%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET926^8 : 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 : 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 08:22:20 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 93 ( 10 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 305 ( 27 ~; 21 |; 5 &; 240 @)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 46 ( 30 ^; 16 !; 0 ?; 46 :)
% 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_28,type,
mor: ( 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_36,type,
empty_set: $i ).
thf(decl_37,type,
qmltpeq: $i > $i > mworld > $o ).
thf(decl_38,type,
in: $i > $i > mworld > $o ).
thf(decl_40,type,
singleton: $i > $i ).
thf(decl_41,type,
set_difference: $i > $i > $i ).
thf(decl_45,type,
esk4_0: $i ).
thf(decl_46,type,
esk5_0: $i ).
thf(t69_zfmisc_1,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X32: $i] :
( mforall_di
@ ^ [X33: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X32 ) @ X33 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X32 ) @ X33 ) @ ( singleton @ X32 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JlxZjCp8B2/E---3.1_3544317.p',t69_zfmisc_1) ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JlxZjCp8B2/E---3.1_3544317.p',mlocal_def) ).
thf(mor_def,axiom,
( mor
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
| ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JlxZjCp8B2/E---3.1_3544317.p',mor_def) ).
thf(mforall_di_def,axiom,
( mforall_di
= ( ^ [X7: $i > mworld > $o,X3: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ X3 )
=> ( X7 @ X6 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JlxZjCp8B2/E---3.1_3544317.p',mforall_di_def) ).
thf(mequiv_def,axiom,
( mequiv
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
<=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JlxZjCp8B2/E---3.1_3544317.p',mequiv_def) ).
thf(mnot_def,axiom,
( mnot
= ( ^ [X2: mworld > $o,X3: mworld] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JlxZjCp8B2/E---3.1_3544317.p',mnot_def) ).
thf(l36_zfmisc_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [X28: $i] :
( mforall_di
@ ^ [X29: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X28 ) @ X29 ) @ empty_set ) @ ( in @ X28 @ X29 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JlxZjCp8B2/E---3.1_3544317.p',l36_zfmisc_1) ).
thf(l34_zfmisc_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [X26: $i] :
( mforall_di
@ ^ [X27: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X26 ) @ X27 ) @ ( singleton @ X26 ) ) @ ( mnot @ ( in @ X26 @ X27 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JlxZjCp8B2/E---3.1_3544317.p',l34_zfmisc_1) ).
thf(c_0_8,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X32: $i] :
( mforall_di
@ ^ [X33: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X32 ) @ X33 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X32 ) @ X33 ) @ ( singleton @ X32 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t69_zfmisc_1]) ).
thf(c_0_9,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_10,plain,
( mor
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor_def]) ).
thf(c_0_11,plain,
( mforall_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ Z1 )
=> ( Z0 @ X6 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mforall_di_def]) ).
thf(c_0_12,plain,
( mequiv
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
<=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv_def]) ).
thf(c_0_13,plain,
( mnot
= ( ^ [Z0: mworld > $o,Z1: mworld] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot_def]) ).
thf(c_0_14,negated_conjecture,
~ ! [X68: $i] :
( ( eiw_di @ X68 @ mactual )
=> ! [X67: $i] :
( ( eiw_di @ X67 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X68 ) @ X67 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ X68 ) @ X67 ) @ ( singleton @ X68 ) @ mactual ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_8]),c_0_9]),c_0_10]),c_0_11]) ).
thf(c_0_15,plain,
! [X64: $i] :
( ( eiw_di @ X64 @ mactual )
=> ! [X63: $i] :
( ( eiw_di @ X63 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X64 ) @ X63 ) @ empty_set @ mactual )
<=> ( in @ X64 @ X63 @ mactual ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[l36_zfmisc_1]),c_0_9]),c_0_12]),c_0_11]) ).
thf(c_0_16,plain,
! [X62: $i] :
( ( eiw_di @ X62 @ mactual )
=> ! [X61: $i] :
( ( eiw_di @ X61 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X62 ) @ X61 ) @ ( singleton @ X62 ) @ mactual )
<=> ~ ( in @ X62 @ X61 @ 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(fof_simplification,[status(thm)],[l34_zfmisc_1]),c_0_9]),c_0_13]),c_0_12]),c_0_11])]) ).
