%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL957^6 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:12:54 AM UTC 2026
% Result : Theorem 0.14s 0.23s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 102 ( 10 equ; 0 cnn)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 225 ( 13 ~; 10 |; 7 &; 179 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 65 ( 28 ^; 33 !; 4 ?; 65 :)
% 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_33,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_34,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_35,type,
big_r: $i > $i > mworld > $o ).
thf(decl_36,type,
esk1_0: mworld ).
thf(decl_37,type,
esk2_2: mworld > $i > mworld ).
thf(decl_38,type,
esk3_1: $i > mworld ).
thf(decl_39,type,
esk4_1: $i > $i ).
thf(decl_40,type,
esk5_1: $i > mworld ).
thf(decl_41,type,
esk6_1: $i > mworld ).
thf(x2122,conjecture,
( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X7: $i] : ( mbox @ ( big_r @ X7 @ X7 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X9: $i] : ( mbox @ ( big_r @ X9 @ X9 ) ) ) ) ) )
@ ( mexists_di
@ ^ [X10: $i] :
( mbox
@ ( mforall_di
@ ^ [X11: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_r @ X10 @ X10 ) ) @ ( mbox @ ( big_r @ X11 @ X11 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QhghdH48XV/E---3.1_610245.p',x2122) ).
thf(mforall_di_def,axiom,
( mforall_di
= ( ^ [X6: $i > mworld > $o,X3: mworld] :
! [X7: $i] : ( X6 @ X7 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QhghdH48XV/E---3.1_610245.p',mforall_di_def) ).
thf(mexists_di_def,axiom,
( mexists_di
= ( ^ [X8: $i > mworld > $o,X3: mworld] :
? [X7: $i] : ( X8 @ X7 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QhghdH48XV/E---3.1_610245.p',mexists_di_def) ).
thf(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QhghdH48XV/E---3.1_610245.p',mimplies_def) ).
thf(mbox_def,axiom,
( mbox
= ( ^ [X1: mworld > $o,X3: mworld] :
! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QhghdH48XV/E---3.1_610245.p',mbox_def) ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QhghdH48XV/E---3.1_610245.p',mlocal_def) ).
thf(mrel_universal,axiom,
! [X3: mworld,X5: mworld] : ( mrel @ X3 @ X5 ),
file('/export/starexec/sandbox/tmp/tmp.QhghdH48XV/E---3.1_610245.p',mrel_universal) ).
thf(c_0_7,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X7: $i] : ( mbox @ ( big_r @ X7 @ X7 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X9: $i] : ( mbox @ ( big_r @ X9 @ X9 ) ) ) ) ) )
@ ( mexists_di
@ ^ [X10: $i] :
( mbox
@ ( mforall_di
@ ^ [X11: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_r @ X10 @ X10 ) ) @ ( mbox @ ( big_r @ X11 @ X11 ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[x2122]) ).
thf(c_0_8,plain,
( mforall_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
! [X7: $i] : ( Z0 @ X7 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_di_def]) ).
thf(c_0_9,plain,
( mexists_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
? [X7: $i] : ( Z0 @ X7 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mexists_di_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,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_13,negated_conjecture,
~ ! [X26: mworld] :
( ( mrel @ mactual @ X26 )
=> ( ! [X19: mworld] :
( ( mrel @ X26 @ X19 )
=> ( ? [X15: $i] :
! [X14: mworld] :
( ( mrel @ X19 @ X14 )
=> ( big_r @ X15 @ X15 @ X14 ) )
=> ! [X18: mworld] :
( ( mrel @ X19 @ X18 )
=> ! [X17: $i,X16: mworld] :
( ( mrel @ X18 @ X16 )
=> ( big_r @ X17 @ X17 @ X16 ) ) ) ) )
=> ? [X25: $i] :
! [X24: mworld] :
( ( mrel @ X26 @ X24 )
=> ! [X23: $i,X22: mworld] :
( ( mrel @ X24 @ X22 )
=> ( ! [X20: mworld] :
( ( mrel @ X22 @ X20 )
=> ( big_r @ X25 @ X25 @ X20 ) )
=> ! [X21: mworld] :
( ( mrel @ X22 @ X21 )
=> ( big_r @ X23 @ X23 @ X21 ) ) ) ) ) ) ),
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]) ).
