%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET044^23 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:21:52 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 12 equ; 0 cnn)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 286 ( 31 ~; 25 |; 9 &; 209 @)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 56 ( 36 ^; 16 !; 4 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mworld: $tType ).
thf(decl_24,type,
mactual: mworld ).
thf(decl_25,type,
mlocal: ( mworld > $o ) > $o ).
thf(decl_26,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(decl_29,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_30,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_33,type,
eiw_di: $i > mworld > $o ).
thf(decl_34,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_35,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_36,type,
element: $i > $i > mworld > $o ).
thf(decl_38,type,
esk2_0: $i ).
thf(decl_39,type,
esk3_1: $i > $i ).
thf(pel40,conjecture,
( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [X10: $i] :
( mforall_di
@ ^ [X7: $i] : ( mequiv @ ( element @ X7 @ X10 ) @ ( element @ X7 @ X7 ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [X11: $i] :
( mexists_di
@ ^ [X12: $i] :
( mforall_di
@ ^ [X13: $i] : ( mequiv @ ( element @ X13 @ X12 ) @ ( mnot @ ( element @ X13 @ X11 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vNJr6dNDtN/E---3.1_1286946.p',pel40) ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vNJr6dNDtN/E---3.1_1286946.p',mlocal_def) ).
thf(mnot_def,axiom,
( mnot
= ( ^ [X2: mworld > $o,X3: mworld] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vNJr6dNDtN/E---3.1_1286946.p',mnot_def) ).
thf(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vNJr6dNDtN/E---3.1_1286946.p',mimplies_def) ).
thf(mequiv_def,axiom,
( mequiv
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
<=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vNJr6dNDtN/E---3.1_1286946.p',mequiv_def) ).
thf(mforall_di_def,axiom,
( mforall_di
= ( ^ [X8: $i > mworld > $o,X3: mworld] :
! [X7: $i] :
( ( eiw_di @ X7 @ X3 )
=> ( X8 @ X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vNJr6dNDtN/E---3.1_1286946.p',mforall_di_def) ).
thf(mexists_di_def,axiom,
( mexists_di
= ( ^ [X9: $i > mworld > $o,X3: mworld] :
? [X7: $i] :
( ( eiw_di @ X7 @ X3 )
& ( X9 @ X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vNJr6dNDtN/E---3.1_1286946.p',mexists_di_def) ).
thf(c_0_7,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [X10: $i] :
( mforall_di
@ ^ [X7: $i] : ( mequiv @ ( element @ X7 @ X10 ) @ ( element @ X7 @ X7 ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [X11: $i] :
( mexists_di
@ ^ [X12: $i] :
( mforall_di
@ ^ [X13: $i] : ( mequiv @ ( element @ X13 @ X12 ) @ ( mnot @ ( element @ X13 @ X11 ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[pel40]) ).
thf(c_0_8,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_9,plain,
( mnot
= ( ^ [Z0: mworld > $o,Z1: mworld] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot_def]) ).
thf(c_0_10,plain,
( mimplies
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies_def]) ).
thf(c_0_11,plain,
( mequiv
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
<=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv_def]) ).
thf(c_0_12,plain,
( mforall_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
! [X7: $i] :
( ( eiw_di @ X7 @ Z1 )
=> ( Z0 @ X7 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mforall_di_def]) ).
thf(c_0_13,plain,
( mexists_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
? [X7: $i] :
( ( eiw_di @ X7 @ Z1 )
& ( Z0 @ X7 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mexists_di_def]) ).
thf(c_0_14,negated_conjecture,
~ ( ? [X24: $i] :
( ( eiw_di @ X24 @ mactual )
& ! [X23: $i] :
( ( eiw_di @ X23 @ mactual )
=> ( ( element @ X23 @ X24 @ mactual )
<=> ( element @ X23 @ X23 @ mactual ) ) ) )
=> ~ ! [X27: $i] :
( ( eiw_di @ X27 @ mactual )
=> ? [X26: $i] :
( ( eiw_di @ X26 @ mactual )
& ! [X25: $i] :
( ( eiw_di @ X25 @ mactual )
=> ( ( element @ X25 @ X26 @ mactual )
<=> ~ ( element @ X25 @ X27 @ mactual ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_7]),c_0_8]),c_0_9]),c_0_10]),c_0_11]),c_0_12]),c_0_13])]) ).
