%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU500^2 : 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 : n005.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 08:24:16 AM UTC 2026
% Result : Theorem 0.06s 0.24s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 4 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 94 ( 11 ~; 5 |; 3 &; 64 @)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 9 ^; 23 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
powerset: $i > $i ).
thf(decl_26,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_27,type,
dsetconstrER: $o ).
thf(decl_28,type,
prop2set: $o > $i ).
thf(decl_29,type,
epred1_0: $o ).
thf(decl_30,type,
esk1_0: $i ).
thf(prop2setE,conjecture,
( dsetconstrER
=> ! [X6: $o,X3: $i] :
( ( in @ X3 @ ( prop2set @ X6 ) )
=> X6 ) ),
file('/export/starexec/sandbox/tmp/tmp.ZB7DDUiPrf/E---3.1_1687919.p',prop2setE) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZB7DDUiPrf/E---3.1_1687919.p',dsetconstrER) ).
thf(prop2set,axiom,
( prop2set
= ( ^ [X5: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X3: $i] : X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZB7DDUiPrf/E---3.1_1687919.p',prop2set) ).
thf(c_0_3,negated_conjecture,
~ ( dsetconstrER
=> ! [X6: $o,X3: $i] :
( ( in @ X3 @ ( prop2set @ X6 ) )
=> X6 ) ),
inference(assume_negation,[status(cth)],[prop2setE]) ).
thf(c_0_4,plain,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X12: $i,X13: $i > $o,X14: $i] :
( ( in @ X14 @ ( dsetconstr @ X12 @ X13 ) )
=> ( X13 @ X14 ) )
=> ! [X6: $o,X3: $i] :
( ( in @ X3 @ ( prop2set @ X6 ) )
=> X6 ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,c_0_4])]) ).
thf(c_0_6,plain,
( prop2set
= ( ^ [Z0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(fof_simplification,[status(thm)],[prop2set]) ).
thf(c_0_7,negated_conjecture,
! [X15: $i,X16: $i > $o,X17: $i] :
( ( ~ ( in @ X17 @ ( dsetconstr @ X15 @ X16 ) )
| ( X16 @ X17 ) )
& ( ~ epred1_0
| ( in @ esk1_0 @ ( prop2set @ $true ) ) )
& ( epred1_0
| ( in @ esk1_0 @ ( prop2set @ $false ) ) )
& ~ epred1_0 ),
inference(fof_nnf,[status(thm)],[inference(fool_unroll,[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_8,plain,
( prop2set
= ( ^ [Z0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
( epred1_0
| ( in @ esk1_0 @ ( prop2set @ ~ $true ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
~ epred1_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X5: $o] :
( ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X5 )
= ( prop2set @ X5 ) ),
inference(arg_cong,[status(thm)],[c_0_8]) ).
thf(c_0_13,negated_conjecture,
in @ esk1_0 @ ( prop2set @ ~ $true ),
inference(sr,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i] :
~ ( in @ X1 @ ( prop2set @ ~ $true ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12])])]) ).
thf(c_0_15,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_13,c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU500^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n005.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 13:46:31 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.22 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.ZB7DDUiPrf/E---3.1_1687919.p
% 0.06/0.24 % Version: 3.5.1-ho
% 0.06/0.24 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.06/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.06/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.06/0.24 % Starting sh4l with 300s (1) cores
% 0.06/0.24 % Starting lpo8_s with 300s (1) cores
% 0.06/0.24 % ho_unfolding_6 with pid 1687952 completed with status 0
% 0.06/0.24 % Result found by ho_unfolding_6
% 0.06/0.24 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.06/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.06/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.06/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.06/0.24 % No SInE strategy applied
% 0.06/0.24 % Search class: HGUSF-FFSF21-MSFFMSBN
% 0.06/0.24 % partial match(1): HGUSF-FFSF21-MSFFMMBN
% 0.06/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.06/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.06/0.24 % SubtermCWHack with pid 1687956 completed with status 0
% 0.06/0.24 % Result found by SubtermCWHack
% 0.06/0.24 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.06/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.06/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.06/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.06/0.24 % No SInE strategy applied
% 0.06/0.24 % Search class: HGUSF-FFSF21-MSFFMSBN
% 0.06/0.24 % partial match(1): HGUSF-FFSF21-MSFFMMBN
% 0.06/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.06/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.06/0.24 % Preprocessing time : 0.001 s
% 0.06/0.24
% 0.06/0.24 % Proof found!
