%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL626^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:12:01 AM UTC 2026
% Result : Theorem 0.09s 0.15s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 15 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 209 ( 25 ~; 16 |; 14 &; 139 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 76 ( 30 ^; 43 !; 3 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_29,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_30,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_34,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_38,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_53,type,
transitive: ( $i > $i > $o ) > $o ).
thf(decl_62,type,
upwards_well_founded: ( $i > $i > $o ) > $o ).
thf(decl_63,type,
r: $i > $i > $o ).
thf(decl_64,type,
esk1_1: ( $i > $o ) > $i ).
thf(decl_65,type,
epred1_0: $i > $o ).
thf(decl_66,type,
esk2_0: $i ).
thf(decl_67,type,
esk3_0: $i ).
thf(decl_68,type,
esk4_0: $i ).
thf(decl_69,type,
esk5_0: $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CDalh4mYJq/E---3.1_4056133.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CDalh4mYJq/E---3.1_4056133.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CDalh4mYJq/E---3.1_4056133.p',mor) ).
thf(transitive,axiom,
( transitive
= ( ^ [X10: $i > $i > $o] :
! [X1: $i,X36: $i,X33: $i] :
( ( ( X10 @ X1 @ X36 )
& ( X10 @ X36 @ X33 ) )
=> ( X10 @ X1 @ X33 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CDalh4mYJq/E---3.1_4056133.p',transitive) ).
thf(upwards_well_founded,axiom,
( upwards_well_founded
= ( ^ [X10: $i > $i > $o] :
! [X45: $i > $o,X33: $i] :
( ( X45 @ X33 )
=> ? [X46: $i] :
( ( X45 @ X46 )
& ! [X15: $i] :
( ( X10 @ X46 @ X46 )
=> ~ ( X45 @ X15 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CDalh4mYJq/E---3.1_4056133.p',upwards_well_founded) ).
thf(k4,conjecture,
! [X47: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X47 ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X47 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CDalh4mYJq/E---3.1_4056133.p',k4) ).
thf(mbox,axiom,
( mbox
= ( ^ [X10: $i > $i > $o,X11: $i > $o,X1: $i] :
! [X12: $i] :
( ( X10 @ X1 @ X12 )
=> ( X11 @ X12 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CDalh4mYJq/E---3.1_4056133.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CDalh4mYJq/E---3.1_4056133.p',mvalid) ).
thf(upwf_trans,axiom,
( ( transitive @ r )
& ( upwards_well_founded @ r ) ),
file('/export/starexec/sandbox2/tmp/tmp.CDalh4mYJq/E---3.1_4056133.p',upwf_trans) ).
thf(c_0_9,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimpl]) ).
thf(c_0_10,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_11,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_12,plain,
( transitive
= ( ^ [Z0: $i > $i > $o] :
! [X1: $i,X36: $i,X33: $i] :
( ( ( Z0 @ X1 @ X36 )
& ( Z0 @ X36 @ X33 ) )
=> ( Z0 @ X1 @ X33 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive]) ).
thf(c_0_13,plain,
( upwards_well_founded
= ( ^ [Z0: $i > $i > $o] :
! [X45: $i > $o,X33: $i] :
( ( X45 @ X33 )
=> ? [X46: $i] :
( ( X45 @ X46 )
& ! [X15: $i] :
( ( Z0 @ X46 @ X46 )
=> ~ ( X45 @ X15 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[upwards_well_founded]) ).
thf(c_0_14,negated_conjecture,
~ ! [X47: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X47 ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X47 ) ) ) ) ),
inference(assume_negation,[status(cth)],[k4]) ).
thf(c_0_15,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
thf(c_0_16,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X12: $i] :
( ( Z0 @ Z2 @ X12 )
=> ( Z1 @ X12 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_17,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_18,plain,
( ! [X57: $i,X58: $i,X59: $i] :
( ( ( r @ X57 @ X58 )
& ( r @ X58 @ X59 ) )
=> ( r @ X57 @ X59 ) )
& ! [X60: $i > $o,X61: $i] :
( ( X60 @ X61 )
=> ? [X62: $i] :
( ( X60 @ X62 )
& ! [X63: $i] :
( ( r @ X62 @ X62 )
=> ~ ( X60 @ X63 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[upwf_trans,c_0_12]),c_0_13]) ).
