%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU828^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 20 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 82 ( 27 ~; 12 |; 2 &; 33 @)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 27 ^; 15 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
seteq: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(decl_24,type,
subseteq: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_25,type,
powerset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_26,type,
emptyset: $i > $o ).
thf(decl_27,type,
epred1_0: $i > $o ).
thf(decl_28,type,
esk1_0: $i ).
thf(decl_29,type,
esk2_0: $i ).
thf(poserset,axiom,
( powerset
= ( ^ [X7: $i > $o,X8: $i > $o] : ( subseteq @ X8 @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.J8jcVb32yB/E---3.1_173421.p',poserset) ).
thf(subseteq,axiom,
( subseteq
= ( ^ [X4: $i > $o,X5: $i > $o] :
! [X6: $i] :
( ( X4 @ X6 )
=> ( X5 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.J8jcVb32yB/E---3.1_173421.p',subseteq) ).
thf(conj,conjecture,
( seteq @ ( powerset @ emptyset )
@ ^ [X10: $i > $o] : ( X10 = emptyset ) ),
file('/export/starexec/sandbox2/tmp/tmp.J8jcVb32yB/E---3.1_173421.p',conj) ).
thf(seteq,axiom,
( seteq
= ( ^ [X1: ( $i > $o ) > $o,X2: ( $i > $o ) > $o] :
! [X3: $i > $o] :
( ( X1 @ X3 )
<=> ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.J8jcVb32yB/E---3.1_173421.p',seteq) ).
thf(emptyset,axiom,
( emptyset
= ( ^ [X9: $i] : ~ $true ) ),
file('/export/starexec/sandbox2/tmp/tmp.J8jcVb32yB/E---3.1_173421.p',emptyset) ).
thf(c_0_5,plain,
( powerset
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X11: $i] :
( ( Z1 @ X11 )
=> ( Z0 @ X11 ) ) ) ),
inference(fof_simplification,[status(thm)],[poserset]) ).
thf(c_0_6,plain,
( subseteq
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X6: $i] :
( ( Z0 @ X6 )
=> ( Z1 @ X6 ) ) ) ),
inference(fof_simplification,[status(thm)],[subseteq]) ).
thf(c_0_7,negated_conjecture,
~ ( seteq @ ( powerset @ emptyset )
@ ^ [X10: $i > $o] : ( X10 = emptyset ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_8,plain,
( seteq
= ( ^ [Z0: ( $i > $o ) > $o,Z1: ( $i > $o ) > $o] :
! [X3: $i > $o] :
( ( Z0 @ X3 )
<=> ( Z1 @ X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[seteq]) ).
thf(c_0_9,plain,
( powerset
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X11: $i] :
( ( Z1 @ X11 )
=> ( Z0 @ X11 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_10,plain,
( emptyset
= ( ^ [Z0: $i] : ~ $true ) ),
inference(fof_simplification,[status(thm)],[emptyset]) ).
thf(c_0_11,negated_conjecture,
~ ! [X13: $i > $o] :
( ! [X12: $i] :
( ( X13 @ X12 )
=> ~ $true )
<=> ( X13
= ( ^ [Z0: $i] : ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_7]),c_0_8]),c_0_9]),c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X16: $i] :
( ( ( epred1_0 @ esk1_0 )
| ( epred1_0
!= ( ^ [Z0: $i] : ~ $true ) ) )
& ( $true
| ( epred1_0
!= ( ^ [Z0: $i] : ~ $true ) ) )
& ( ~ ( epred1_0 @ X16 )
| ~ $true
| ( epred1_0
= ( ^ [Z0: $i] : ~ $true ) ) ) ),
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_11])])])])])]) ).
thf(c_0_13,negated_conjecture,
! [X6: $i] :
( ( epred1_0
= ( ^ [Z0: $i] : ~ $true ) )
| ~ ( epred1_0 @ X6 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X6: $i] :
( ( epred1_0
= ( ^ [Z0: $i] : ~ $true ) )
| ~ ( epred1_0 @ X6 ) ),
inference(cn,[status(thm)],[c_0_13]) ).
thf(c_0_15,negated_conjecture,
( ( epred1_0 @ esk1_0 )
| ( epred1_0
!= ( ^ [Z0: $i] : ~ $true ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X6: $i] :
( ( ( ^ [Z0: $i] : ~ $true )
= epred1_0 )
| ~ ( epred1_0 @ X6 ) ),
inference(cn,[status(thm)],[c_0_14]) ).