% 0.06/0.24 % SZS status Theorem
% 0.06/0.24 % SZS output start CNFRefutation
% See solution above
% 0.06/0.24 % Parsed axioms : 9
% 0.06/0.24 % Removed by relevancy pruning/SinE : 0
% 0.06/0.24 % Initial clauses : 11
% 0.06/0.24 % Removed in clause preprocessing : 6
% 0.06/0.24 % Initial clauses in saturation : 5
% 0.06/0.24 % Processed clauses : 7
% 0.06/0.24 % ...of these trivial : 0
% 0.06/0.24 % ...subsumed : 1
% 0.06/0.24 % ...remaining for further processing : 6
% 0.06/0.24 % Other redundant clauses eliminated : 0
% 0.06/0.24 % Clauses deleted for lack of memory : 0
% 0.06/0.24 % Backward-subsumed : 0
% 0.06/0.24 % Backward-rewritten : 0
% 0.06/0.24 % Generated clauses : 3
% 0.06/0.24 % ...of the previous two non-redundant : 2
% 0.06/0.24 % ...aggressively subsumed : 0
% 0.06/0.24 % Contextual simplify-reflections : 0
% 0.06/0.24 % Paramodulations : 1
% 0.06/0.24 % Factorizations : 0
% 0.06/0.24 % NegExts : 0
% 0.06/0.24 % Equation resolutions : 0
% 0.06/0.24 % Disequality decompositions : 0
% 0.06/0.24 % Total rewrite steps : 0
% 0.06/0.24 % ...of those cached : 0
% 0.06/0.24 % Propositional unsat checks : 0
% 0.06/0.24 % Propositional check models : 0
% 0.06/0.24 % Propositional check unsatisfiable : 0
% 0.06/0.24 % Propositional clauses : 0
% 0.06/0.24 % Propositional clauses after purity: 0
% 0.06/0.24 % Propositional unsat core size : 0
% 0.06/0.24 % Propositional preprocessing time : 0.000
% 0.06/0.24 % Propositional encoding time : 0.000
% 0.06/0.24 % Propositional solver time : 0.000
% 0.06/0.24 % Success case prop preproc time : 0.000
% 0.06/0.24 % Success case prop encoding time : 0.000
% 0.06/0.24 % Success case prop solver time : 0.000
% 0.06/0.24 % Current number of processed clauses : 5
% 0.06/0.24 % Positive orientable unit clauses : 2
% 0.06/0.24 % Positive unorientable unit clauses: 0
% 0.06/0.24 % Negative unit clauses : 2
% 0.06/0.24 % Non-unit-clauses : 1
% 0.06/0.24 % Current number of unprocessed clauses: 0
% 0.06/0.24 % ...number of literals in the above : 0
% 0.06/0.24 % Current number of archived formulas : 0
% 0.06/0.24 % Current number of archived clauses : 1
% 0.06/0.24 % Clause-clause subsumption calls (NU) : 0
% 0.06/0.24 % Rec. Clause-clause subsumption calls : 0
% 0.06/0.24 % Non-unit clause-clause subsumptions : 0
% 0.06/0.24 % Unit Clause-clause subsumption calls : 1
% 0.06/0.24 % Rewrite failures with RHS unbound : 0
% 0.06/0.24 % BW rewrite match attempts : 0
% 0.06/0.24 % BW rewrite match successes : 0
% 0.06/0.24 % Condensation attempts : 0
% 0.06/0.24 % Condensation successes : 0
% 0.06/0.24 % Termbank termtop insertions : 549
% 0.06/0.24 % Search garbage collected termcells : 146
% 0.06/0.24
% 0.06/0.24 % -------------------------------------------------
% 0.06/0.24 % User time : 0.003 s
% 0.06/0.24 % System time : 0.002 s
% 0.06/0.24 % Total time : 0.005 s
% 0.06/0.24 % Maximum resident set size: 3636 pages
% 0.06/0.24
% 0.06/0.24 % -------------------------------------------------
% 0.06/0.24 % User time : 0.005 s
% 0.06/0.24 % System time : 0.006 s
% 0.06/0.24 % Total time : 0.011 s
% 0.06/0.24 % Maximum resident set size: 4864 pages
% 0.06/0.24 % E exiting
%------------------------------------------------------------------------------