%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL608^1 : 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 : n013.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 08:12:00 AM UTC 2026
% Result : Theorem 0.10s 0.23s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 9 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 64 ( 11 ~; 7 |; 5 &; 38 @)
% ( 0 <=>; 3 =>; 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 : 9 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 36 ( 20 ^; 16 !; 0 ?; 36 :)
% 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_38,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_42,type,
epred1_0: $i > $o ).
thf(decl_43,type,
epred2_0: $i > $o ).
thf(decl_44,type,
esk1_0: $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rYoMI1FED0/E---3.1_1845269.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rYoMI1FED0/E---3.1_1845269.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rYoMI1FED0/E---3.1_1845269.p',mor) ).
thf(thm,conjecture,
! [X19: $i > $o,X20: $i > $o] :
( ( ( mvalid @ X19 )
& ( mvalid @ ( mimpl @ X19 @ X20 ) ) )
=> ( mvalid @ X20 ) ),
file('/export/starexec/sandbox/tmp/tmp.rYoMI1FED0/E---3.1_1845269.p',thm) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rYoMI1FED0/E---3.1_1845269.p',mvalid) ).
thf(c_0_5,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimpl]) ).
thf(c_0_6,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_7,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_8,negated_conjecture,
~ ! [X19: $i > $o,X20: $i > $o] :
( ( ( mvalid @ X19 )
& ( mvalid @ ( mimpl @ X19 @ X20 ) ) )
=> ( mvalid @ X20 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_9,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_5,c_0_6]),c_0_7]) ).
thf(c_0_10,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_11,negated_conjecture,
~ ! [X19: $i > $o,X20: $i > $o] :
( ( ! [X23: $i] : ( X19 @ X23 )
& ! [X24: $i] :
( ~ ( X19 @ X24 )
| ( X20 @ X24 ) ) )
=> ! [X25: $i] : ( X20 @ X25 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X28: $i,X29: $i] :
( ( epred1_0 @ X28 )
& ( ~ ( epred1_0 @ X29 )
| ( epred2_0 @ X29 ) )
& ~ ( epred2_0 @ 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_11])])])])]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i] :
( ( epred2_0 @ X1 )
| ~ ( epred1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i] : ( epred1_0 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
~ ( epred2_0 @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] : ( epred2_0 @ X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL608^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n013.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 09:18:36 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.21 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.rYoMI1FED0/E---3.1_1845269.p
% 0.10/0.23 % Version: 3.5.1-ho
% 0.10/0.23 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.10/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.23 % Starting new_ho_9 with 1500s (5) cores
% 0.10/0.23 % Starting post_as_ho1 with 300s (1) cores
% 0.10/0.23 % Starting sh1l with 300s (1) cores
% 0.10/0.23 % Starting post_as_ho10 with 300s (1) cores
% 0.10/0.23 % post_as_ho1 with pid 1845297 completed with status 0
% 0.10/0.23 % Result found by post_as_ho1
% 0.10/0.23 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.10/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.23 % Starting new_ho_9 with 1500s (5) cores
% 0.10/0.23 % Starting post_as_ho1 with 300s (1) cores
% 0.10/0.23 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.23 % No SInE strategy applied
% 0.10/0.23 % Search class: HHUNF-FFSF00-SHSSMFNN
% 0.10/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.23 % SubtermCWHack with pid 1845300 completed with status 0
% 0.10/0.23 % Result found by SubtermCWHack
% 0.10/0.23 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.10/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.23 % Starting new_ho_9 with 1500s (5) cores
% 0.10/0.23 % Starting post_as_ho1 with 300s (1) cores
% 0.10/0.23 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.23 % No SInE strategy applied
% 0.10/0.23 % Search class: HHUNF-FFSF00-SHSSMFNN
% 0.10/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.23 % Preprocessing time : 0.001 s
% 0.10/0.23
% 0.10/0.23 % Proof found!
