%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU819^2 : 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 : n015.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 08:25:45 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 133 ( 14 equ; 0 cnn)
% Maximal formula atoms : 26 ( 6 avg)
% Number of connectives : 366 ( 26 ~; 32 |; 22 &; 245 @)
% ( 1 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 7 ^; 48 !; 5 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_25,type,
powerset: $i > $i ).
thf(decl_26,type,
setunion: $i > $i ).
thf(decl_27,type,
nonempty: $i > $o ).
thf(decl_28,type,
subset: $i > $i > $o ).
thf(decl_29,type,
transitiveset: $i > $o ).
thf(decl_30,type,
setunionTransitive: $o ).
thf(decl_31,type,
stricttotalorderedByIn: $i > $o ).
thf(decl_32,type,
wellorderedByIn: $i > $o ).
thf(decl_33,type,
ordinal: $i > $o ).
thf(decl_34,type,
esk1_1: $i > $i ).
thf(decl_35,type,
esk2_1: $i > $i ).
thf(decl_36,type,
esk3_0: $i ).
thf(decl_37,type,
esk4_2: $i > $i > $i ).
thf(decl_38,type,
esk5_0: $i ).
thf(ordinal,axiom,
( ordinal
= ( ^ [X1: $i] :
( ( transitiveset @ X1 )
& ( wellorderedByIn @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.G82k8xXeCX/E---3.1_3611353.p',ordinal) ).
thf(wellorderedByIn,axiom,
( wellorderedByIn
= ( ^ [X2: $i] :
( ( stricttotalorderedByIn @ X2 )
& ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
=> ( ( nonempty @ X3 )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ( ( X1 = X4 )
| ( in @ X1 @ X4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.G82k8xXeCX/E---3.1_3611353.p',wellorderedByIn) ).
thf(transitiveset,axiom,
( transitiveset
= ( ^ [X2: $i] :
! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.G82k8xXeCX/E---3.1_3611353.p',transitiveset) ).
thf(setunionOrdinalLem1,conjecture,
( setunionTransitive
=> ! [X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ordinal @ X1 ) )
=> ( transitiveset @ ( setunion @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.G82k8xXeCX/E---3.1_3611353.p',setunionOrdinalLem1) ).
thf(setunionTransitive,axiom,
( setunionTransitive
<=> ! [X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( transitiveset @ X1 ) )
=> ( transitiveset @ ( setunion @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.G82k8xXeCX/E---3.1_3611353.p',setunionTransitive) ).
thf(c_0_5,plain,
( ordinal
= ( ^ [Z0: $i] :
( ! [X11: $i] :
( ( in @ X11 @ Z0 )
=> ( subset @ X11 @ Z0 ) )
& ( stricttotalorderedByIn @ Z0 )
& ! [X12: $i] :
( ( in @ X12 @ ( powerset @ Z0 ) )
=> ( ( nonempty @ X12 )
=> ? [X13: $i] :
( ( in @ X13 @ X12 )
& ! [X14: $i] :
( ( in @ X14 @ X12 )
=> ( ( X13 = X14 )
| ( in @ X13 @ X14 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ordinal]) ).
thf(c_0_6,plain,
( wellorderedByIn
= ( ^ [Z0: $i] :
( ( stricttotalorderedByIn @ Z0 )
& ! [X3: $i] :
( ( in @ X3 @ ( powerset @ Z0 ) )
=> ( ( nonempty @ X3 )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ( ( X1 = X4 )
| ( in @ X1 @ X4 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[wellorderedByIn]) ).
thf(c_0_7,plain,
( transitiveset
= ( ^ [Z0: $i] :
! [X3: $i] :
( ( in @ X3 @ Z0 )
=> ( subset @ X3 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitiveset]) ).
thf(c_0_8,negated_conjecture,
~ ( setunionTransitive
=> ! [X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ordinal @ X1 ) )
=> ( transitiveset @ ( setunion @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[setunionOrdinalLem1]) ).
thf(c_0_9,plain,
( ordinal
= ( ^ [Z0: $i] :
( ! [X11: $i] :
( ( in @ X11 @ Z0 )
=> ( subset @ X11 @ Z0 ) )
& ( stricttotalorderedByIn @ Z0 )
& ! [X12: $i] :
( ( in @ X12 @ ( powerset @ Z0 ) )
=> ( ( nonempty @ X12 )
=> ? [X13: $i] :
( ( in @ X13 @ X12 )
& ! [X14: $i] :
( ( in @ X14 @ X12 )
=> ( ( X13 = X14 )
| ( in @ X13 @ X14 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).
thf(c_0_10,axiom,
( setunionTransitive
= ( ! [X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X9: $i] :
( ( in @ X9 @ X1 )
=> ( subset @ X9 @ X1 ) ) )
=> ! [X10: $i] :
( ( in @ X10 @ ( setunion @ X3 ) )
=> ( subset @ X10 @ ( setunion @ X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[setunionTransitive,c_0_7]) ).
