubleComplementE1]) ).
thf(c_0_4,negated_conjecture,
~ ( ! [X14: $i,X15: $i,X16: $i] :
( ( in @ X16 @ X14 )
=> ( ~ ( in @ X16 @ X15 )
=> ( in @ X16 @ ( setminus @ X14 @ X15 ) ) ) )
=> ( ! [X17: $i,X18: $i,X19: $i] :
( ( in @ X19 @ ( setminus @ X17 @ X18 ) )
=> ~ ( in @ X19 @ X18 ) )
=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( setminus @ X1 @ X4 ) ) )
=> ( in @ X3 @ X4 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,setminusI]),setminusER])]) ).
thf(c_0_5,negated_conjecture,
! [X20: $i,X21: $i,X22: $i,X23: $i,X24: $i,X25: $i] :
( ( ~ ( in @ X22 @ X20 )
| ( in @ X22 @ X21 )
| ( in @ X22 @ ( setminus @ X20 @ X21 ) ) )
& ( ~ ( in @ X25 @ ( setminus @ X23 @ X24 ) )
| ~ ( in @ X25 @ X24 ) )
& ( in @ esk2_0 @ ( powerset @ esk1_0 ) )
& ( in @ esk3_0 @ esk1_0 )
& ( in @ esk3_0 @ ( setminus @ esk1_0 @ ( setminus @ esk1_0 @ esk2_0 ) ) )
& ~ ( in @ esk3_0 @ esk2_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,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( in @ X1 @ ( setminus @ X2 @ X3 ) )
| ~ ( in @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
in @ esk3_0 @ ( setminus @ esk1_0 @ ( setminus @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
~ ( in @ esk3_0 @ ( setminus @ esk1_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ X1 @ X3 )
| ( in @ X1 @ ( setminus @ X2 @ X3 ) )
| ~ ( in @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,negated_conjecture,
in @ esk3_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_11,negated_conjecture,
~ ( in @ esk3_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]),c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU728^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n018.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:19:26 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.21 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.23/0.26 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.aAKPvgJ13Z/E---3.1_145855.p
% 0.23/0.29 % Version: 3.5.1-ho
% 0.23/0.29 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.23/0.29 % Starting post_as_ho8 with 300s (1) cores
% 0.23/0.29 % Starting post_as_ho3 with 300s (1) cores
% 0.23/0.29 % Starting post_as_ho2 with 300s (1) cores
% 0.23/0.29 % post_as_ho2 with pid 145871 completed with status 0
% 0.23/0.29 % Result found by post_as_ho2
% 0.23/0.29 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.23/0.29 % Starting post_as_ho8 with 300s (1) cores
% 0.23/0.29 % Starting post_as_ho3 with 300s (1) cores
% 0.23/0.29 % Starting post_as_ho2 with 300s (1) cores
% 0.23/0.29 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.29 % No SInE strategy applied
% 0.23/0.29 % Search class: HGHNF-FFSS21-SFFFMFNN
% 0.23/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.29 % SubtermCWHack with pid 145872 completed with status 0
% 0.23/0.29 % Result found by SubtermCWHack
% 0.23/0.29 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.23/0.29 % Starting post_as_ho8 with 300s (1) cores
% 0.23/0.29 % Starting post_as_ho3 with 300s (1) cores
% 0.23/0.29 % Starting post_as_ho2 with 300s (1) cores
% 0.23/0.29 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.29 % No SInE strategy applied
% 0.23/0.29 % Search class: HGHNF-FFSS21-SFFFMFNN
% 0.23/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.29 % Preprocessing time : 0.001 s
% 0.23/0.29
% 0.23/0.29 % Proof found!