% 0.10/0.23 % SZS status Theorem
% 0.10/0.23 % SZS output start CNFRefutation
% See solution above
% 0.10/0.23 % Parsed axioms : 36
% 0.10/0.23 % Removed by relevancy pruning/SinE : 0
% 0.10/0.23 % Initial clauses : 23
% 0.10/0.23 % Removed in clause preprocessing : 20
% 0.10/0.23 % Initial clauses in saturation : 3
% 0.10/0.23 % Processed clauses : 3
% 0.10/0.23 % ...of these trivial : 0
% 0.10/0.23 % ...subsumed : 0
% 0.10/0.23 % ...remaining for further processing : 3
% 0.10/0.23 % Other redundant clauses eliminated : 0
% 0.10/0.23 % Clauses deleted for lack of memory : 0
% 0.10/0.23 % Backward-subsumed : 0
% 0.10/0.23 % Backward-rewritten : 1
% 0.10/0.23 % Generated clauses : 0
% 0.10/0.23 % ...of the previous two non-redundant : 0
% 0.10/0.23 % ...aggressively subsumed : 0
% 0.10/0.23 % Contextual simplify-reflections : 0
% 0.10/0.23 % Paramodulations : 0
% 0.10/0.23 % Factorizations : 0
% 0.10/0.23 % NegExts : 0
% 0.10/0.23 % Equation resolutions : 0
% 0.10/0.23 % Disequality decompositions : 0
% 0.10/0.23 % Total rewrite steps : 2
% 0.10/0.23 % ...of those cached : 0
% 0.10/0.23 % Propositional unsat checks : 0
% 0.10/0.23 % Propositional check models : 0
% 0.10/0.23 % Propositional check unsatisfiable : 0
% 0.10/0.23 % Propositional clauses : 0
% 0.10/0.23 % Propositional clauses after purity: 0
% 0.10/0.23 % Propositional unsat core size : 0
% 0.10/0.23 % Propositional preprocessing time : 0.000
% 0.10/0.23 % Propositional encoding time : 0.000
% 0.10/0.23 % Propositional solver time : 0.000
% 0.10/0.23 % Success case prop preproc time : 0.000
% 0.10/0.23 % Success case prop encoding time : 0.000
% 0.10/0.23 % Success case prop solver time : 0.000
% 0.10/0.23 % Current number of processed clauses : 2
% 0.10/0.23 % Positive orientable unit clauses : 2
% 0.10/0.23 % Positive unorientable unit clauses: 0
% 0.10/0.23 % Negative unit clauses : 0
% 0.10/0.23 % Non-unit-clauses : 0
% 0.10/0.23 % Current number of unprocessed clauses: 0
% 0.10/0.23 % ...number of literals in the above : 0
% 0.10/0.23 % Current number of archived formulas : 0
% 0.10/0.23 % Current number of archived clauses : 1
% 0.10/0.23 % Clause-clause subsumption calls (NU) : 0
% 0.10/0.23 % Rec. Clause-clause subsumption calls : 0
% 0.10/0.23 % Non-unit clause-clause subsumptions : 0
% 0.10/0.23 % Unit Clause-clause subsumption calls : 0
% 0.10/0.23 % Rewrite failures with RHS unbound : 0
% 0.10/0.23 % BW rewrite match attempts : 1
% 0.10/0.23 % BW rewrite match successes : 1
% 0.10/0.23 % Condensation attempts : 0
% 0.10/0.23 % Condensation successes : 0
% 0.10/0.23 % Termbank termtop insertions : 973
% 0.10/0.23 % Search garbage collected termcells : 191
% 0.10/0.23
% 0.10/0.23 % -------------------------------------------------
% 0.10/0.23 % User time : 0.004 s
% 0.10/0.23 % System time : 0.000 s
% 0.10/0.23 % Total time : 0.004 s
% 0.10/0.23 % Maximum resident set size: 3616 pages
% 0.10/0.23
% 0.10/0.23 % -------------------------------------------------
% 0.10/0.23 % User time : 0.005 s
% 0.10/0.23 % System time : 0.005 s
% 0.10/0.23 % Total time : 0.010 s
% 0.10/0.23 % Maximum resident set size: 4864 pages
% 0.10/0.23 % E exiting
%------------------------------------------------------------------------------