thf(c_0_11,negated_conjecture,
~ ( ! [X15: $i] :
( ! [X16: $i] :
( ( in @ X16 @ X15 )
=> ! [X17: $i] :
( ( in @ X17 @ X16 )
=> ( subset @ X17 @ X16 ) ) )
=> ! [X18: $i] :
( ( in @ X18 @ ( setunion @ X15 ) )
=> ( subset @ X18 @ ( setunion @ X15 ) ) ) )
=> ! [X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ! [X19: $i] :
( ( in @ X19 @ X1 )
=> ( subset @ X19 @ X1 ) )
& ( stricttotalorderedByIn @ X1 )
& ! [X20: $i] :
( ( in @ X20 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X20 )
=> ? [X21: $i] :
( ( in @ X21 @ X20 )
& ! [X22: $i] :
( ( in @ X22 @ X20 )
=> ( ( X21 = X22 )
| ( in @ X21 @ X22 ) ) ) ) ) ) ) )
=> ! [X23: $i] :
( ( in @ X23 @ ( setunion @ X3 ) )
=> ( subset @ X23 @ ( setunion @ X3 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_9]),c_0_10]),c_0_7]) ).
thf(c_0_12,negated_conjecture,
! [X24: $i,X27: $i,X29: $i,X30: $i,X31: $i,X33: $i] :
( ( ( in @ ( esk1_1 @ X24 ) @ X24 )
| ~ ( in @ X27 @ ( setunion @ X24 ) )
| ( subset @ X27 @ ( setunion @ X24 ) ) )
& ( ( in @ ( esk2_1 @ X24 ) @ ( esk1_1 @ X24 ) )
| ~ ( in @ X27 @ ( setunion @ X24 ) )
| ( subset @ X27 @ ( setunion @ X24 ) ) )
& ( ~ ( subset @ ( esk2_1 @ X24 ) @ ( esk1_1 @ X24 ) )
| ~ ( in @ X27 @ ( setunion @ X24 ) )
| ( subset @ X27 @ ( setunion @ X24 ) ) )
& ( ~ ( in @ X30 @ X29 )
| ( subset @ X30 @ X29 )
| ~ ( in @ X29 @ esk3_0 ) )
& ( ( stricttotalorderedByIn @ X29 )
| ~ ( in @ X29 @ esk3_0 ) )
& ( ( in @ ( esk4_2 @ X29 @ X31 ) @ X31 )
| ~ ( nonempty @ X31 )
| ~ ( in @ X31 @ ( powerset @ X29 ) )
| ~ ( in @ X29 @ esk3_0 ) )
& ( ~ ( in @ X33 @ X31 )
| ( ( esk4_2 @ X29 @ X31 )
= X33 )
| ( in @ ( esk4_2 @ X29 @ X31 ) @ X33 )
| ~ ( nonempty @ X31 )
| ~ ( in @ X31 @ ( powerset @ X29 ) )
| ~ ( in @ X29 @ esk3_0 ) )
& ( in @ esk5_0 @ ( setunion @ esk3_0 ) )
& ~ ( subset @ esk5_0 @ ( setunion @ esk3_0 ) ) ),
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,
! [X2: $i,X1: $i] :
( ( subset @ X2 @ ( setunion @ X1 ) )
| ~ ( subset @ ( esk2_1 @ X1 ) @ ( esk1_1 @ X1 ) )
| ~ ( in @ X2 @ ( setunion @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X2 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
! [X2: $i,X1: $i] :
( ( in @ ( esk2_1 @ X1 ) @ ( esk1_1 @ X1 ) )
| ( subset @ X2 @ ( setunion @ X1 ) )
| ~ ( in @ X2 @ ( setunion @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X2: $i,X1: $i] :
( ( in @ ( esk1_1 @ X1 ) @ X1 )
| ( subset @ X2 @ ( setunion @ X1 ) )
| ~ ( in @ X2 @ ( setunion @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,negated_conjecture,
in @ esk5_0 @ ( setunion @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,negated_conjecture,
~ ( subset @ esk5_0 @ ( setunion @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ ( setunion @ X2 ) )
| ~ ( in @ ( esk1_1 @ X2 ) @ esk3_0 )
| ~ ( in @ X1 @ ( setunion @ X2 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_20,negated_conjecture,
in @ ( esk1_1 @ esk3_0 ) @ esk3_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU819^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n015.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 14:37:47 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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.G82k8xXeCX/E---3.1_3611353.p
% 0.09/0.25 % Version: 3.5.1-ho
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho5 with 300s (1) cores
% 0.09/0.25 % Starting sh4l with 300s (1) cores
% 0.09/0.25 % Starting ho_unfolding_2 with 300s (1) cores
% 0.09/0.25 % post_as_ho5 with pid 3611367 completed with status 0
% 0.09/0.25 % Result found by post_as_ho5
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho5 with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.09/0.25 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.09/0.25 % Search class: HGUSF-FFSF21-SSFFMFNN
% 0.09/0.25 % partial match(1): HGUSF-FFSF22-SSFFMFNN
% 0.09/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.25 % SubtermCWHack with pid 3611371 completed with status 0
% 0.09/0.25 % Result found by SubtermCWHack
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho5 with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.09/0.25 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.09/0.25 % Search class: HGUSF-FFSF21-SSFFMFNN
% 0.09/0.25 % partial match(1): HGUSF-FFSF22-SSFFMFNN
% 0.09/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.25 % Preprocessing time : 0.001 s
% 0.09/0.25
% 0.09/0.25 % Proof found!