thf(c_0_14,negated_conjecture,
! [X28: mworld,X29: $i,X31: mworld,X32: $i,X33: mworld,X34: $i,X38: mworld] :
( ( mrel @ mactual @ esk1_0 )
& ( ( mrel @ X28 @ ( esk2_2 @ X28 @ X29 ) )
| ~ ( mrel @ X28 @ X31 )
| ~ ( mrel @ X31 @ X33 )
| ( big_r @ X32 @ X32 @ X33 )
| ~ ( mrel @ esk1_0 @ X28 ) )
& ( ~ ( big_r @ X29 @ X29 @ ( esk2_2 @ X28 @ X29 ) )
| ~ ( mrel @ X28 @ X31 )
| ~ ( mrel @ X31 @ X33 )
| ( big_r @ X32 @ X32 @ X33 )
| ~ ( mrel @ esk1_0 @ X28 ) )
& ( mrel @ esk1_0 @ ( esk3_1 @ X34 ) )
& ( mrel @ ( esk3_1 @ X34 ) @ ( esk5_1 @ X34 ) )
& ( ~ ( mrel @ ( esk5_1 @ X34 ) @ X38 )
| ( big_r @ X34 @ X34 @ X38 ) )
& ( mrel @ ( esk5_1 @ X34 ) @ ( esk6_1 @ X34 ) )
& ~ ( big_r @ ( esk4_1 @ X34 ) @ ( esk4_1 @ X34 ) @ ( esk6_1 @ X34 ) ) ),
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_13])])])])])]) ).
thf(c_0_15,plain,
! [X40: mworld,X41: mworld] : ( mrel @ X40 @ X41 ),
inference(variable_rename,[status(thm)],[mrel_universal]) ).
thf(c_0_16,negated_conjecture,
! [X7: $i,X3: mworld] :
( ( big_r @ X7 @ X7 @ X3 )
| ~ ( mrel @ ( esk5_1 @ X7 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,plain,
! [X3: mworld,X5: mworld] : ( mrel @ X3 @ X5 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X7: $i] :
~ ( big_r @ ( esk4_1 @ X7 ) @ ( esk4_1 @ X7 ) @ ( esk6_1 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,negated_conjecture,
! [X7: $i,X3: mworld] : ( big_r @ X7 @ X7 @ X3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL957^6 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.16 % Computer : n019.cluster.edu
% 0.14/0.16 % Model : x86_64 x86_64
% 0.14/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.16 % Memory : 8046.5625MB
% 0.14/0.16 % OS : Linux 6.8.0-71-generic
% 0.14/0.16 % CPULimit : 300
% 0.14/0.16 % WCLimit : 300
% 0.14/0.16 % DateTime : Tue Sep 29 10:59:17 UTC 2026
% 0.14/0.16 % CPUTime :
% 0.14/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.20 Running higher-order theorem proving
% 0.14/0.21 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.QhghdH48XV/E---3.1_610245.p
% 0.14/0.23 % Version: 3.5.1-ho
% 0.14/0.23 % Preprocessing class: HSSSSMSSMLMNHSN.
% 0.14/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.14/0.23 % Starting sh5l with 300s (1) cores
% 0.14/0.23 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.23 % Starting new_bool_2 with 300s (1) cores
% 0.14/0.23 % sh5l with pid 610259 completed with status 0
% 0.14/0.23 % Result found by sh5l
% 0.14/0.23 % Preprocessing class: HSSSSMSSMLMNHSN.
% 0.14/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.14/0.23 % Starting sh5l with 300s (1) cores
% 0.14/0.23 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.23 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.23 % Search class: HGUNM-FFSF21-SHSSMFNN
% 0.14/0.23 % partial match(2): HGUNF-FFSF11-SHSSMFNN
% 0.14/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.23 % SubtermCWHack with pid 610267 completed with status 0
% 0.14/0.23 % Result found by SubtermCWHack
% 0.14/0.23 % Preprocessing class: HSSSSMSSMLMNHSN.
% 0.14/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.14/0.23 % Starting sh5l with 300s (1) cores
% 0.14/0.23 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.23 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.23 % Search class: HGUNM-FFSF21-SHSSMFNN
% 0.14/0.23 % partial match(2): HGUNF-FFSF11-SHSSMFNN
% 0.14/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.23 % Preprocessing time : 0.001 s
% 0.14/0.23
% 0.14/0.23 % Proof found!
