%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU526^2 : 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 : n001.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 08:24:22 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 15 equ; 0 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 144 ( 18 ~; 14 |; 9 &; 82 @)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 31 ( 2 ^; 26 !; 3 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
emptysetE: $o ).
thf(decl_26,type,
setext: $o ).
thf(decl_27,type,
nonempty: $i > $o ).
thf(decl_28,type,
esk1_2: $i > $i > $i ).
thf(decl_29,type,
esk2_2: $i > $i > $i ).
thf(decl_30,type,
esk3_0: $i ).
thf(nonemptyImpWitness,conjecture,
( emptysetE
=> ( setext
=> ! [X3: $i] :
( ( nonempty @ X3 )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& $true ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.QSShWIV2mL/E---3.1_1273197.p',nonemptyImpWitness) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X1: $i] : ( X1 != emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.QSShWIV2mL/E---3.1_1273197.p',nonempty) ).
thf(setext,axiom,
( setext
<=> ! [X3: $i,X4: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ X4 ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) )
=> ( X3 = X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.QSShWIV2mL/E---3.1_1273197.p',setext) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $o] : X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.QSShWIV2mL/E---3.1_1273197.p',emptysetE) ).
thf(c_0_4,negated_conjecture,
~ ( emptysetE
=> ( setext
=> ! [X3: $i] :
( ( nonempty @ X3 )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& $true ) ) ) ),
inference(assume_negation,[status(cth)],[nonemptyImpWitness]) ).
thf(c_0_5,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X13: $i] :
( ( in @ X13 @ emptyset )
=> ! [X14: $o] : X14 )
=> ( ! [X15: $i,X16: $i] :
( ! [X17: $i] :
( ( in @ X17 @ X15 )
=> ( in @ X17 @ X16 ) )
=> ( ! [X18: $i] :
( ( in @ X18 @ X16 )
=> ( in @ X18 @ X15 ) )
=> ( X15 = X16 ) ) )
=> ! [X3: $i] :
( ( X3 != emptyset )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& $true ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,setext]),c_0_5]),emptysetE])]) ).
thf(c_0_7,negated_conjecture,
! [X19: $i,X20: $o,X21: $i,X22: $i,X26: $i] :
( ( ~ ( in @ X19 @ emptyset )
| X20 )
& ( ( in @ ( esk2_2 @ X21 @ X22 ) @ X22 )
| ( X21 = X22 )
| ( in @ ( esk1_2 @ X21 @ X22 ) @ X21 ) )
& ( ~ ( in @ ( esk2_2 @ X21 @ X22 ) @ X21 )
| ( X21 = X22 )
| ( in @ ( esk1_2 @ X21 @ X22 ) @ X21 ) )
& ( ( in @ ( esk2_2 @ X21 @ X22 ) @ X22 )
| ( X21 = X22 )
| ~ ( in @ ( esk1_2 @ X21 @ X22 ) @ X22 ) )
& ( ~ ( in @ ( esk2_2 @ X21 @ X22 ) @ X21 )
| ( X21 = X22 )
| ~ ( in @ ( esk1_2 @ X21 @ X22 ) @ X22 ) )
& ( esk3_0 != emptyset )
& ( ~ ( in @ X26 @ esk3_0 )
| ~ $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_6])])])])])]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ esk3_0 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i] :
~ ( in @ X1 @ esk3_0 ),
inference(cn,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X3: $i,X1: $i] :
( ( in @ ( esk2_2 @ X1 @ X3 ) @ X3 )
| ( X1 = X3 )
| ( in @ ( esk1_2 @ X1 @ X3 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i] :
~ ( in @ X1 @ emptyset ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7])])]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ( esk3_0 = X1 )
| ( in @ ( esk2_2 @ esk3_0 @ X1 ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,negated_conjecture,
esk3_0 != emptyset,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU526^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n001.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 13:54:05 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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.QSShWIV2mL/E---3.1_1273197.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.25 % Starting lpo1_def_fix with 300s (1) cores
% 0.07/0.25 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.07/0.25 % ehoh_best_sine_rwall with pid 1273216 completed with status 0
% 0.07/0.25 % Result found by ehoh_best_sine_rwall
% 0.07/0.25 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.25 % Search class: HGUSF-FFSF22-SSFFMFNN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 1273221 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.25 % Search class: HGUSF-FFSF22-SSFFMFNN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 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 : 9
% 0.07/0.25 % Removed by relevancy pruning/SinE : 5
% 0.07/0.25 % Initial clauses : 7
% 0.07/0.25 % Removed in clause preprocessing : 0
% 0.07/0.25 % Initial clauses in saturation : 7
% 0.07/0.25 % Processed clauses : 5
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 0
% 0.07/0.25 % ...remaining for further processing : 5
% 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 : 0
% 0.07/0.25 % Backward-rewritten : 0
% 0.07/0.25 % Generated clauses : 3
% 0.07/0.25 % ...of the previous two non-redundant : 2
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 3
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 0
% 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 : 5
% 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 : 3
% 0.07/0.25 % Non-unit-clauses : 2
% 0.07/0.25 % Current number of unprocessed clauses: 4
% 0.07/0.25 % ...number of literals in the above : 11
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 0
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 1
% 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 : 0
% 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 : 0
% 0.07/0.25 % Condensation successes : 0
% 0.07/0.25 % Termbank termtop insertions : 705
% 0.07/0.25 % Search garbage collected termcells : 263
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.002 s
% 0.07/0.25 % System time : 0.002 s
% 0.07/0.25 % Total time : 0.004 s
% 0.07/0.25 % Maximum resident set size: 3580 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.003 s
% 0.07/0.25 % System time : 0.007 s
% 0.07/0.25 % Total time : 0.010 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------