%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU534^2 : 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 : n008.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 08:24:24 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 5 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 125 ( 13 ~; 6 |; 8 &; 75 @)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 36 ( 4 ^; 29 !; 3 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_26,type,
dsetconstrI: $o ).
thf(decl_27,type,
emptysetE: $o ).
thf(decl_28,type,
esk1_0: $i ).
thf(decl_29,type,
epred1_0: $i > $o ).
thf(decl_30,type,
esk2_0: $i ).
thf(emptyE1,conjecture,
( dsetconstrI
=> ( emptysetE
=> ! [X1: $i,X2: $i > $o] :
( ? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X2 @ X3 ) )
=> ( ( ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
= emptyset )
=> ~ $true ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.aVlCsaXZya/E---3.1_3181532.p',emptyE1) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.aVlCsaXZya/E---3.1_3181532.p',dsetconstrI) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X3: $i] :
( ( in @ X3 @ emptyset )
=> ! [X5: $o] : X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.aVlCsaXZya/E---3.1_3181532.p',emptysetE) ).
thf(c_0_3,negated_conjecture,
~ ( dsetconstrI
=> ( emptysetE
=> ! [X1: $i,X2: $i > $o] :
( ? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X2 @ X3 ) )
=> ( ( ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
= emptyset )
=> ~ $true ) ) ) ),
inference(assume_negation,[status(cth)],[emptyE1]) ).
thf(c_0_4,plain,
( dsetconstrI
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrI]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X14: $i,X15: $i > $o,X16: $i] :
( ( in @ X16 @ X14 )
=> ( ( X15 @ X16 )
=> ( in @ X16 @ ( dsetconstr @ X14 @ X15 ) ) ) )
=> ( ! [X17: $i] :
( ( in @ X17 @ emptyset )
=> ! [X18: $o] : X18 )
=> ! [X1: $i,X2: $i > $o] :
( ? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X2 @ X3 ) )
=> ( ( ( dsetconstr @ X1 @ X2 )
= emptyset )
=> ~ $true ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_3]),c_0_4]),emptysetE])]) ).
thf(c_0_6,negated_conjecture,
! [X19: $i,X20: $i > $o,X21: $i,X22: $i,X23: $o] :
( ( ~ ( in @ X21 @ X19 )
| ~ ( X20 @ X21 )
| ( in @ X21 @ ( dsetconstr @ X19 @ X20 ) ) )
& ( ~ ( in @ X22 @ emptyset )
| X23 )
& ( in @ esk2_0 @ esk1_0 )
& ( epred1_0 @ esk2_0 )
& ( ( dsetconstr @ esk1_0 @ epred1_0 )
= emptyset )
& $true ),
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 > $o,X1: $i] :
( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
| ~ ( in @ X1 @ X3 )
| ~ ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
( ( dsetconstr @ esk1_0 @ epred1_0 )
= emptyset ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i] :
~ ( in @ X1 @ emptyset ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_6])])]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ esk1_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
thf(c_0_11,negated_conjecture,
in @ esk2_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_12,negated_conjecture,
epred1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU534^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n008.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 13:49:24 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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.aVlCsaXZya/E---3.1_3181532.p
% 0.10/0.26 % Version: 3.5.1-ho
% 0.10/0.26 % Preprocessing class: HSSSSLSSSLMNSSA.
% 0.10/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.10/0.26 % Starting new_bool_9 with 300s (1) cores
% 0.10/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.10/0.26 % new_ho_10 with pid 3181569 completed with status 0
% 0.10/0.26 % Result found by new_ho_10
% 0.10/0.26 % Preprocessing class: HSSSSLSSSLMNSSA.
% 0.10/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.26 % No SInE strategy applied
% 0.10/0.26 % Search class: HHUSF-FFSS22-SSSFMSBN
% 0.10/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.10/0.26 % Starting new_ho_10 with 901s (1) cores
% 0.10/0.26 % Starting sh5l with 151s (1) cores
% 0.10/0.26 % Starting new_bool_1 with 151s (1) cores
% 0.10/0.26 % Starting new_bool_2 with 146s (1) cores
% 0.10/0.26 % SubtermCWHack with pid 3181574 completed with status 0
% 0.10/0.26 % Result found by SubtermCWHack
% 0.10/0.26 % Preprocessing class: HSSSSLSSSLMNSSA.