% 0.14/0.23 % SZS status Theorem
% 0.14/0.23 % SZS output start CNFRefutation
% See solution above
% 0.14/0.23 % Parsed axioms : 26
% 0.14/0.23 % Removed by relevancy pruning/SinE : 18
% 0.14/0.23 % Initial clauses : 9
% 0.14/0.23 % Removed in clause preprocessing : 0
% 0.14/0.23 % Initial clauses in saturation : 9
% 0.14/0.23 % Processed clauses : 7
% 0.14/0.23 % ...of these trivial : 3
% 0.14/0.23 % ...subsumed : 0
% 0.14/0.23 % ...remaining for further processing : 4
% 0.14/0.23 % Other redundant clauses eliminated : 0
% 0.14/0.23 % Clauses deleted for lack of memory : 0
% 0.14/0.23 % Backward-subsumed : 0
% 0.14/0.23 % Backward-rewritten : 2
% 0.14/0.23 % Generated clauses : 0
% 0.14/0.23 % ...of the previous two non-redundant : 0
% 0.14/0.23 % ...aggressively subsumed : 0
% 0.14/0.23 % Contextual simplify-reflections : 0
% 0.14/0.23 % Paramodulations : 0
% 0.14/0.23 % Factorizations : 0
% 0.14/0.23 % NegExts : 0
% 0.14/0.23 % Equation resolutions : 0
% 0.14/0.23 % Disequality decompositions : 0
% 0.14/0.23 % Total rewrite steps : 6
% 0.14/0.23 % ...of those cached : 0
% 0.14/0.23 % Propositional unsat checks : 0
% 0.14/0.23 % Propositional check models : 0
% 0.14/0.23 % Propositional check unsatisfiable : 0
% 0.14/0.23 % Propositional clauses : 0
% 0.14/0.23 % Propositional clauses after purity: 0
% 0.14/0.23 % Propositional unsat core size : 0
% 0.14/0.23 % Propositional preprocessing time : 0.000
% 0.14/0.23 % Propositional encoding time : 0.000
% 0.14/0.23 % Propositional solver time : 0.000
% 0.14/0.23 % Success case prop preproc time : 0.000
% 0.14/0.23 % Success case prop encoding time : 0.000
% 0.14/0.23 % Success case prop solver time : 0.000
% 0.14/0.23 % Current number of processed clauses : 2
% 0.14/0.23 % Positive orientable unit clauses : 2
% 0.14/0.23 % Positive unorientable unit clauses: 0
% 0.14/0.23 % Negative unit clauses : 0
% 0.14/0.23 % Non-unit-clauses : 0
% 0.14/0.23 % Current number of unprocessed clauses: 2
% 0.14/0.23 % ...number of literals in the above : 10
% 0.14/0.23 % Current number of archived formulas : 0
% 0.14/0.23 % Current number of archived clauses : 2
% 0.14/0.23 % Clause-clause subsumption calls (NU) : 0
% 0.14/0.23 % Rec. Clause-clause subsumption calls : 0
% 0.14/0.23 % Non-unit clause-clause subsumptions : 0
% 0.14/0.23 % Unit Clause-clause subsumption calls : 0
% 0.14/0.23 % Rewrite failures with RHS unbound : 0
% 0.14/0.23 % BW rewrite match attempts : 2
% 0.14/0.23 % BW rewrite match successes : 2
% 0.14/0.23 % Condensation attempts : 0
% 0.14/0.23 % Condensation successes : 0
% 0.14/0.23 % Termbank termtop insertions : 1428
% 0.14/0.23 % Search garbage collected termcells : 671
% 0.14/0.23
% 0.14/0.23 % -------------------------------------------------
% 0.14/0.23 % User time : 0.006 s
% 0.14/0.23 % System time : 0.001 s
% 0.14/0.23 % Total time : 0.007 s
% 0.14/0.23 % Maximum resident set size: 3912 pages
% 0.14/0.23
% 0.14/0.23 % -------------------------------------------------
% 0.14/0.23 % User time : 0.008 s
% 0.14/0.23 % System time : 0.006 s
% 0.14/0.23 % Total time : 0.014 s
% 0.14/0.23 % Maximum resident set size: 4864 pages
% 0.14/0.23 % E exiting
%------------------------------------------------------------------------------