% 0.09/0.25 % SZS status Theorem
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25 % Parsed axioms : 18
% 0.09/0.25 % Removed by relevancy pruning/SinE : 13
% 0.09/0.25 % Initial clauses : 9
% 0.09/0.25 % Removed in clause preprocessing : 0
% 0.09/0.25 % Initial clauses in saturation : 9
% 0.09/0.25 % Processed clauses : 12
% 0.09/0.25 % ...of these trivial : 0
% 0.09/0.25 % ...subsumed : 0
% 0.09/0.25 % ...remaining for further processing : 12
% 0.09/0.25 % Other redundant clauses eliminated : 0
% 0.09/0.25 % Clauses deleted for lack of memory : 0
% 0.09/0.25 % Backward-subsumed : 0
% 0.09/0.25 % Backward-rewritten : 0
% 0.09/0.25 % Generated clauses : 7
% 0.09/0.25 % ...of the previous two non-redundant : 6
% 0.09/0.25 % ...aggressively subsumed : 0
% 0.09/0.25 % Contextual simplify-reflections : 1
% 0.09/0.25 % Paramodulations : 7
% 0.09/0.25 % Factorizations : 0
% 0.09/0.25 % NegExts : 0
% 0.09/0.25 % Equation resolutions : 0
% 0.09/0.25 % Disequality decompositions : 0
% 0.09/0.25 % Total rewrite steps : 3
% 0.09/0.25 % ...of those cached : 1
% 0.09/0.25 % Propositional unsat checks : 0
% 0.09/0.25 % Propositional check models : 0
% 0.09/0.25 % Propositional check unsatisfiable : 0
% 0.09/0.25 % Propositional clauses : 0
% 0.09/0.25 % Propositional clauses after purity: 0
% 0.09/0.25 % Propositional unsat core size : 0
% 0.09/0.25 % Propositional preprocessing time : 0.000
% 0.09/0.25 % Propositional encoding time : 0.000
% 0.09/0.25 % Propositional solver time : 0.000
% 0.09/0.25 % Success case prop preproc time : 0.000
% 0.09/0.25 % Success case prop encoding time : 0.000
% 0.09/0.25 % Success case prop solver time : 0.000
% 0.09/0.25 % Current number of processed clauses : 12
% 0.09/0.25 % Positive orientable unit clauses : 3
% 0.09/0.25 % Positive unorientable unit clauses: 0
% 0.09/0.25 % Negative unit clauses : 2
% 0.09/0.25 % Non-unit-clauses : 7
% 0.09/0.25 % Current number of unprocessed clauses: 3
% 0.09/0.25 % ...number of literals in the above : 16
% 0.09/0.25 % Current number of archived formulas : 0
% 0.09/0.25 % Current number of archived clauses : 0
% 0.09/0.25 % Clause-clause subsumption calls (NU) : 15
% 0.09/0.25 % Rec. Clause-clause subsumption calls : 13
% 0.09/0.25 % Non-unit clause-clause subsumptions : 1
% 0.09/0.25 % Unit Clause-clause subsumption calls : 0
% 0.09/0.25 % Rewrite failures with RHS unbound : 0
% 0.09/0.25 % BW rewrite match attempts : 0
% 0.09/0.25 % BW rewrite match successes : 0
% 0.09/0.25 % Condensation attempts : 0
% 0.09/0.25 % Condensation successes : 0
% 0.09/0.25 % Termbank termtop insertions : 1490
% 0.09/0.25 % Search garbage collected termcells : 473
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.005 s
% 0.09/0.25 % System time : 0.002 s
% 0.09/0.25 % Total time : 0.007 s
% 0.09/0.25 % Maximum resident set size: 3644 pages
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.007 s
% 0.09/0.25 % System time : 0.006 s
% 0.09/0.25 % Total time : 0.014 s
% 0.09/0.25 % Maximum resident set size: 4864 pages
% 0.09/0.25 % E exiting
%------------------------------------------------------------------------------