%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL624^1 : 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 : 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 08:12:01 AM UTC 2026
% Result : Theorem 0.13s 0.25s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 15 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 190 ( 24 ~; 18 |; 14 &; 130 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 70 ( 38 ^; 26 !; 6 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_29,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_30,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_31,type,
mand: ( $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,
epred1_0: $i > $i > $o ).
thf(decl_43,type,
epred2_0: $i > $o ).
thf(decl_44,type,
epred3_0: $i > $o ).
thf(decl_45,type,
esk1_0: $i ).
thf(decl_46,type,
esk2_0: $i ).
thf(decl_47,type,
esk3_1: $i > $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SKOKjeMvqV/E---3.1_519788.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SKOKjeMvqV/E---3.1_519788.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SKOKjeMvqV/E---3.1_519788.p',mor) ).
thf(thm,conjecture,
! [X10: $i > $i > $o,X11: $i > $o,X19: $i > $o] : ( mvalid @ ( mimpl @ ( mand @ ( mdia @ X10 @ ( mbox @ X10 @ X11 ) ) @ ( mbox @ X10 @ ( mdia @ X10 @ X19 ) ) ) @ ( mdia @ X10 @ ( mdia @ X10 @ ( mand @ X11 @ X19 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SKOKjeMvqV/E---3.1_519788.p',thm) ).
thf(mand,axiom,
( mand
= ( ^ [X6: $i > $o,X5: $i > $o,X3: $i] :
( ( X6 @ X3 )
& ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SKOKjeMvqV/E---3.1_519788.p',mand) ).
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.SKOKjeMvqV/E---3.1_519788.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.SKOKjeMvqV/E---3.1_519788.p',mdia) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SKOKjeMvqV/E---3.1_519788.p',mvalid) ).
thf(c_0_8,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimpl]) ).
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,
~ ! [X10: $i > $i > $o,X11: $i > $o,X19: $i > $o] : ( mvalid @ ( mimpl @ ( mand @ ( mdia @ X10 @ ( mbox @ X10 @ X11 ) ) @ ( mbox @ X10 @ ( mdia @ X10 @ X19 ) ) ) @ ( mdia @ X10 @ ( mdia @ X10 @ ( mand @ X11 @ X19 ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_12,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_13,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_8,c_0_9]),c_0_10]) ).
thf(c_0_14,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_15,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_16,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_17,negated_conjecture,
~ ! [X10: $i > $i > $o,X11: $i > $o,X19: $i > $o,X29: $i] :
( ~ ( ? [X24: $i] :
( ( X10 @ X29 @ X24 )
& ! [X23: $i] :
( ( X10 @ X24 @ X23 )
=> ( X11 @ X23 ) ) )
& ! [X26: $i] :
( ( X10 @ X29 @ X26 )
=> ? [X25: $i] :
( ( X10 @ X26 @ X25 )
& ( X19 @ X25 ) ) ) )
| ? [X28: $i] :
( ( X10 @ X29 @ X28 )
& ? [X27: $i] :
( ( X10 @ X28 @ X27 )
& ( X11 @ X27 )
& ( X19 @ X27 ) ) ) ),
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_11,c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16]) ).
thf(c_0_18,negated_conjecture,
! [X35: $i,X36: $i,X38: $i,X39: $i] :
( ( epred1_0 @ esk1_0 @ esk2_0 )
& ( ~ ( epred1_0 @ esk2_0 @ X35 )
| ( epred2_0 @ X35 ) )
& ( ( epred1_0 @ X36 @ ( esk3_1 @ X36 ) )
| ~ ( epred1_0 @ esk1_0 @ X36 ) )
& ( ( epred3_0 @ ( esk3_1 @ X36 ) )
| ~ ( epred1_0 @ esk1_0 @ X36 ) )
& ( ~ ( epred1_0 @ esk1_0 @ X38 )
| ~ ( epred1_0 @ X38 @ X39 )
| ~ ( epred2_0 @ X39 )
| ~ ( epred3_0 @ X39 ) ) ),
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_17])])])])])]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( epred1_0 @ esk1_0 @ X1 )
| ~ ( epred1_0 @ X1 @ X3 )
| ~ ( epred2_0 @ X3 )
| ~ ( epred3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_20,negated_conjecture,
epred1_0 @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i] :
( ( epred2_0 @ X1 )
| ~ ( epred1_0 @ esk2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i] :
( ~ ( epred1_0 @ esk2_0 @ X1 )
| ~ ( epred3_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ X1 @ ( esk3_1 @ X1 ) )
| ~ ( epred1_0 @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,negated_conjecture,
~ ( epred3_0 @ ( esk3_1 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20])]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i] :
( ( epred3_0 @ ( esk3_1 @ X1 ) )
| ~ ( epred1_0 @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL624^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.17 % Computer : n019.cluster.edu
% 0.13/0.17 % Model : x86_64 x86_64
% 0.13/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.17 % Memory : 8046.5625MB
% 0.13/0.17 % OS : Linux 6.8.0-71-generic
% 0.13/0.17 % CPULimit : 300
% 0.13/0.17 % WCLimit : 300
% 0.13/0.17 % DateTime : Tue Sep 29 09:29:32 UTC 2026
% 0.13/0.17 % CPUTime :
% 0.13/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.22 Running higher-order theorem proving
% 0.13/0.23 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.SKOKjeMvqV/E---3.1_519788.p
% 0.13/0.25 % Version: 3.5.1-ho
% 0.13/0.25 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.13/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.25 % Starting new_ho_9 with 1500s (5) cores
% 0.13/0.25 % Starting post_as_ho1 with 300s (1) cores
% 0.13/0.25 % Starting sh1l with 300s (1) cores
% 0.13/0.25 % Starting post_as_ho10 with 300s (1) cores
% 0.13/0.25 % new_ho_9 with pid 519813 completed with status 0
% 0.13/0.25 % Result found by new_ho_9
% 0.13/0.25 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.13/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.25 % Starting new_ho_9 with 1500s (5) cores
% 0.13/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.25 % No SInE strategy applied
% 0.13/0.25 % Search class: HHHNF-FFSF11-SHSSMFNN
% 0.13/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.25 % Starting new_ho_9 with 151s (1) cores
% 0.13/0.25 % Starting lpo1_def_fix with 136s (1) cores
% 0.13/0.25 % Starting lpo1_lambda_fix with 136s (1) cores
% 0.13/0.25 % Starting new_ho_7 with 136s (1) cores
% 0.13/0.25 % SubtermCWHack with pid 519817 completed with status 0
% 0.13/0.25 % Result found by SubtermCWHack
% 0.13/0.25 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.13/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.25 % Starting new_ho_9 with 1500s (5) cores
% 0.13/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.25 % No SInE strategy applied
% 0.13/0.25 % Search class: HHHNF-FFSF11-SHSSMFNN
% 0.13/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.25 % Preprocessing time : 0.001 s
% 0.13/0.25
% 0.13/0.25 % Proof found!