thf(c_0_19,negated_conjecture,
~ ! [X47: $i > $o,X68: $i] :
( ~ ! [X64: $i] :
( ( r @ X68 @ X64 )
=> ( X47 @ X64 ) )
| ! [X67: $i] :
( ( r @ X68 @ X67 )
=> ! [X66: $i] :
( ( r @ X67 @ X66 )
=> ! [X65: $i] :
( ( r @ X66 @ X65 )
=> ( X47 @ X65 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]) ).
thf(c_0_20,plain,
! [X69: $i,X70: $i,X71: $i,X72: $i > $o,X73: $i,X75: $i] :
( ( ~ ( r @ X69 @ X70 )
| ~ ( r @ X70 @ X71 )
| ( r @ X69 @ X71 ) )
& ( ( X72 @ ( esk1_1 @ X72 ) )
| ~ ( X72 @ X73 ) )
& ( ~ ( r @ ( esk1_1 @ X72 ) @ ( esk1_1 @ X72 ) )
| ~ ( X72 @ X75 )
| ~ ( X72 @ X73 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])])])]) ).
thf(c_0_21,negated_conjecture,
! [X78: $i] :
( ( ~ ( r @ esk2_0 @ X78 )
| ( epred1_0 @ X78 ) )
& ( r @ esk2_0 @ esk3_0 )
& ( r @ esk3_0 @ esk4_0 )
& ( r @ esk4_0 @ esk5_0 )
& ~ ( epred1_0 @ esk5_0 ) ),
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_19])])])])]) ).
thf(c_0_22,plain,
! [X1: $i,X3: $i,X12: $i] :
( ( r @ X1 @ X12 )
| ~ ( r @ X1 @ X3 )
| ~ ( r @ X3 @ X12 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_23,negated_conjecture,
r @ esk4_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ X1 )
| ~ ( r @ esk2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i] :
( ( r @ X1 @ esk5_0 )
| ~ ( r @ X1 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_26,negated_conjecture,
~ ( epred1_0 @ esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_27,negated_conjecture,
r @ esk3_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_28,negated_conjecture,
~ ( r @ esk2_0 @ esk4_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i] :
( ( r @ X1 @ esk4_0 )
| ~ ( r @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
thf(c_0_30,negated_conjecture,
r @ esk2_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL626^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 09:33:03 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.13 Running higher-order theorem proving
% 0.09/0.14 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.CDalh4mYJq/E---3.1_4056133.p
% 0.09/0.15 % Version: 3.5.1-ho
% 0.09/0.15 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.09/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.15 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.15 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.15 % Starting post_as_ho11 with 300s (1) cores
% 0.09/0.15 % Starting full_lambda_8 with 300s (1) cores
% 0.09/0.15 % post_as_ho3 with pid 4056147 completed with status 0
% 0.09/0.15 % Result found by post_as_ho3
% 0.09/0.15 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.09/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.15 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.15 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.15 % No SInE strategy applied
% 0.09/0.15 % Search class: HHHNF-FFSS11-SHSSMSBC
% 0.09/0.15 % partial match(2): HHHNF-FFSF11-SHSSMMBC
% 0.09/0.15 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.15 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.15 % SubtermCWHack with pid 4056151 completed with status 0
% 0.09/0.15 % Result found by SubtermCWHack
% 0.09/0.15 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.09/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.15 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.15 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.15 % No SInE strategy applied
% 0.09/0.15 % Search class: HHHNF-FFSS11-SHSSMSBC
% 0.09/0.15 % partial match(2): HHHNF-FFSF11-SHSSMMBC
% 0.09/0.15 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.15 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.15 % Preprocessing time : 0.001 s
% 0.09/0.15
% 0.09/0.15 % Proof found!
