%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU510^2 : 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 : n004.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 0.25s 0.27s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 7 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 127 ( 13 ~; 6 |; 4 &; 81 @)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 42 ( 10 ^; 32 !; 0 ?; 42 :)
% 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,
nonempty: $i > $o ).
thf(decl_29,type,
esk1_0: $i ).
thf(decl_30,type,
epred1_0: $i > $o ).
thf(decl_31,type,
esk2_0: $i ).
thf(nonemptyI,conjecture,
( dsetconstrI
=> ( emptysetE
=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( nonempty
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.anVsoJeHPN/E---3.1_1309672.p',nonemptyI) ).
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/sandbox/tmp/tmp.anVsoJeHPN/E---3.1_1309672.p',dsetconstrI) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X3: $i] : ( X3 != emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.anVsoJeHPN/E---3.1_1309672.p',nonempty) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X3: $i] :
( ( in @ X3 @ emptyset )
=> ! [X5: $o] : X5 ) ),
file('/export/starexec/sandbox/tmp/tmp.anVsoJeHPN/E---3.1_1309672.p',emptysetE) ).
thf(c_0_4,negated_conjecture,
~ ( dsetconstrI
=> ( emptysetE
=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( nonempty
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[nonemptyI]) ).
thf(c_0_5,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_6,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_7,negated_conjecture,
~ ( ! [X14: $i,X15: $i > $o,X16: $i] :
( ( in @ X16 @ X14 )
=> ( ( X15 @ X16 )
=> ( in @ X16
@ ( dsetconstr @ X14
@ ^ [Z0: $i] : ( X15 @ Z0 ) ) ) ) )
=> ( ! [X17: $i] :
( ( in @ X17 @ emptyset )
=> ! [X18: $o] : X18 )
=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_4]),emptysetE]),c_0_5]),c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X19: $i,X20: $i > $o,X21: $i,X22: $i,X23: $o] :
( ( ~ ( in @ X21 @ X19 )
| ~ ( X20 @ X21 )
| ( in @ X21
@ ( dsetconstr @ X19
@ ^ [Z0: $i] : ( X20 @ Z0 ) ) ) )
& ( ~ ( in @ X22 @ emptyset )
| X23 )
& ( in @ esk2_0 @ esk1_0 )
& ( epred1_0 @ esk2_0 )
& ( ( dsetconstr @ esk1_0
@ ^ [Z0: $i] : ( epred1_0 @ Z0 ) )
= emptyset ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
thf(c_0_9,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_8]) ).
thf(c_0_10,negated_conjecture,
( ( dsetconstr @ esk1_0 @ epred1_0 )
= emptyset ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
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_8])])]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ esk1_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
thf(c_0_13,negated_conjecture,
in @ esk2_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,negated_conjecture,
epred1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU510^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n004.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 13:47:07 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.24 Running higher-order theorem proving
% 0.06/0.25 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.anVsoJeHPN/E---3.1_1309672.p
% 0.25/0.27 % Version: 3.5.1-ho
% 0.25/0.27 % Preprocessing class: HSSSSLSSSLMNSSA.
% 0.25/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.25/0.27 % Starting new_bool_9 with 300s (1) cores
% 0.25/0.27 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.25/0.27 % new_bool_2 with pid 1309705 completed with status 0
% 0.25/0.27 % Result found by new_bool_2
% 0.25/0.27 % Preprocessing class: HSSSSLSSSLMNSSA.
% 0.25/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.25/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.27 % Search class: HHUSF-FFSS22-SSSFMSBN
% 0.25/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.27 % SubtermCWHack with pid 1309711 completed with status 0
% 0.25/0.27 % Result found by SubtermCWHack
% 0.25/0.27 % Preprocessing class: HSSSSLSSSLMNSSA.
% 0.25/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.25/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.27 % Search class: HHUSF-FFSS22-SSSFMSBN
% 0.25/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.27 % Preprocessing time : 0.001 s
% 0.25/0.27
% 0.25/0.27 % Proof found!