% 0.23/0.29 % SZS status Theorem
% 0.23/0.29 % SZS output start CNFRefutation
% See solution above
% 0.23/0.29 % Parsed axioms : 8
% 0.23/0.29 % Removed by relevancy pruning/SinE : 0
% 0.23/0.29 % Initial clauses : 11
% 0.23/0.29 % Removed in clause preprocessing : 5
% 0.23/0.29 % Initial clauses in saturation : 6
% 0.23/0.29 % Processed clauses : 7
% 0.23/0.29 % ...of these trivial : 0
% 0.23/0.29 % ...subsumed : 0
% 0.23/0.29 % ...remaining for further processing : 7
% 0.23/0.29 % Other redundant clauses eliminated : 0
% 0.23/0.29 % Clauses deleted for lack of memory : 0
% 0.23/0.29 % Backward-subsumed : 0
% 0.23/0.29 % Backward-rewritten : 0
% 0.23/0.29 % Generated clauses : 3
% 0.23/0.29 % ...of the previous two non-redundant : 1
% 0.23/0.29 % ...aggressively subsumed : 0
% 0.23/0.29 % Contextual simplify-reflections : 0
% 0.23/0.29 % Paramodulations : 3
% 0.23/0.29 % Factorizations : 0
% 0.23/0.29 % NegExts : 0
% 0.23/0.29 % Equation resolutions : 0
% 0.23/0.29 % Disequality decompositions : 0
% 0.23/0.29 % Total rewrite steps : 1
% 0.23/0.29 % ...of those cached : 0
% 0.23/0.29 % Propositional unsat checks : 0
% 0.23/0.29 % Propositional check models : 0
% 0.23/0.29 % Propositional check unsatisfiable : 0
% 0.23/0.29 % Propositional clauses : 0
% 0.23/0.29 % Propositional clauses after purity: 0
% 0.23/0.29 % Propositional unsat core size : 0
% 0.23/0.29 % Propositional preprocessing time : 0.000
% 0.23/0.29 % Propositional encoding time : 0.000
% 0.23/0.29 % Propositional solver time : 0.000
% 0.23/0.29 % Success case prop preproc time : 0.000
% 0.23/0.29 % Success case prop encoding time : 0.000
% 0.23/0.29 % Success case prop solver time : 0.000
% 0.23/0.29 % Current number of processed clauses : 7
% 0.23/0.29 % Positive orientable unit clauses : 3
% 0.23/0.29 % Positive unorientable unit clauses: 0
% 0.23/0.29 % Negative unit clauses : 2
% 0.23/0.29 % Non-unit-clauses : 2
% 0.23/0.29 % Current number of unprocessed clauses: 0
% 0.23/0.29 % ...number of literals in the above : 0
% 0.23/0.29 % Current number of archived formulas : 0
% 0.23/0.29 % Current number of archived clauses : 0
% 0.23/0.29 % Clause-clause subsumption calls (NU) : 1
% 0.23/0.29 % Rec. Clause-clause subsumption calls : 1
% 0.23/0.29 % Non-unit clause-clause subsumptions : 0
% 0.23/0.29 % Unit Clause-clause subsumption calls : 0
% 0.23/0.29 % Rewrite failures with RHS unbound : 0
% 0.23/0.29 % BW rewrite match attempts : 0
% 0.23/0.29 % BW rewrite match successes : 0
% 0.23/0.29 % Condensation attempts : 0
% 0.23/0.29 % Condensation successes : 0
% 0.23/0.29 % Termbank termtop insertions : 707
% 0.23/0.29 % Search garbage collected termcells : 239
% 0.23/0.29
% 0.23/0.29 % -------------------------------------------------
% 0.23/0.29 % User time : 0.004 s
% 0.23/0.29 % System time : 0.000 s
% 0.23/0.29 % Total time : 0.004 s
% 0.23/0.29 % Maximum resident set size: 3632 pages
% 0.23/0.29
% 0.23/0.29 % -------------------------------------------------
% 0.23/0.29 % User time : 0.005 s
% 0.23/0.29 % System time : 0.006 s
% 0.23/0.29 % Total time : 0.011 s
% 0.23/0.29 % Maximum resident set size: 4608 pages
% 0.23/0.29 % E exiting
%------------------------------------------------------------------------------