%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU513^2 : 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 : n012.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 08:24:19 AM UTC 2026
% Result : Theorem 0.08s 0.13s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 8 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 45 ( 4 ~; 0 |; 1 &; 36 @)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
setadjoin: $i > $i > $i ).
thf(decl_26,type,
setadjoinIL: $o ).
thf(emptyinunitempty,conjecture,
( setadjoinIL
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wLpk89MZxp/E---3.1_125826.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wLpk89MZxp/E---3.1_125826.p',setadjoinIL) ).
thf(c_0_2,negated_conjecture,
~ ( setadjoinIL
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(assume_negation,[status(cth)],[emptyinunitempty]) ).
thf(c_0_3,negated_conjecture,
~ ( ! [X5: $i,X6: $i] : ( in @ X5 @ ( setadjoin @ X5 @ X6 ) )
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(apply_def,[status(thm)],[c_0_2,setadjoinIL]) ).
thf(c_0_4,negated_conjecture,
! [X7: $i,X8: $i] :
( ( in @ X7 @ ( setadjoin @ X7 @ X8 ) )
& ~ ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
thf(c_0_5,negated_conjecture,
~ ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_7,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_6])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU513^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 13:47:03 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.13 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.wLpk89MZxp/E---3.1_125826.p
% 0.08/0.13 % Version: 3.5.1-ho
% 0.08/0.13 % Preprocessing class: HSSSSMSSSLSNFFN.
% 0.08/0.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.13 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.13 % Starting sh5l with 300s (1) cores
% 0.08/0.13 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.13 % Starting lpo1_def_fix with 300s (1) cores
% 0.08/0.13 % sh5l with pid 125840 completed with status 0
% 0.08/0.13 % Result found by sh5l
% 0.08/0.13 % Preprocessing class: HSSSSMSSSLSNFFN.
% 0.08/0.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.13 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.13 % Starting sh5l with 300s (1) cores
% 0.08/0.13 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.08/0.13 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.08/0.13 % Search class: HUUNF-FFSF22-SFFFMFNN
% 0.08/0.13 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.13 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.13 % SubtermCWHack with pid 125843 completed with status 0
% 0.08/0.13 % Result found by SubtermCWHack
% 0.08/0.13 % Preprocessing class: HSSSSMSSSLSNFFN.
% 0.08/0.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.13 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.13 % Starting sh5l with 300s (1) cores
% 0.08/0.13 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.08/0.13 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.08/0.13 % Search class: HUUNF-FFSF22-SFFFMFNN
% 0.08/0.13 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.13 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.13 % Preprocessing time : 0.001 s
% 0.08/0.13
% 0.08/0.13 % Proof found!
% 0.08/0.13 % SZS status Theorem
% 0.08/0.13 % SZS output start CNFRefutation
% See solution above
% 0.08/0.13 % Parsed axioms : 6
% 0.08/0.13 % Removed by relevancy pruning/SinE : 4
% 0.08/0.13 % Initial clauses : 2
% 0.08/0.13 % Removed in clause preprocessing : 0
% 0.08/0.13 % Initial clauses in saturation : 2
% 0.08/0.13 % Processed clauses : 2
% 0.08/0.13 % ...of these trivial : 0
% 0.08/0.13 % ...subsumed : 0
% 0.08/0.13 % ...remaining for further processing : 1
% 0.08/0.13 % Other redundant clauses eliminated : 0
% 0.08/0.13 % Clauses deleted for lack of memory : 0
% 0.08/0.13 % Backward-subsumed : 0
% 0.08/0.13 % Backward-rewritten : 0
% 0.08/0.13 % Generated clauses : 0
% 0.08/0.13 % ...of the previous two non-redundant : 0
% 0.08/0.13 % ...aggressively subsumed : 0
% 0.08/0.13 % Contextual simplify-reflections : 0
% 0.08/0.13 % Paramodulations : 0
% 0.08/0.13 % Factorizations : 0
% 0.08/0.13 % NegExts : 0
% 0.08/0.13 % Equation resolutions : 0
% 0.08/0.13 % Disequality decompositions : 0
% 0.08/0.13 % Total rewrite steps : 1
% 0.08/0.13 % ...of those cached : 0
% 0.08/0.13 % Propositional unsat checks : 0
% 0.08/0.13 % Propositional check models : 0
% 0.08/0.13 % Propositional check unsatisfiable : 0
% 0.08/0.13 % Propositional clauses : 0
% 0.08/0.13 % Propositional clauses after purity: 0
% 0.08/0.13 % Propositional unsat core size : 0
% 0.08/0.13 % Propositional preprocessing time : 0.000
% 0.08/0.13 % Propositional encoding time : 0.000
% 0.08/0.13 % Propositional solver time : 0.000
% 0.08/0.13 % Success case prop preproc time : 0.000
% 0.08/0.13 % Success case prop encoding time : 0.000
% 0.08/0.13 % Success case prop solver time : 0.000
% 0.08/0.13 % Current number of processed clauses : 1
% 0.08/0.13 % Positive orientable unit clauses : 1
% 0.08/0.13 % Positive unorientable unit clauses: 0
% 0.08/0.13 % Negative unit clauses : 0
% 0.08/0.13 % Non-unit-clauses : 0
% 0.08/0.13 % Current number of unprocessed clauses: 0
% 0.08/0.13 % ...number of literals in the above : 0
% 0.08/0.13 % Current number of archived formulas : 0
% 0.08/0.13 % Current number of archived clauses : 0
% 0.08/0.13 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.13 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.13 % Non-unit clause-clause subsumptions : 0
% 0.08/0.13 % Unit Clause-clause subsumption calls : 0
% 0.08/0.13 % Rewrite failures with RHS unbound : 0
% 0.08/0.13 % BW rewrite match attempts : 0
% 0.08/0.13 % BW rewrite match successes : 0
% 0.08/0.13 % Condensation attempts : 0
% 0.08/0.13 % Condensation successes : 0
% 0.08/0.13 % Termbank termtop insertions : 155
% 0.08/0.13 % Search garbage collected termcells : 37
% 0.08/0.13
% 0.08/0.13 % -------------------------------------------------
% 0.08/0.13 % User time : 0.002 s
% 0.08/0.13 % System time : 0.001 s
% 0.08/0.13 % Total time : 0.002 s
% 0.08/0.13 % Maximum resident set size: 3576 pages
% 0.08/0.13
% 0.08/0.13 % -------------------------------------------------
% 0.08/0.13 % User time : 0.002 s
% 0.08/0.13 % System time : 0.004 s
% 0.08/0.13 % Total time : 0.005 s
% 0.08/0.13 % Maximum resident set size: 4864 pages
% 0.08/0.13 % E exiting
%------------------------------------------------------------------------------