% 0.25/0.27 % SZS status Theorem
% 0.25/0.27 % SZS output start CNFRefutation
% See solution above
% 0.25/0.27 % Parsed axioms : 10
% 0.25/0.27 % Removed by relevancy pruning/SinE : 6
% 0.25/0.27 % Initial clauses : 5
% 0.25/0.27 % Removed in clause preprocessing : 0
% 0.25/0.27 % Initial clauses in saturation : 5
% 0.25/0.27 % Processed clauses : 6
% 0.25/0.27 % ...of these trivial : 0
% 0.25/0.27 % ...subsumed : 0
% 0.25/0.27 % ...remaining for further processing : 6
% 0.25/0.27 % Other redundant clauses eliminated : 0
% 0.25/0.27 % Clauses deleted for lack of memory : 0
% 0.25/0.27 % Backward-subsumed : 0
% 0.25/0.27 % Backward-rewritten : 0
% 0.25/0.27 % Generated clauses : 2
% 0.25/0.27 % ...of the previous two non-redundant : 1
% 0.25/0.27 % ...aggressively subsumed : 0
% 0.25/0.27 % Contextual simplify-reflections : 0
% 0.25/0.27 % Paramodulations : 2
% 0.25/0.27 % Factorizations : 0
% 0.25/0.27 % NegExts : 0
% 0.25/0.27 % Equation resolutions : 0
% 0.25/0.27 % Disequality decompositions : 0
% 0.25/0.27 % Total rewrite steps : 1
% 0.25/0.27 % ...of those cached : 0
% 0.25/0.27 % Propositional unsat checks : 0
% 0.25/0.27 % Propositional check models : 0
% 0.25/0.27 % Propositional check unsatisfiable : 0
% 0.25/0.27 % Propositional clauses : 0
% 0.25/0.27 % Propositional clauses after purity: 0
% 0.25/0.27 % Propositional unsat core size : 0
% 0.25/0.27 % Propositional preprocessing time : 0.000
% 0.25/0.27 % Propositional encoding time : 0.000
% 0.25/0.27 % Propositional solver time : 0.000
% 0.25/0.27 % Success case prop preproc time : 0.000
% 0.25/0.27 % Success case prop encoding time : 0.000
% 0.25/0.27 % Success case prop solver time : 0.000
% 0.25/0.27 % Current number of processed clauses : 6
% 0.25/0.27 % Positive orientable unit clauses : 3
% 0.25/0.27 % Positive unorientable unit clauses: 0
% 0.25/0.27 % Negative unit clauses : 1
% 0.25/0.27 % Non-unit-clauses : 2
% 0.25/0.27 % Current number of unprocessed clauses: 0
% 0.25/0.27 % ...number of literals in the above : 0
% 0.25/0.27 % Current number of archived formulas : 0
% 0.25/0.27 % Current number of archived clauses : 0
% 0.25/0.27 % Clause-clause subsumption calls (NU) : 1
% 0.25/0.27 % Rec. Clause-clause subsumption calls : 1
% 0.25/0.27 % Non-unit clause-clause subsumptions : 0
% 0.25/0.27 % Unit Clause-clause subsumption calls : 0
% 0.25/0.27 % Rewrite failures with RHS unbound : 0
% 0.25/0.27 % BW rewrite match attempts : 0
% 0.25/0.27 % BW rewrite match successes : 0
% 0.25/0.27 % Condensation attempts : 0
% 0.25/0.27 % Condensation successes : 0
% 0.25/0.27 % Termbank termtop insertions : 594
% 0.25/0.27 % Search garbage collected termcells : 206
% 0.25/0.27
% 0.25/0.27 % -------------------------------------------------
% 0.25/0.27 % User time : 0.001 s
% 0.25/0.27 % System time : 0.003 s
% 0.25/0.27 % Total time : 0.004 s
% 0.25/0.27 % Maximum resident set size: 3628 pages
% 0.25/0.27
% 0.25/0.27 % -------------------------------------------------
% 0.25/0.27 % User time : 0.002 s
% 0.25/0.27 % System time : 0.008 s
% 0.25/0.27 % Total time : 0.011 s
% 0.25/0.27 % Maximum resident set size: 4608 pages
% 0.25/0.27 % E exiting
%------------------------------------------------------------------------------