%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO891^16 : 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 : n008.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 08:43:31 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 12 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 209 ( 18 ~; 13 |; 15 &; 152 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 63 ( 32 ^; 22 !; 9 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mworld: $tType ).
thf(decl_23,type,
mrel: mworld > mworld > $o ).
thf(decl_24,type,
mactual: mworld ).
thf(decl_25,type,
mlocal: ( mworld > $o ) > $o ).
thf(decl_29,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_31,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(decl_32,type,
mdia: ( 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,
qmltpeq: $i > $i > mworld > $o ).
thf(decl_37,type,
p: $i > mworld > $o ).
thf(decl_39,type,
esk2_2: $i > mworld > $i ).
thf(decl_40,type,
esk3_0: $i ).
thf(decl_41,type,
esk4_0: mworld ).
thf(con,conjecture,
( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X7: $i] :
( mbox
@ ( mexists_di
@ ^ [X10: $i] : ( qmltpeq @ X7 @ X10 ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [X7: $i] : ( mdia @ ( p @ X7 ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X7: $i] : ( p @ X7 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8PC9oKzAgC/E---3.1_3465877.p',con) ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8PC9oKzAgC/E---3.1_3465877.p',mlocal_def) ).
thf(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8PC9oKzAgC/E---3.1_3465877.p',mimplies_def) ).
thf(mbox_def,axiom,
( mbox
= ( ^ [X1: mworld > $o,X3: mworld] :
! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8PC9oKzAgC/E---3.1_3465877.p',mbox_def) ).
thf(mdia_def,axiom,
( mdia
= ( ^ [X1: mworld > $o,X3: mworld] :
? [X5: mworld] :
( ( mrel @ X3 @ X5 )
& ( X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8PC9oKzAgC/E---3.1_3465877.p',mdia_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.8PC9oKzAgC/E---3.1_3465877.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.8PC9oKzAgC/E---3.1_3465877.p',mexists_di_def) ).
thf(eiw_di_cumul,axiom,
! [X3: mworld,X5: mworld,X7: $i] :
( ( ( eiw_di @ X7 @ X3 )
& ( mrel @ X3 @ X5 ) )
=> ( eiw_di @ X7 @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.8PC9oKzAgC/E---3.1_3465877.p',eiw_di_cumul) ).
thf(c_0_8,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X7: $i] :
( mbox
@ ( mexists_di
@ ^ [X10: $i] : ( qmltpeq @ X7 @ X10 ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [X7: $i] : ( mdia @ ( p @ X7 ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X7: $i] : ( p @ X7 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_9,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_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,
( mbox
= ( ^ [Z0: mworld > $o,Z1: mworld] :
! [X5: mworld] :
( ( mrel @ Z1 @ X5 )
=> ( Z0 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_def]) ).
thf(c_0_12,plain,
( mdia
= ( ^ [Z0: mworld > $o,Z1: mworld] :
? [X5: mworld] :
( ( mrel @ Z1 @ X5 )
& ( Z0 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[mdia_def]) ).
thf(c_0_13,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_14,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_15,negated_conjecture,
~ ( ! [X33: $i] :
( ( eiw_di @ X33 @ mactual )
=> ! [X32: mworld] :
( ( mrel @ mactual @ X32 )
=> ? [X31: $i] :
( ( eiw_di @ X31 @ X32 )
& ( qmltpeq @ X33 @ X31 @ X32 ) ) ) )
=> ( ? [X35: $i] :
( ( eiw_di @ X35 @ mactual )
& ? [X34: mworld] :
( ( mrel @ mactual @ X34 )
& ( p @ X35 @ X34 ) ) )
=> ? [X37: mworld] :
( ( mrel @ mactual @ X37 )
& ? [X36: $i] :
( ( eiw_di @ X36 @ X37 )
& ( p @ X36 @ X37 ) ) ) ) ),
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_8]),c_0_9]),c_0_10]),c_0_11]),c_0_12]),c_0_13]),c_0_14]) ).