thf(c_0_17,negated_conjecture,
( ( eiw_di @ esk4_0 @ mactual )
& ( eiw_di @ esk5_0 @ mactual )
& ~ ( qmltpeq @ ( set_difference @ ( singleton @ esk4_0 ) @ esk5_0 ) @ empty_set @ mactual )
& ~ ( qmltpeq @ ( set_difference @ ( singleton @ esk4_0 ) @ esk5_0 ) @ ( singleton @ esk4_0 ) @ mactual ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
thf(c_0_18,plain,
! [X98: $i,X99: $i] :
( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X98 ) @ X99 ) @ empty_set @ mactual )
| ( in @ X98 @ X99 @ mactual )
| ~ ( eiw_di @ X99 @ mactual )
| ~ ( eiw_di @ X98 @ mactual ) )
& ( ~ ( in @ X98 @ X99 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ X98 ) @ X99 ) @ empty_set @ mactual )
| ~ ( eiw_di @ X99 @ mactual )
| ~ ( eiw_di @ X98 @ mactual ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).
thf(c_0_19,plain,
! [X96: $i,X97: $i] :
( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X96 ) @ X97 ) @ ( singleton @ X96 ) @ mactual )
| ~ ( in @ X96 @ X97 @ mactual )
| ~ ( eiw_di @ X97 @ mactual )
| ~ ( eiw_di @ X96 @ mactual ) )
& ( ( in @ X96 @ X97 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ X96 ) @ X97 ) @ ( singleton @ X96 ) @ mactual )
| ~ ( eiw_di @ X97 @ mactual )
| ~ ( eiw_di @ X96 @ mactual ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).
thf(c_0_20,negated_conjecture,
~ ( qmltpeq @ ( set_difference @ ( singleton @ esk4_0 ) @ esk5_0 ) @ empty_set @ mactual ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_21,plain,
! [X9: $i,X6: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ X6 ) @ X9 ) @ empty_set @ mactual )
| ~ ( in @ X6 @ X9 @ mactual )
| ~ ( eiw_di @ X9 @ mactual )
| ~ ( eiw_di @ X6 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,negated_conjecture,
eiw_di @ esk5_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,negated_conjecture,
eiw_di @ esk4_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_24,negated_conjecture,
~ ( qmltpeq @ ( set_difference @ ( singleton @ esk4_0 ) @ esk5_0 ) @ ( singleton @ esk4_0 ) @ mactual ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_25,plain,
! [X9: $i,X6: $i] :
( ( in @ X6 @ X9 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ X6 ) @ X9 ) @ ( singleton @ X6 ) @ mactual )
| ~ ( eiw_di @ X9 @ mactual )
| ~ ( eiw_di @ X6 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_26,negated_conjecture,
~ ( in @ esk4_0 @ esk5_0 @ mactual ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
thf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_22]),c_0_23])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET926^8 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n015.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 13:44:32 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 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.JlxZjCp8B2/E---3.1_3544317.p
% 0.07/0.26 % Version: 3.5.1-ho
% 0.07/0.26 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.26 % Starting new_ho_12 with 300s (1) cores
% 0.07/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.26 % new_ho_12 with pid 3544332 completed with status 0
% 0.07/0.26 % Result found by new_ho_12
% 0.07/0.26 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.26 % Starting new_ho_12 with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.26 % No SInE strategy applied
% 0.07/0.26 % Search class: HGHNS-FFMM21-SHSSMFNN
% 0.07/0.26 % partial match(2): HGUNS-FFMF21-SHSSMFNN
% 0.07/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.26 % SubtermCWHack with pid 3544334 completed with status 0
% 0.07/0.26 % Result found by SubtermCWHack
% 0.07/0.26 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.26 % Starting new_ho_12 with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.26 % No SInE strategy applied
% 0.07/0.26 % Search class: HGHNS-FFMM21-SHSSMFNN
% 0.07/0.26 % partial match(2): HGUNS-FFMF21-SHSSMFNN
% 0.07/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.26 % Preprocessing time : 0.002 s
% 0.07/0.26
% 0.07/0.26 % Proof found!