thf(c_0_17,negated_conjecture,
( ( epred1_0 @ esk1_0 )
| ( ( ^ [Z0: $i] : ~ $true )
!= epred1_0 ) ),
inference(cn,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X6: $i,X9: $i] :
( ~ ( epred1_0 @ X6 )
| ~ ( epred1_0 @ X9 ) ),
inference(arg_cong,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
( ( epred1_0 @ esk1_0 )
| ( epred1_0 @ esk2_0 ) ),
inference(neg_ext,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X6: $i] :
~ ( epred1_0 @ X6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_16]),c_0_18]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_19,c_0_20]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU828^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n011.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 14:39:46 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.J8jcVb32yB/E---3.1_173421.p
% 0.09/0.24 % Version: 3.5.1-ho
% 0.09/0.24 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.09/0.24 % Starting sh5l with 300s (1) cores
% 0.09/0.24 % Starting full_lambda_10 with 300s (1) cores
% 0.09/0.24 % Starting full_lambda_6 with 300s (1) cores
% 0.09/0.24 % ehoh_best_nonlift_nonlambdatoforall with pid 173434 completed with status 0
% 0.09/0.24 % Result found by ehoh_best_nonlift_nonlambdatoforall
% 0.09/0.24 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.09/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.24 % No SInE strategy applied
% 0.09/0.24 % Search class: HHUSF-FFSF00-SHHFMFNN
% 0.09/0.24 % partial match(2): HHUNF-FFSF00-SHHSMFNN
% 0.09/0.24 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.24 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.24 % Starting ehoh_best_nonlift_nonlambdatoforall with 151s (1) cores
% 0.09/0.24 % Starting sh5l with 136s (1) cores
% 0.09/0.24 % Starting new_bool_1 with 136s (1) cores
% 0.09/0.24 % Starting new_bool_2 with 136s (1) cores
% 0.09/0.24 % SubtermCWHack with pid 173438 completed with status 10
% 0.09/0.24 % Starting new_bool_9 with 136s (1) cores
% 0.09/0.24 % new_bool_2 with pid 173442 completed with status 0
% 0.09/0.24 % Result found by new_bool_2
% 0.09/0.24 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.09/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.24 % No SInE strategy applied
% 0.09/0.24 % Search class: HHUSF-FFSF00-SHHFMFNN
% 0.09/0.24 % partial match(2): HHUNF-FFSF00-SHHSMFNN
% 0.09/0.24 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.24 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.24 % Starting ehoh_best_nonlift_nonlambdatoforall with 151s (1) cores
% 0.09/0.24 % Starting sh5l with 136s (1) cores
% 0.09/0.24 % Starting new_bool_1 with 136s (1) cores
% 0.09/0.24 % Starting new_bool_2 with 136s (1) cores
% 0.09/0.24 % Preprocessing time : 0.001 s
% 0.09/0.24 % Presaturation interreduction done
% 0.09/0.24
% 0.09/0.24 % Proof found!
% 0.09/0.24 % SZS status Theorem
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.24 % Parsed axioms : 9
% 0.09/0.24 % Removed by relevancy pruning/SinE : 0
% 0.09/0.24 % Initial clauses : 7
% 0.09/0.24 % Removed in clause preprocessing : 5
% 0.09/0.24 % Initial clauses in saturation : 2
% 0.09/0.24 % Processed clauses : 7
% 0.09/0.24 % ...of these trivial : 0
% 0.09/0.24 % ...subsumed : 0
% 0.09/0.24 % ...remaining for further processing : 7
% 0.09/0.24 % Other redundant clauses eliminated : 0
% 0.09/0.24 % Clauses deleted for lack of memory : 0
% 0.09/0.24 % Backward-subsumed : 2
% 0.09/0.24 % Backward-rewritten : 0
% 0.09/0.24 % Generated clauses : 6
% 0.09/0.24 % ...of the previous two non-redundant : 5
% 0.09/0.24 % ...aggressively subsumed : 0
% 0.09/0.24 % Contextual simplify-reflections : 1
% 0.09/0.24 % Paramodulations : 3
% 0.09/0.24 % Factorizations : 0
% 0.09/0.24 % NegExts : 1
% 0.09/0.24 % Equation resolutions : 0
% 0.09/0.24 % Disequality decompositions : 0
% 0.09/0.24 % Total rewrite steps : 0
% 0.09/0.24 % ...of those cached : 0
% 0.09/0.24 % Propositional unsat checks : 0
% 0.09/0.24 % Propositional check models : 0
% 0.09/0.24 % Propositional check unsatisfiable : 0
% 0.09/0.24 % Propositional clauses : 0
% 0.09/0.24 % Propositional clauses after purity: 0
% 0.09/0.24 % Propositional unsat core size : 0
% 0.09/0.24 % Propositional preprocessing time : 0.000
% 0.09/0.24 % Propositional encoding time : 0.000
% 0.09/0.24 % Propositional solver time : 0.000
% 0.09/0.24 % Success case prop preproc time : 0.000
% 0.09/0.24 % Success case prop encoding time : 0.000
% 0.09/0.24 % Success case prop solver time : 0.000
% 0.09/0.24 % Current number of processed clauses : 2
% 0.09/0.24 % Positive orientable unit clauses : 0
% 0.09/0.24 % Positive unorientable unit clauses: 0
% 0.09/0.24 % Negative unit clauses : 1
% 0.09/0.24 % Non-unit-clauses : 1
% 0.09/0.24 % Current number of unprocessed clauses: 2
% 0.09/0.24 % ...number of literals in the above : 4
% 0.09/0.24 % Current number of archived formulas : 0
% 0.09/0.24 % Current number of archived clauses : 5
% 0.09/0.24 % Clause-clause subsumption calls (NU) : 2
% 0.09/0.24 % Rec. Clause-clause subsumption calls : 1
% 0.09/0.24 % Non-unit clause-clause subsumptions : 1
% 0.09/0.24 % Unit Clause-clause subsumption calls : 2
% 0.09/0.24 % Rewrite failures with RHS unbound : 0
% 0.09/0.24 % BW rewrite match attempts : 0
% 0.09/0.24 % BW rewrite match successes : 0
% 0.09/0.24 % Condensation attempts : 0
% 0.09/0.24 % Condensation successes : 0
% 0.09/0.24 % Termbank termtop insertions : 601
% 0.09/0.24 % Search garbage collected termcells : 146
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.003 s
% 0.09/0.24 % System time : 0.002 s
% 0.09/0.24 % Total time : 0.006 s
% 0.09/0.24 % Maximum resident set size: 3636 pages
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.010 s
% 0.09/0.24 % System time : 0.009 s
% 0.09/0.24 % Total time : 0.019 s
% 0.09/0.24 % Maximum resident set size: 4864 pages
% 0.09/0.24 % E exiting
%------------------------------------------------------------------------------