thf(c_0_16,negated_conjecture,
! [X55: $i,X56: mworld,X60: mworld,X61: $i] :
( ( ( eiw_di @ ( esk2_2 @ X55 @ X56 ) @ X56 )
| ~ ( mrel @ mactual @ X56 )
| ~ ( eiw_di @ X55 @ mactual ) )
& ( ( qmltpeq @ X55 @ ( esk2_2 @ X55 @ X56 ) @ X56 )
| ~ ( mrel @ mactual @ X56 )
| ~ ( eiw_di @ X55 @ mactual ) )
& ( eiw_di @ esk3_0 @ mactual )
& ( mrel @ mactual @ esk4_0 )
& ( p @ esk3_0 @ esk4_0 )
& ( ~ ( mrel @ mactual @ X60 )
| ~ ( eiw_di @ X61 @ X60 )
| ~ ( p @ X61 @ X60 ) ) ),
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_15])])])])])]) ).
thf(c_0_17,plain,
! [X44: mworld,X45: mworld,X46: $i] :
( ~ ( eiw_di @ X46 @ X44 )
| ~ ( mrel @ X44 @ X45 )
| ( eiw_di @ X46 @ X45 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[eiw_di_cumul])])]) ).
thf(c_0_18,negated_conjecture,
! [X7: $i,X3: mworld] :
( ~ ( mrel @ mactual @ X3 )
| ~ ( eiw_di @ X7 @ X3 )
| ~ ( p @ X7 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
p @ esk3_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_20,negated_conjecture,
mrel @ mactual @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_21,plain,
! [X3: mworld,X7: $i,X5: mworld] :
( ( eiw_di @ X7 @ X5 )
| ~ ( eiw_di @ X7 @ X3 )
| ~ ( mrel @ X3 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,negated_conjecture,
~ ( eiw_di @ esk3_0 @ esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
thf(c_0_23,negated_conjecture,
! [X7: $i] :
( ( eiw_di @ X7 @ esk4_0 )
| ~ ( eiw_di @ X7 @ mactual ) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
thf(c_0_24,negated_conjecture,
eiw_di @ esk3_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO891^16 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n008.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 17:26:39 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
% 0.07/0.23 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.8PC9oKzAgC/E---3.1_3465877.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.25 % Starting new_ho_12 with 300s (1) cores
% 0.07/0.25 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.25 % post_as_ho3 with pid 3465891 completed with status 0
% 0.07/0.25 % Result found by post_as_ho3
% 0.07/0.25 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HHHNS-FFSS21-SHSSMFNN
% 0.07/0.25 % partial match(2): HHHNS-FFSF11-SHSSMFNN
% 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 3465895 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HHHNS-FFSS21-SHSSMFNN
% 0.07/0.25 % partial match(2): HHHNS-FFSF11-SHSSMFNN
% 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 : 35
% 0.07/0.25 % Removed by relevancy pruning/SinE : 0
% 0.07/0.25 % Initial clauses : 30
% 0.07/0.25 % Removed in clause preprocessing : 16
% 0.07/0.25 % Initial clauses in saturation : 14
% 0.07/0.25 % Processed clauses : 12
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 0
% 0.07/0.25 % ...remaining for further processing : 12
% 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 : 8
% 0.07/0.25 % ...of the previous two non-redundant : 5
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 8
% 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 : 2
% 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 : 12
% 0.07/0.25 % Positive orientable unit clauses : 5
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 1
% 0.07/0.25 % Non-unit-clauses : 6
% 0.07/0.25 % Current number of unprocessed clauses: 7
% 0.07/0.25 % ...number of literals in the above : 27
% 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) : 0
% 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 : 1
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 1
% 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 : 2704
% 0.07/0.25 % Search garbage collected termcells : 951
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.004 s
% 0.07/0.25 % System time : 0.004 s
% 0.07/0.25 % Total time : 0.008 s
% 0.07/0.25 % Maximum resident set size: 3920 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.004 s
% 0.07/0.25 % System time : 0.010 s
% 0.07/0.25 % Total time : 0.014 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------