% 0.13/0.25 % SZS status Theorem
% 0.13/0.25 % SZS output start CNFRefutation
% See solution above
% 0.13/0.25 % Parsed axioms : 36
% 0.13/0.25 % Removed by relevancy pruning/SinE : 0
% 0.13/0.25 % Initial clauses : 25
% 0.13/0.25 % Removed in clause preprocessing : 20
% 0.13/0.25 % Initial clauses in saturation : 5
% 0.13/0.25 % Processed clauses : 8
% 0.13/0.25 % ...of these trivial : 0
% 0.13/0.25 % ...subsumed : 0
% 0.13/0.25 % ...remaining for further processing : 8
% 0.13/0.25 % Other redundant clauses eliminated : 0
% 0.13/0.25 % Clauses deleted for lack of memory : 0
% 0.13/0.25 % Backward-subsumed : 0
% 0.13/0.25 % Backward-rewritten : 0
% 0.13/0.25 % Generated clauses : 5
% 0.13/0.25 % ...of the previous two non-redundant : 4
% 0.13/0.25 % ...aggressively subsumed : 0
% 0.13/0.25 % Contextual simplify-reflections : 1
% 0.13/0.25 % Paramodulations : 5
% 0.13/0.25 % Factorizations : 0
% 0.13/0.25 % NegExts : 0
% 0.13/0.25 % Equation resolutions : 0
% 0.13/0.25 % Disequality decompositions : 0
% 0.13/0.25 % Total rewrite steps : 3
% 0.13/0.25 % ...of those cached : 2
% 0.13/0.25 % Propositional unsat checks : 0
% 0.13/0.25 % Propositional check models : 0
% 0.13/0.25 % Propositional check unsatisfiable : 0
% 0.13/0.25 % Propositional clauses : 0
% 0.13/0.25 % Propositional clauses after purity: 0
% 0.13/0.25 % Propositional unsat core size : 0
% 0.13/0.25 % Propositional preprocessing time : 0.000
% 0.13/0.25 % Propositional encoding time : 0.000
% 0.13/0.25 % Propositional solver time : 0.000
% 0.13/0.25 % Success case prop preproc time : 0.000
% 0.13/0.25 % Success case prop encoding time : 0.000
% 0.13/0.25 % Success case prop solver time : 0.000
% 0.13/0.25 % Current number of processed clauses : 8
% 0.13/0.25 % Positive orientable unit clauses : 2
% 0.13/0.25 % Positive unorientable unit clauses: 0
% 0.13/0.25 % Negative unit clauses : 1
% 0.13/0.25 % Non-unit-clauses : 5
% 0.13/0.25 % Current number of unprocessed clauses: 1
% 0.13/0.25 % ...number of literals in the above : 4
% 0.13/0.25 % Current number of archived formulas : 0
% 0.13/0.25 % Current number of archived clauses : 0
% 0.13/0.25 % Clause-clause subsumption calls (NU) : 1
% 0.13/0.25 % Rec. Clause-clause subsumption calls : 1
% 0.13/0.25 % Non-unit clause-clause subsumptions : 1
% 0.13/0.25 % Unit Clause-clause subsumption calls : 1
% 0.13/0.25 % Rewrite failures with RHS unbound : 0
% 0.13/0.25 % BW rewrite match attempts : 0
% 0.13/0.25 % BW rewrite match successes : 0
% 0.13/0.25 % Condensation attempts : 0
% 0.13/0.25 % Condensation successes : 0
% 0.13/0.25 % Termbank termtop insertions : 1460
% 0.13/0.25 % Search garbage collected termcells : 425
% 0.13/0.25
% 0.13/0.25 % -------------------------------------------------
% 0.13/0.25 % User time : 0.002 s
% 0.13/0.25 % System time : 0.002 s
% 0.13/0.25 % Total time : 0.004 s
% 0.13/0.25 % Maximum resident set size: 3668 pages
% 0.13/0.25
% 0.13/0.25 % -------------------------------------------------
% 0.13/0.25 % User time : 0.006 s
% 0.13/0.25 % System time : 0.011 s
% 0.13/0.25 % Total time : 0.017 s
% 0.13/0.25 % Maximum resident set size: 4864 pages
% 0.13/0.25 % E exiting
%------------------------------------------------------------------------------