% 0.07/0.26 % SZS status Theorem
% 0.07/0.26 % SZS output start CNFRefutation
% See solution above
% 0.07/0.26 % Parsed axioms : 48
% 0.07/0.26 % Removed by relevancy pruning/SinE : 0
% 0.07/0.26 % Initial clauses : 45
% 0.07/0.26 % Removed in clause preprocessing : 20
% 0.07/0.26 % Initial clauses in saturation : 25
% 0.07/0.26 % Processed clauses : 21
% 0.07/0.26 % ...of these trivial : 0
% 0.07/0.26 % ...subsumed : 1
% 0.07/0.26 % ...remaining for further processing : 20
% 0.07/0.26 % Other redundant clauses eliminated : 0
% 0.07/0.26 % Clauses deleted for lack of memory : 0
% 0.07/0.26 % Backward-subsumed : 0
% 0.07/0.26 % Backward-rewritten : 0
% 0.07/0.26 % Generated clauses : 11
% 0.07/0.26 % ...of the previous two non-redundant : 7
% 0.07/0.26 % ...aggressively subsumed : 0
% 0.07/0.26 % Contextual simplify-reflections : 0
% 0.07/0.26 % Paramodulations : 11
% 0.07/0.26 % Factorizations : 0
% 0.07/0.26 % NegExts : 0
% 0.07/0.26 % Equation resolutions : 0
% 0.07/0.26 % Disequality decompositions : 0
% 0.07/0.26 % Total rewrite steps : 5
% 0.07/0.26 % ...of those cached : 2
% 0.07/0.26 % Propositional unsat checks : 0
% 0.07/0.26 % Propositional check models : 0
% 0.07/0.26 % Propositional check unsatisfiable : 0
% 0.07/0.26 % Propositional clauses : 0
% 0.07/0.26 % Propositional clauses after purity: 0
% 0.07/0.26 % Propositional unsat core size : 0
% 0.07/0.26 % Propositional preprocessing time : 0.000
% 0.07/0.26 % Propositional encoding time : 0.000
% 0.07/0.26 % Propositional solver time : 0.000
% 0.07/0.26 % Success case prop preproc time : 0.000
% 0.07/0.26 % Success case prop encoding time : 0.000
% 0.07/0.26 % Success case prop solver time : 0.000
% 0.07/0.26 % Current number of processed clauses : 20
% 0.07/0.26 % Positive orientable unit clauses : 8
% 0.07/0.26 % Positive unorientable unit clauses: 0
% 0.07/0.26 % Negative unit clauses : 4
% 0.07/0.26 % Non-unit-clauses : 8
% 0.07/0.26 % Current number of unprocessed clauses: 9
% 0.07/0.26 % ...number of literals in the above : 51
% 0.07/0.26 % Current number of archived formulas : 0
% 0.07/0.26 % Current number of archived clauses : 0
% 0.07/0.26 % Clause-clause subsumption calls (NU) : 21
% 0.07/0.26 % Rec. Clause-clause subsumption calls : 13
% 0.07/0.26 % Non-unit clause-clause subsumptions : 1
% 0.07/0.26 % Unit Clause-clause subsumption calls : 0
% 0.07/0.26 % Rewrite failures with RHS unbound : 0
% 0.07/0.26 % BW rewrite match attempts : 0
% 0.07/0.26 % BW rewrite match successes : 0
% 0.07/0.26 % Condensation attempts : 0
% 0.07/0.26 % Condensation successes : 0
% 0.07/0.26 % Termbank termtop insertions : 5447
% 0.07/0.26 % Search garbage collected termcells : 2030
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.006 s
% 0.07/0.26 % System time : 0.003 s
% 0.07/0.26 % Total time : 0.008 s
% 0.07/0.26 % Maximum resident set size: 3896 pages
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.009 s
% 0.07/0.26 % System time : 0.006 s
% 0.07/0.26 % Total time : 0.015 s
% 0.07/0.26 % Maximum resident set size: 4864 pages
% 0.07/0.26 % E exiting
%------------------------------------------------------------------------------