%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL722^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:12:05 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 13 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 77 ( 14 ~; 10 |; 1 &; 52 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 39 ( 26 ^; 13 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_28,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_40,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
rel_m: $i > $i > $o ).
thf(decl_55,type,
mbox_m: ( $i > $o ) > $i > $o ).
thf(decl_57,type,
phi: $i > $o ).
thf(decl_58,type,
esk1_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x9oig0sqa2/E---3.1_134415.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x9oig0sqa2/E---3.1_134415.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x9oig0sqa2/E---3.1_134415.p',mor) ).
thf(conj,conjecture,
mvalid @ ( mimplies @ ( mbox_m @ phi ) @ phi ),
file('/export/starexec/sandbox/tmp/tmp.x9oig0sqa2/E---3.1_134415.p',conj) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x9oig0sqa2/E---3.1_134415.p',mvalid) ).
thf(mbox_m,axiom,
( mbox_m
= ( ^ [X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( rel_m @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x9oig0sqa2/E---3.1_134415.p',mbox_m) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X13: $i > $i > $o] :
! [X15: $i] : ( X13 @ X15 @ X15 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x9oig0sqa2/E---3.1_134415.p',mreflexive) ).
thf(a1,axiom,
mreflexive @ rel_m,
file('/export/starexec/sandbox/tmp/tmp.x9oig0sqa2/E---3.1_134415.p',a1) ).
thf(c_0_8,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_9,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_10,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_11,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_m @ phi ) @ phi ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_12,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
thf(c_0_13,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_14,plain,
( mbox_m
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X14: $i] :
( ~ ( rel_m @ Z1 @ X14 )
| ( Z0 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_m]) ).
thf(c_0_15,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i] : ( Z0 @ X15 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_16,negated_conjecture,
~ ! [X24: $i] :
( ~ ! [X23: $i] :
( ~ ( rel_m @ X24 @ X23 )
| ( phi @ X23 ) )
| ( phi @ X24 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).
thf(c_0_17,plain,
! [X22: $i] : ( rel_m @ X22 @ X22 ),
inference(apply_def,[status(thm)],[a1,c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X27: $i] :
( ( ~ ( rel_m @ esk1_0 @ X27 )
| ( phi @ X27 ) )
& ~ ( phi @ esk1_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_16])])])])]) ).
thf(c_0_19,plain,
! [X25: $i] : ( rel_m @ X25 @ X25 ),
inference(variable_rename,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X3: $i] :
( ( phi @ X3 )
| ~ ( rel_m @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,plain,
! [X3: $i] : ( rel_m @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_22,negated_conjecture,
~ ( phi @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL722^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n016.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 10:01:34 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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.x9oig0sqa2/E---3.1_134415.p
% 0.09/0.26 % Version: 3.5.1-ho
% 0.09/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.26 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.26 % Starting almost_fo_3_lam with 300s (1) cores
% 0.09/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.26 % almost_fo_3_lam with pid 134431 completed with status 0
% 0.09/0.26 % Result found by almost_fo_3_lam
% 0.09/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.26 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.26 % Starting almost_fo_3_lam with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HHUNF-FFSF00-SHSSMFNN
% 0.09/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.26 % SubtermCWHack with pid 134435 completed with status 0
% 0.09/0.26 % Result found by SubtermCWHack
% 0.09/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.26 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.26 % Starting almost_fo_3_lam with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HHUNF-FFSF00-SHSSMFNN
% 0.09/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.26 % Preprocessing time : 0.001 s
% 0.09/0.26
% 0.09/0.26 % Proof found!
% 0.09/0.26 % SZS status Theorem
% 0.09/0.26 % SZS output start CNFRefutation
% See solution above
% 0.09/0.26 % Parsed axioms : 71
% 0.09/0.26 % Removed by relevancy pruning/SinE : 0
% 0.09/0.26 % Initial clauses : 39
% 0.09/0.26 % Removed in clause preprocessing : 36
% 0.09/0.26 % Initial clauses in saturation : 3
% 0.09/0.26 % Processed clauses : 3
% 0.09/0.26 % ...of these trivial : 0
% 0.09/0.26 % ...subsumed : 0
% 0.09/0.26 % ...remaining for further processing : 3
% 0.09/0.26 % Other redundant clauses eliminated : 0
% 0.09/0.26 % Clauses deleted for lack of memory : 0
% 0.09/0.26 % Backward-subsumed : 0
% 0.09/0.26 % Backward-rewritten : 0
% 0.09/0.26 % Generated clauses : 1
% 0.09/0.26 % ...of the previous two non-redundant : 0
% 0.09/0.26 % ...aggressively subsumed : 0
% 0.09/0.26 % Contextual simplify-reflections : 0
% 0.09/0.26 % Paramodulations : 1
% 0.09/0.26 % Factorizations : 0
% 0.09/0.26 % NegExts : 0
% 0.09/0.26 % Equation resolutions : 0
% 0.09/0.26 % Disequality decompositions : 0
% 0.09/0.26 % Total rewrite steps : 0
% 0.09/0.26 % ...of those cached : 0
% 0.09/0.26 % Propositional unsat checks : 0
% 0.09/0.26 % Propositional check models : 0
% 0.09/0.26 % Propositional check unsatisfiable : 0
% 0.09/0.26 % Propositional clauses : 0
% 0.09/0.26 % Propositional clauses after purity: 0
% 0.09/0.26 % Propositional unsat core size : 0
% 0.09/0.26 % Propositional preprocessing time : 0.000
% 0.09/0.26 % Propositional encoding time : 0.000
% 0.09/0.26 % Propositional solver time : 0.000
% 0.09/0.26 % Success case prop preproc time : 0.000
% 0.09/0.26 % Success case prop encoding time : 0.000
% 0.09/0.26 % Success case prop solver time : 0.000
% 0.09/0.26 % Current number of processed clauses : 3
% 0.09/0.26 % Positive orientable unit clauses : 1
% 0.09/0.26 % Positive unorientable unit clauses: 0
% 0.09/0.26 % Negative unit clauses : 1
% 0.09/0.26 % Non-unit-clauses : 1
% 0.09/0.26 % Current number of unprocessed clauses: 0
% 0.09/0.26 % ...number of literals in the above : 0
% 0.09/0.26 % Current number of archived formulas : 0
% 0.09/0.26 % Current number of archived clauses : 0
% 0.09/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.26 % Non-unit clause-clause subsumptions : 0
% 0.09/0.26 % Unit Clause-clause subsumption calls : 0
% 0.09/0.26 % Rewrite failures with RHS unbound : 0
% 0.09/0.26 % BW rewrite match attempts : 0
% 0.09/0.26 % BW rewrite match successes : 0
% 0.09/0.26 % Condensation attempts : 0
% 0.09/0.26 % Condensation successes : 0
% 0.09/0.26 % Termbank termtop insertions : 2077
% 0.09/0.26 % Search garbage collected termcells : 323
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.006 s
% 0.09/0.26 % System time : 0.001 s
% 0.09/0.26 % Total time : 0.007 s
% 0.09/0.26 % Maximum resident set size: 3696 pages
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.008 s
% 0.09/0.26 % System time : 0.003 s
% 0.09/0.26 % Total time : 0.012 s
% 0.09/0.26 % Maximum resident set size: 4608 pages
% 0.09/0.26 % E exiting
%------------------------------------------------------------------------------