%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU829^1 : 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 : n011.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 08:25:47 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 20 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 52 ( 19 ~; 3 |; 0 &; 21 @)
% ( 0 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 26 ^; 10 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
subseteq: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_24,type,
powerset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_25,type,
emptyset: $i > $o ).
thf(decl_26,type,
esk1_1: $i > $o ).
thf(decl_27,type,
esk1_0: $i ).
thf(decl_28,type,
esk2_0: $i ).
thf(poserset,axiom,
( powerset
= ( ^ [X1: $i > $o,X2: $i > $o] : ( subseteq @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CDEjUGavKW/E---3.1_171826.p',poserset) ).
thf(subseteq,axiom,
( subseteq
= ( ^ [X1: $i > $o,X2: $i > $o] :
! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CDEjUGavKW/E---3.1_171826.p',subseteq) ).
thf(conj,conjecture,
( ( powerset @ emptyset )
= ( ^ [X1: $i > $o] : ( X1 = emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CDEjUGavKW/E---3.1_171826.p',conj) ).
thf(emptyset,axiom,
( emptyset
= ( ^ [X4: $i] : ~ $true ) ),
file('/export/starexec/sandbox/tmp/tmp.CDEjUGavKW/E---3.1_171826.p',emptyset) ).
thf(c_0_4,plain,
( powerset
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X5: $i] :
( ( Z1 @ X5 )
=> ( Z0 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[poserset]) ).
thf(c_0_5,plain,
( subseteq
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X3: $i] :
( ( Z0 @ X3 )
=> ( Z1 @ X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[subseteq]) ).
thf(c_0_6,negated_conjecture,
( ( powerset @ emptyset )
!= ( ^ [X1: $i > $o] : ( X1 = emptyset ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_7,plain,
( powerset
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X5: $i] :
( ( Z1 @ X5 )
=> ( Z0 @ X5 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_8,plain,
( emptyset
= ( ^ [Z0: $i] : ~ $true ) ),
inference(fof_simplification,[status(thm)],[emptyset]) ).
thf(c_0_9,negated_conjecture,
( ( ^ [Z0: $i > $o] :
! [X6: $i] :
( ( Z0 @ X6 )
=> ~ $true ) )
!= ( ^ [Z0: $i > $o] :
( Z0
= ( ^ [Z1: $i] : ~ $true ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_6]),c_0_7]),c_0_8])]) ).
thf(c_0_10,negated_conjecture,
( ( ^ [Z0: $i > $o] :
! [X6: $i] :
( ( Z0 @ X6 )
=> ~ $true ) )
!= ( ^ [Z0: $i > $o] :
( Z0
= ( ^ [Z1: $i] : ~ $true ) ) ) ),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
( ( ^ [Z0: $i > $o] :
! [X11: $i] :
( ( Z0 @ X11 )
=> ~ $true ) )
!= ( ^ [Z0: $i > $o] :
( Z0
= ( ^ [Z1: $i] : ~ $true ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
( ! [X12: $i] :
( ( esk1_1 @ X12 )
=> ~ $true )
<~> ( esk1_1
= ( ^ [Z0: $i] : ~ $true ) ) ),
inference(neg_ext,[status(thm)],[c_0_11]) ).
thf(c_0_13,negated_conjecture,
( ( esk1_1 @ esk1_0 )
| ( ( ^ [Z0: $i] : ~ $true )
!= esk1_1 ) ),
inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_12])]) ).
thf(c_0_14,negated_conjecture,
! [X3: $i] :
( ( ( ^ [Z0: $i] : ~ $true )
= esk1_1 )
| ~ ( esk1_1 @ X3 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_12])])]) ).
thf(c_0_15,negated_conjecture,
( ( esk1_1 @ esk1_0 )
| ( esk1_1 @ esk2_0 ) ),
inference(neg_ext,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X3: $i] :
~ ( esk1_1 @ X3 ),
inference(condense,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_14])]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_15,c_0_16]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU829^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n011.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:35:31 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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.CDEjUGavKW/E---3.1_171826.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.07/0.25 % Starting sh5l with 300s (1) cores
% 0.07/0.25 % Starting full_lambda_10 with 300s (1) cores
% 0.07/0.25 % Starting full_lambda_6 with 300s (1) cores
% 0.07/0.25 % ehoh_best_nonlift_nonlambdatoforall with pid 171839 completed with status 0
% 0.07/0.25 % Result found by ehoh_best_nonlift_nonlambdatoforall
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HUUPF-FFSF00-MHHFMFNN
% 0.07/0.25 % partial match(3): HUHPF-FFSF00-SHHFFFNN
% 0.07/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 151s (1) cores
% 0.07/0.25 % Starting sh5l with 136s (1) cores
% 0.07/0.25 % Starting new_bool_1 with 136s (1) cores
% 0.07/0.25 % Starting new_bool_2 with 136s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 171845 completed with status 10
% 0.07/0.25 % Starting new_bool_9 with 136s (1) cores
% 0.07/0.25 % sh5l with pid 171848 completed with status 0
% 0.07/0.25 % Result found by sh5l
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HUUPF-FFSF00-MHHFMFNN
% 0.07/0.25 % partial match(3): HUHPF-FFSF00-SHHFFFNN
% 0.07/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 151s (1) cores
% 0.07/0.25 % Starting sh5l with 136s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25 % Presaturation interreduction done
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 7
% 0.07/0.25 % Removed by relevancy pruning/SinE : 0
% 0.07/0.25 % Initial clauses : 4
% 0.07/0.25 % Removed in clause preprocessing : 3
% 0.07/0.25 % Initial clauses in saturation : 1
% 0.07/0.25 % Processed clauses : 8
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 1
% 0.07/0.25 % ...remaining for further processing : 7
% 0.07/0.25 % Other redundant clauses eliminated : 0
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 1
% 0.07/0.25 % Backward-rewritten : 0
% 0.07/0.25 % Generated clauses : 9
% 0.07/0.25 % ...of the previous two non-redundant : 7
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 1
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 2
% 0.07/0.25 % Equation resolutions : 0
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 0
% 0.07/0.25 % ...of those cached : 0
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 3
% 0.07/0.25 % Positive orientable unit clauses : 0
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 2
% 0.07/0.25 % Non-unit-clauses : 1
% 0.07/0.25 % Current number of unprocessed clauses: 1
% 0.07/0.25 % ...number of literals in the above : 2
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 4
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.25 % Non-unit clause-clause subsumptions : 0
% 0.07/0.25 % Unit Clause-clause subsumption calls : 3
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 0
% 0.07/0.25 % BW rewrite match successes : 0
% 0.07/0.25 % Condensation attempts : 8
% 0.07/0.25 % Condensation successes : 1
% 0.07/0.25 % Termbank termtop insertions : 605
% 0.07/0.25 % Search garbage collected termcells : 52
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.006 s
% 0.07/0.25 % System time : 0.002 s
% 0.07/0.25 % Total time : 0.008 s
% 0.07/0.25 % Maximum resident set size: 3632 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.011 s
% 0.07/0.25 % System time : 0.009 s
% 0.07/0.25 % Total time : 0.020 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------