thf(c_0_15,negated_conjecture,
! [X38: $i,X39: $i,X41: $i] :
( ( eiw_di @ esk2_0 @ mactual )
& ( ~ ( element @ X38 @ esk2_0 @ mactual )
| ( element @ X38 @ X38 @ mactual )
| ~ ( eiw_di @ X38 @ mactual ) )
& ( ~ ( element @ X38 @ X38 @ mactual )
| ( element @ X38 @ esk2_0 @ mactual )
| ~ ( eiw_di @ X38 @ mactual ) )
& ( ( eiw_di @ ( esk3_1 @ X39 ) @ mactual )
| ~ ( eiw_di @ X39 @ mactual ) )
& ( ~ ( element @ X41 @ ( esk3_1 @ X39 ) @ mactual )
| ~ ( element @ X41 @ X39 @ mactual )
| ~ ( eiw_di @ X41 @ mactual )
| ~ ( eiw_di @ X39 @ mactual ) )
& ( ( element @ X41 @ X39 @ mactual )
| ( element @ X41 @ ( esk3_1 @ X39 ) @ mactual )
| ~ ( eiw_di @ X41 @ mactual )
| ~ ( eiw_di @ X39 @ mactual ) ) ),
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_14])])])])])]) ).
thf(c_0_16,negated_conjecture,
! [X7: $i] :
( ( element @ X7 @ esk2_0 @ mactual )
| ~ ( element @ X7 @ X7 @ mactual )
| ~ ( eiw_di @ X7 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X7: $i,X10: $i] :
( ( element @ X7 @ X10 @ mactual )
| ( element @ X7 @ ( esk3_1 @ X10 ) @ mactual )
| ~ ( eiw_di @ X7 @ mactual )
| ~ ( eiw_di @ X10 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X7: $i] :
( ( eiw_di @ ( esk3_1 @ X7 ) @ mactual )
| ~ ( eiw_di @ X7 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_19,negated_conjecture,
! [X7: $i] :
( ( element @ ( esk3_1 @ X7 ) @ esk2_0 @ mactual )
| ( element @ ( esk3_1 @ X7 ) @ X7 @ mactual )
| ~ ( eiw_di @ X7 @ mactual ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
thf(c_0_20,negated_conjecture,
eiw_di @ esk2_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_21,negated_conjecture,
! [X7: $i] :
( ( element @ X7 @ X7 @ mactual )
| ~ ( element @ X7 @ esk2_0 @ mactual )
| ~ ( eiw_di @ X7 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_22,negated_conjecture,
element @ ( esk3_1 @ esk2_0 ) @ esk2_0 @ mactual,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_23,negated_conjecture,
! [X7: $i,X10: $i] :
( ~ ( element @ X7 @ ( esk3_1 @ X10 ) @ mactual )
| ~ ( element @ X7 @ X10 @ mactual )
| ~ ( eiw_di @ X7 @ mactual )
| ~ ( eiw_di @ X10 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_24,negated_conjecture,
( ( element @ ( esk3_1 @ esk2_0 ) @ ( esk3_1 @ esk2_0 ) @ mactual )
| ~ ( eiw_di @ ( esk3_1 @ esk2_0 ) @ mactual ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_25,negated_conjecture,
~ ( eiw_di @ ( esk3_1 @ esk2_0 ) @ mactual ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_22]),c_0_20])]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET044^23 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.15 % Computer : n002.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Tue Sep 29 13:38:52 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.21 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.vNJr6dNDtN/E---3.1_1286946.p
% 0.09/0.23 % Version: 3.5.1-ho
% 0.09/0.23 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.23 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.23 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.23 % Starting almost_fo_3_lam with 300s (1) cores
% 0.09/0.23 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.23 % ehoh_best2_full_lfho with pid 1286985 completed with status 0
% 0.09/0.23 % Result found by ehoh_best2_full_lfho
% 0.09/0.23 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.23 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.23 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.23 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.23 % No SInE strategy applied
% 0.09/0.23 % Search class: HGHNS-FFSF11-SHSSMFNN
% 0.09/0.23 % partial match(1): HHHNS-FFSF11-SHSSMFNN
% 0.09/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.23 % SubtermCWHack with pid 1286989 completed with status 0
% 0.09/0.23 % Result found by SubtermCWHack
% 0.09/0.23 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.23 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.23 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.23 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.23 % No SInE strategy applied
% 0.09/0.23 % Search class: HGHNS-FFSF11-SHSSMFNN
% 0.09/0.23 % partial match(1): HHHNS-FFSF11-SHSSMFNN
% 0.09/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.23 % Preprocessing time : 0.001 s
% 0.09/0.23
% 0.09/0.23 % Proof found!
