%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL586^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:11:57 AM UTC 2026
% Result : Theorem 0.25s 0.34s
% Output : CNFRefutation 0.25s
% 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 : 65 ( 13 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 98 ( 14 ~; 8 |; 6 &; 67 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 43 ( 32 ^; 8 !; 3 ?; 43 :)
% 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_35,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_38,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_42,type,
a: $i > $o ).
thf(decl_43,type,
b: $i > $o ).
thf(decl_44,type,
r: $i > $i > $o ).
thf(decl_45,type,
esk1_0: $i ).
thf(decl_46,type,
esk2_0: $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lhmgkOBM34/E---3.1_2265288.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lhmgkOBM34/E---3.1_2265288.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lhmgkOBM34/E---3.1_2265288.p',mor) ).
thf(thm,conjecture,
mvalid @ ( mimpl @ ( mnot @ ( mdia @ r @ a ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lhmgkOBM34/E---3.1_2265288.p',thm) ).
thf(mbox,axiom,
( mbox
= ( ^ [X10: $i > $i > $o,X11: $i > $o,X1: $i] :
! [X12: $i] :
( ( X10 @ X1 @ X12 )
=> ( X11 @ X12 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lhmgkOBM34/E---3.1_2265288.p',mbox) ).
thf(mdia,axiom,
( mdia
= ( ^ [X10: $i > $i > $o,X11: $i > $o,X1: $i] :
? [X13: $i] :
( ( X10 @ X1 @ X13 )
& ( X11 @ X13 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lhmgkOBM34/E---3.1_2265288.p',mdia) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lhmgkOBM34/E---3.1_2265288.p',mvalid) ).
thf(c_0_7,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimpl]) ).
thf(c_0_8,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_9,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_10,negated_conjecture,
~ ( mvalid @ ( mimpl @ ( mnot @ ( mdia @ r @ a ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_11,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_7,c_0_8]),c_0_9]) ).
thf(c_0_12,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_13,plain,
( mdia
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
? [X13: $i] :
( ( Z0 @ Z2 @ X13 )
& ( Z1 @ X13 ) ) ) ),
inference(fof_simplification,[status(thm)],[mdia]) ).
thf(c_0_14,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_15,negated_conjecture,
~ ! [X21: $i] :
( ~ ~ ? [X19: $i] :
( ( r @ X21 @ X19 )
& ( a @ X19 ) )
| ! [X20: $i] :
( ( r @ X21 @ X20 )
=> ( ~ ( a @ X20 )
| ( b @ X20 ) ) ) ),
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)],[c_0_10,c_0_8]),c_0_11]),c_0_12]),c_0_13]),c_0_14])]) ).
thf(c_0_16,negated_conjecture,
! [X23: $i] :
( ( ~ ( r @ esk1_0 @ X23 )
| ~ ( a @ X23 ) )
& ( r @ esk1_0 @ esk2_0 )
& ( a @ esk2_0 )
& ~ ( b @ esk2_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_15])])])])]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i] :
( ~ ( r @ esk1_0 @ X1 )
| ~ ( a @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_18,negated_conjecture,
r @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
a @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL586^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 % Computer : n003.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.24 % CPULimit : 300
% 0.08/0.24 % WCLimit : 300
% 0.08/0.24 % DateTime : Tue Sep 29 09:02:43 UTC 2026
% 0.08/0.24 % CPUTime :
% 0.08/0.24 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.30 Running higher-order theorem proving
% 0.25/0.32 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.lhmgkOBM34/E---3.1_2265288.p
% 0.25/0.34 % Version: 3.5.1-ho
% 0.25/0.34 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.25/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.34 % Starting new_ho_9 with 1500s (5) cores
% 0.25/0.34 % Starting post_as_ho1 with 300s (1) cores
% 0.25/0.34 % Starting sh1l with 300s (1) cores
% 0.25/0.34 % Starting post_as_ho10 with 300s (1) cores
% 0.25/0.34 % new_ho_9 with pid 2265302 completed with status 0
% 0.25/0.34 % Result found by new_ho_9
% 0.25/0.34 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.25/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.34 % Starting new_ho_9 with 1500s (5) cores
% 0.25/0.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.34 % No SInE strategy applied
% 0.25/0.34 % Search class: HUHNF-FFSF00-SHSSMFNN
% 0.25/0.34 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.34 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.34 % Starting new_ho_9 with 151s (1) cores
% 0.25/0.34 % Starting sh5l with 136s (1) cores
% 0.25/0.34 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.25/0.34 % Starting lpo1_def_fix with 136s (1) cores
% 0.25/0.34 % ehoh_best_sine_rwall with pid 2265310 completed with status 0
% 0.25/0.34 % Result found by ehoh_best_sine_rwall
% 0.25/0.34 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.25/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.34 % Starting new_ho_9 with 1500s (5) cores
% 0.25/0.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.34 % No SInE strategy applied
% 0.25/0.34 % Search class: HUHNF-FFSF00-SHSSMFNN
% 0.25/0.34 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.34 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.34 % Starting new_ho_9 with 151s (1) cores
% 0.25/0.34 % Starting sh5l with 136s (1) cores
% 0.25/0.34 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.25/0.34 % Preprocessing time : 0.001 s
% 0.25/0.34 % Presaturation interreduction done
% 0.25/0.34
% 0.25/0.34 % Proof found!