% 0.09/0.15 % SZS status Theorem
% 0.09/0.15 % SZS output start CNFRefutation
% See solution above
% 0.09/0.15 % Parsed axioms : 80
% 0.09/0.15 % Removed by relevancy pruning/SinE : 0
% 0.09/0.15 % Initial clauses : 50
% 0.09/0.15 % Removed in clause preprocessing : 42
% 0.09/0.15 % Initial clauses in saturation : 8
% 0.09/0.15 % Processed clauses : 16
% 0.09/0.15 % ...of these trivial : 0
% 0.09/0.15 % ...subsumed : 0
% 0.09/0.15 % ...remaining for further processing : 16
% 0.09/0.15 % Other redundant clauses eliminated : 0
% 0.09/0.15 % Clauses deleted for lack of memory : 0
% 0.09/0.15 % Backward-subsumed : 0
% 0.09/0.15 % Backward-rewritten : 0
% 0.09/0.15 % Generated clauses : 24
% 0.09/0.15 % ...of the previous two non-redundant : 17
% 0.09/0.15 % ...aggressively subsumed : 0
% 0.09/0.15 % Contextual simplify-reflections : 0
% 0.09/0.15 % Paramodulations : 24
% 0.09/0.15 % Factorizations : 0
% 0.09/0.15 % NegExts : 0
% 0.09/0.15 % Equation resolutions : 0
% 0.09/0.15 % Disequality decompositions : 0
% 0.09/0.15 % Total rewrite steps : 7
% 0.09/0.15 % ...of those cached : 2
% 0.09/0.15 % Propositional unsat checks : 0
% 0.09/0.15 % Propositional check models : 0
% 0.09/0.15 % Propositional check unsatisfiable : 0
% 0.09/0.15 % Propositional clauses : 0
% 0.09/0.15 % Propositional clauses after purity: 0
% 0.09/0.15 % Propositional unsat core size : 0
% 0.09/0.15 % Propositional preprocessing time : 0.000
% 0.09/0.15 % Propositional encoding time : 0.000
% 0.09/0.15 % Propositional solver time : 0.000
% 0.09/0.15 % Success case prop preproc time : 0.000
% 0.09/0.15 % Success case prop encoding time : 0.000
% 0.09/0.15 % Success case prop solver time : 0.000
% 0.09/0.15 % Current number of processed clauses : 16
% 0.09/0.15 % Positive orientable unit clauses : 9
% 0.09/0.15 % Positive unorientable unit clauses: 0
% 0.09/0.15 % Negative unit clauses : 2
% 0.09/0.15 % Non-unit-clauses : 5
% 0.09/0.15 % Current number of unprocessed clauses: 7
% 0.09/0.15 % ...number of literals in the above : 16
% 0.09/0.15 % Current number of archived formulas : 0
% 0.09/0.15 % Current number of archived clauses : 0
% 0.09/0.15 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.15 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.15 % Non-unit clause-clause subsumptions : 0
% 0.09/0.15 % Unit Clause-clause subsumption calls : 1
% 0.09/0.15 % Rewrite failures with RHS unbound : 0
% 0.09/0.15 % BW rewrite match attempts : 0
% 0.09/0.15 % BW rewrite match successes : 0
% 0.09/0.15 % Condensation attempts : 0
% 0.09/0.15 % Condensation successes : 0
% 0.09/0.15 % Termbank termtop insertions : 2748
% 0.09/0.15 % Search garbage collected termcells : 425
% 0.09/0.15
% 0.09/0.15 % -------------------------------------------------
% 0.09/0.15 % User time : 0.003 s
% 0.09/0.15 % System time : 0.001 s
% 0.09/0.15 % Total time : 0.004 s
% 0.09/0.15 % Maximum resident set size: 3720 pages
% 0.09/0.15
% 0.09/0.15 % -------------------------------------------------
% 0.09/0.15 % User time : 0.006 s
% 0.09/0.15 % System time : 0.002 s
% 0.09/0.15 % Total time : 0.008 s
% 0.09/0.15 % Maximum resident set size: 4608 pages
% 0.09/0.15 % E exiting
%------------------------------------------------------------------------------