% 0.09/0.23 % SZS status Theorem
% 0.09/0.23 % SZS output start CNFRefutation
% See solution above
% 0.09/0.23 % Parsed axioms : 30
% 0.09/0.23 % Removed by relevancy pruning/SinE : 0
% 0.09/0.23 % Initial clauses : 25
% 0.09/0.23 % Removed in clause preprocessing : 15
% 0.09/0.23 % Initial clauses in saturation : 10
% 0.09/0.23 % Processed clauses : 15
% 0.09/0.23 % ...of these trivial : 0
% 0.09/0.23 % ...subsumed : 0
% 0.09/0.23 % ...remaining for further processing : 15
% 0.09/0.23 % Other redundant clauses eliminated : 0
% 0.09/0.23 % Clauses deleted for lack of memory : 0
% 0.09/0.23 % Backward-subsumed : 1
% 0.09/0.23 % Backward-rewritten : 0
% 0.09/0.23 % Generated clauses : 12
% 0.09/0.23 % ...of the previous two non-redundant : 7
% 0.09/0.23 % ...aggressively subsumed : 0
% 0.09/0.23 % Contextual simplify-reflections : 1
% 0.09/0.23 % Paramodulations : 12
% 0.09/0.23 % Factorizations : 0
% 0.09/0.23 % NegExts : 0
% 0.09/0.23 % Equation resolutions : 0
% 0.09/0.23 % Disequality decompositions : 0
% 0.09/0.23 % Total rewrite steps : 5
% 0.09/0.23 % ...of those cached : 2
% 0.09/0.23 % Propositional unsat checks : 0
% 0.09/0.23 % Propositional check models : 0
% 0.09/0.23 % Propositional check unsatisfiable : 0
% 0.09/0.23 % Propositional clauses : 0
% 0.09/0.23 % Propositional clauses after purity: 0
% 0.09/0.23 % Propositional unsat core size : 0
% 0.09/0.23 % Propositional preprocessing time : 0.000
% 0.09/0.23 % Propositional encoding time : 0.000
% 0.09/0.23 % Propositional solver time : 0.000
% 0.09/0.23 % Success case prop preproc time : 0.000
% 0.09/0.23 % Success case prop encoding time : 0.000
% 0.09/0.23 % Success case prop solver time : 0.000
% 0.09/0.23 % Current number of processed clauses : 14
% 0.09/0.23 % Positive orientable unit clauses : 4
% 0.09/0.23 % Positive unorientable unit clauses: 0
% 0.09/0.23 % Negative unit clauses : 1
% 0.09/0.23 % Non-unit-clauses : 9
% 0.09/0.23 % Current number of unprocessed clauses: 2
% 0.09/0.23 % ...number of literals in the above : 5
% 0.09/0.23 % Current number of archived formulas : 0
% 0.09/0.23 % Current number of archived clauses : 1
% 0.09/0.23 % Clause-clause subsumption calls (NU) : 8
% 0.09/0.23 % Rec. Clause-clause subsumption calls : 5
% 0.09/0.23 % Non-unit clause-clause subsumptions : 1
% 0.09/0.23 % Unit Clause-clause subsumption calls : 1
% 0.09/0.23 % Rewrite failures with RHS unbound : 0
% 0.09/0.23 % BW rewrite match attempts : 0
% 0.09/0.23 % BW rewrite match successes : 0
% 0.09/0.23 % Condensation attempts : 0
% 0.09/0.23 % Condensation successes : 0
% 0.09/0.23 % Termbank termtop insertions : 2030
% 0.09/0.23 % Search garbage collected termcells : 561
% 0.09/0.23
% 0.09/0.23 % -------------------------------------------------
% 0.09/0.23 % User time : 0.007 s
% 0.09/0.23 % System time : 0.001 s
% 0.09/0.23 % Total time : 0.008 s
% 0.09/0.23 % Maximum resident set size: 3608 pages
% 0.09/0.23
% 0.09/0.23 % -------------------------------------------------
% 0.09/0.23 % User time : 0.008 s
% 0.09/0.23 % System time : 0.004 s
% 0.09/0.23 % Total time : 0.012 s
% 0.09/0.23 % Maximum resident set size: 4864 pages
% 0.09/0.23 % E exiting
%------------------------------------------------------------------------------