% 0.25/0.34 % SZS status Theorem
% 0.25/0.34 % SZS output start CNFRefutation
% See solution above
% 0.25/0.34 % Parsed axioms : 39
% 0.25/0.34 % Removed by relevancy pruning/SinE : 0
% 0.25/0.34 % Initial clauses : 27
% 0.25/0.34 % Removed in clause preprocessing : 23
% 0.25/0.34 % Initial clauses in saturation : 4
% 0.25/0.34 % Processed clauses : 8
% 0.25/0.34 % ...of these trivial : 0
% 0.25/0.34 % ...subsumed : 0
% 0.25/0.34 % ...remaining for further processing : 8
% 0.25/0.34 % Other redundant clauses eliminated : 0
% 0.25/0.34 % Clauses deleted for lack of memory : 0
% 0.25/0.34 % Backward-subsumed : 0
% 0.25/0.34 % Backward-rewritten : 0
% 0.25/0.34 % Generated clauses : 1
% 0.25/0.34 % ...of the previous two non-redundant : 0
% 0.25/0.34 % ...aggressively subsumed : 0
% 0.25/0.34 % Contextual simplify-reflections : 0
% 0.25/0.34 % Paramodulations : 1
% 0.25/0.34 % Factorizations : 0
% 0.25/0.34 % NegExts : 0
% 0.25/0.34 % Equation resolutions : 0
% 0.25/0.34 % Disequality decompositions : 0
% 0.25/0.34 % Total rewrite steps : 1
% 0.25/0.34 % ...of those cached : 0
% 0.25/0.34 % Propositional unsat checks : 0
% 0.25/0.34 % Propositional check models : 0
% 0.25/0.34 % Propositional check unsatisfiable : 0
% 0.25/0.34 % Propositional clauses : 0
% 0.25/0.34 % Propositional clauses after purity: 0
% 0.25/0.34 % Propositional unsat core size : 0
% 0.25/0.34 % Propositional preprocessing time : 0.000
% 0.25/0.34 % Propositional encoding time : 0.000
% 0.25/0.34 % Propositional solver time : 0.000
% 0.25/0.34 % Success case prop preproc time : 0.000
% 0.25/0.34 % Success case prop encoding time : 0.000
% 0.25/0.34 % Success case prop solver time : 0.000
% 0.25/0.34 % Current number of processed clauses : 4
% 0.25/0.34 % Positive orientable unit clauses : 2
% 0.25/0.34 % Positive unorientable unit clauses: 0
% 0.25/0.34 % Negative unit clauses : 1
% 0.25/0.34 % Non-unit-clauses : 1
% 0.25/0.34 % Current number of unprocessed clauses: 0
% 0.25/0.34 % ...number of literals in the above : 0
% 0.25/0.34 % Current number of archived formulas : 0
% 0.25/0.34 % Current number of archived clauses : 4
% 0.25/0.34 % Clause-clause subsumption calls (NU) : 0
% 0.25/0.34 % Rec. Clause-clause subsumption calls : 0
% 0.25/0.34 % Non-unit clause-clause subsumptions : 0
% 0.25/0.34 % Unit Clause-clause subsumption calls : 0
% 0.25/0.34 % Rewrite failures with RHS unbound : 0
% 0.25/0.34 % BW rewrite match attempts : 0
% 0.25/0.34 % BW rewrite match successes : 0
% 0.25/0.34 % Condensation attempts : 0
% 0.25/0.34 % Condensation successes : 0
% 0.25/0.34 % Termbank termtop insertions : 1074
% 0.25/0.34 % Search garbage collected termcells : 202
% 0.25/0.34
% 0.25/0.34 % -------------------------------------------------
% 0.25/0.34 % User time : 0.003 s
% 0.25/0.34 % System time : 0.004 s
% 0.25/0.34 % Total time : 0.007 s
% 0.25/0.34 % Maximum resident set size: 3668 pages
% 0.25/0.34
% 0.25/0.34 % -------------------------------------------------
% 0.25/0.34 % User time : 0.012 s
% 0.25/0.34 % System time : 0.014 s
% 0.25/0.34 % Total time : 0.026 s
% 0.25/0.34 % Maximum resident set size: 4864 pages
% 0.25/0.34 % E exiting
%------------------------------------------------------------------------------