% 0.10/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.26 % No SInE strategy applied
% 0.10/0.26 % Search class: HHUSF-FFSS22-SSSFMSBN
% 0.10/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.10/0.26 % Preprocessing time : 0.001 s
% 0.10/0.26
% 0.10/0.26 % Proof found!
% 0.10/0.26 % SZS status Theorem
% 0.10/0.26 % SZS output start CNFRefutation
% See solution above
% 0.10/0.26 % Parsed axioms : 8
% 0.10/0.26 % Removed by relevancy pruning/SinE : 0
% 0.10/0.26 % Initial clauses : 11
% 0.10/0.26 % Removed in clause preprocessing : 6
% 0.10/0.26 % Initial clauses in saturation : 5
% 0.10/0.26 % Processed clauses : 6
% 0.10/0.26 % ...of these trivial : 0
% 0.10/0.26 % ...subsumed : 0
% 0.10/0.26 % ...remaining for further processing : 6
% 0.10/0.26 % Other redundant clauses eliminated : 0
% 0.10/0.26 % Clauses deleted for lack of memory : 0
% 0.10/0.26 % Backward-subsumed : 0
% 0.10/0.26 % Backward-rewritten : 0
% 0.10/0.26 % Generated clauses : 2
% 0.10/0.26 % ...of the previous two non-redundant : 1
% 0.10/0.26 % ...aggressively subsumed : 0
% 0.10/0.26 % Contextual simplify-reflections : 0
% 0.10/0.26 % Paramodulations : 2
% 0.10/0.26 % Factorizations : 0
% 0.10/0.26 % NegExts : 0
% 0.10/0.26 % Equation resolutions : 0
% 0.10/0.26 % Disequality decompositions : 0
% 0.10/0.26 % Total rewrite steps : 1
% 0.10/0.26 % ...of those cached : 0
% 0.10/0.26 % Propositional unsat checks : 0
% 0.10/0.26 % Propositional check models : 0
% 0.10/0.26 % Propositional check unsatisfiable : 0
% 0.10/0.26 % Propositional clauses : 0
% 0.10/0.26 % Propositional clauses after purity: 0
% 0.10/0.26 % Propositional unsat core size : 0
% 0.10/0.26 % Propositional preprocessing time : 0.000
% 0.10/0.26 % Propositional encoding time : 0.000
% 0.10/0.26 % Propositional solver time : 0.000
% 0.10/0.26 % Success case prop preproc time : 0.000
% 0.10/0.26 % Success case prop encoding time : 0.000
% 0.10/0.26 % Success case prop solver time : 0.000
% 0.10/0.26 % Current number of processed clauses : 6
% 0.10/0.26 % Positive orientable unit clauses : 3
% 0.10/0.26 % Positive unorientable unit clauses: 0
% 0.10/0.26 % Negative unit clauses : 1
% 0.10/0.26 % Non-unit-clauses : 2
% 0.10/0.26 % Current number of unprocessed clauses: 0
% 0.10/0.26 % ...number of literals in the above : 0
% 0.10/0.26 % Current number of archived formulas : 0
% 0.10/0.26 % Current number of archived clauses : 0
% 0.10/0.26 % Clause-clause subsumption calls (NU) : 1
% 0.10/0.26 % Rec. Clause-clause subsumption calls : 1
% 0.10/0.26 % Non-unit clause-clause subsumptions : 0
% 0.10/0.26 % Unit Clause-clause subsumption calls : 0
% 0.10/0.26 % Rewrite failures with RHS unbound : 0
% 0.10/0.26 % BW rewrite match attempts : 0
% 0.10/0.26 % BW rewrite match successes : 0
% 0.10/0.26 % Condensation attempts : 0
% 0.10/0.26 % Condensation successes : 0
% 0.10/0.26 % Termbank termtop insertions : 725
% 0.10/0.26 % Search garbage collected termcells : 252
% 0.10/0.26
% 0.10/0.26 % -------------------------------------------------
% 0.10/0.26 % User time : 0.002 s
% 0.10/0.26 % System time : 0.003 s
% 0.10/0.26 % Total time : 0.005 s
% 0.10/0.26 % Maximum resident set size: 3636 pages
% 0.10/0.26
% 0.10/0.26 % -------------------------------------------------
% 0.10/0.26 % User time : 0.007 s
% 0.10/0.26 % System time : 0.012 s
% 0.10/0.26 % Total time : 0.020 s
% 0.10/0.26 % Maximum resident set size: 4864 pages
% 0.10/0.26 % E exiting
%------------------------------------------------------------------------------