%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL607^1 : 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 : n008.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 08:11:59 AM UTC 2026
% Result : Theorem 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 104 ( 18 equ; 0 cnn)
% Maximal formula atoms : 24 ( 2 avg)
% Number of connectives : 249 ( 40 ~; 39 |; 17 &; 149 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 71 ( 46 ^; 21 !; 4 ?; 71 :)
% 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_33,type,
miff: ( $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,
esk1_0: $i ).
thf(decl_45,type,
esk2_0: $i ).
thf(decl_46,type,
esk3_0: $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SYSxuQo1nZ/E---3.1_2902453.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SYSxuQo1nZ/E---3.1_2902453.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SYSxuQo1nZ/E---3.1_2902453.p',mor) ).
thf(miff,axiom,
( miff
= ( ^ [X9: $i > $o,X8: $i > $o] : ( mand @ ( mimpl @ X9 @ X8 ) @ ( mimpl @ X8 @ X9 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SYSxuQo1nZ/E---3.1_2902453.p',miff) ).
thf(mand,axiom,
( mand
= ( ^ [X6: $i > $o,X5: $i > $o,X3: $i] :
( ( X6 @ X3 )
& ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SYSxuQo1nZ/E---3.1_2902453.p',mand) ).
thf(thm,conjecture,
! [X10: $i > $i > $o,X19: $i > $o] : ( mvalid @ ( miff @ ( mdia @ X10 @ X19 ) @ ( mnot @ ( mbox @ X10 @ ( mnot @ X19 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SYSxuQo1nZ/E---3.1_2902453.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.SYSxuQo1nZ/E---3.1_2902453.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.SYSxuQo1nZ/E---3.1_2902453.p',mdia) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SYSxuQo1nZ/E---3.1_2902453.p',mvalid) ).
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,
( miff
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) )
& ( ~ ( Z1 @ Z2 )
| ( Z0 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[miff]) ).
thf(c_0_13,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_14,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_15,negated_conjecture,
~ ! [X10: $i > $i > $o,X19: $i > $o] : ( mvalid @ ( miff @ ( mdia @ X10 @ X19 ) @ ( mnot @ ( mbox @ X10 @ ( mnot @ X19 ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_16,plain,
( miff
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) )
& ( ~ ( Z1 @ Z2 )
| ( Z0 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
thf(c_0_17,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_18,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_19,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_20,negated_conjecture,
~ ! [X10: $i > $i > $o,X19: $i > $o,X24: $i] :
( ( ~ ? [X22: $i] :
( ( X10 @ X24 @ X22 )
& ( X19 @ X22 ) )
| ~ ! [X23: $i] :
( ( X10 @ X24 @ X23 )
=> ~ ( X19 @ X23 ) ) )
& ( ~ ~ ! [X23: $i] :
( ( X10 @ X24 @ X23 )
=> ~ ( X19 @ X23 ) )
| ? [X22: $i] :
( ( X10 @ X24 @ X22 )
& ( X19 @ X22 ) ) ) ),
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_15,c_0_10]),c_0_16]),c_0_17]),c_0_18]),c_0_19]) ).
thf(c_0_21,negated_conjecture,
! [X29: $i,X31: $i] :
( ( ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ( epred2_0 @ esk3_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ~ ( epred1_0 @ esk1_0 @ X31 )
| ~ ( epred2_0 @ X31 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 ) )
& ( ( epred2_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 ) )
& ( ~ ( epred1_0 @ esk1_0 @ X31 )
| ~ ( epred2_0 @ X31 )
| ( epred2_0 @ esk2_0 ) )
& ( ( epred1_0 @ esk1_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ X29 )
| ~ ( epred2_0 @ X29 ) )
& ( ( epred2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ X29 )
| ~ ( epred2_0 @ X29 ) )
& ( ~ ( epred1_0 @ esk1_0 @ X31 )
| ~ ( epred2_0 @ X31 )
| ~ ( epred1_0 @ esk1_0 @ X29 )
| ~ ( epred2_0 @ X29 ) ) ),
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_20])])])])])]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i] :
( ( epred2_0 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X1 )
| ~ ( epred2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_23,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
( ( epred2_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ esk1_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ X1 )
| ~ ( epred2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_26,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_27,negated_conjecture,
epred2_0 @ esk2_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i] :
( ( epred2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ X1 )
| ~ ( epred2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_29,negated_conjecture,
( ( epred2_0 @ esk3_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( epred1_0 @ esk1_0 @ X1 )
| ~ ( epred2_0 @ X1 )
| ~ ( epred1_0 @ esk1_0 @ X3 )
| ~ ( epred2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_31,negated_conjecture,
epred1_0 @ esk1_0 @ esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
thf(c_0_32,negated_conjecture,
epred2_0 @ esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_27])]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i] :
( ~ ( epred1_0 @ esk1_0 @ X1 )
| ~ ( epred2_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
thf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL607^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.15 % Computer : n008.cluster.edu
% 0.07/0.15 % Model : x86_64 x86_64
% 0.07/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.15 % Memory : 8046.5625MB
% 0.07/0.15 % OS : Linux 6.8.0-71-generic
% 0.07/0.15 % CPULimit : 300
% 0.07/0.15 % WCLimit : 300
% 0.07/0.15 % DateTime : Tue Sep 29 09:19:39 UTC 2026
% 0.07/0.15 % CPUTime :
% 0.07/0.15 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 Running higher-order theorem proving
% 0.07/0.20 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.SYSxuQo1nZ/E---3.1_2902453.p
% 0.07/0.22 % Version: 3.5.1-ho
% 0.07/0.22 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.07/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.22 % Starting new_ho_9 with 1500s (5) cores
% 0.07/0.22 % Starting post_as_ho1 with 300s (1) cores
% 0.07/0.22 % Starting sh1l with 300s (1) cores
% 0.07/0.22 % Starting post_as_ho10 with 300s (1) cores
% 0.07/0.22 % post_as_ho1 with pid 2902467 completed with status 0
% 0.07/0.22 % Result found by post_as_ho1
% 0.07/0.22 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.07/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.22 % Starting new_ho_9 with 1500s (5) cores
% 0.07/0.22 % Starting post_as_ho1 with 300s (1) cores
% 0.07/0.22 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.22 % No SInE strategy applied
% 0.07/0.22 % Search class: HGHNF-FFSS00-SHSSMFNN
% 0.07/0.22 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.22 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.22 % SubtermCWHack with pid 2902471 completed with status 0
% 0.07/0.22 % Result found by SubtermCWHack
% 0.07/0.22 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.07/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.22 % Starting new_ho_9 with 1500s (5) cores
% 0.07/0.22 % Starting post_as_ho1 with 300s (1) cores
% 0.07/0.22 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.22 % No SInE strategy applied
% 0.07/0.22 % Search class: HGHNF-FFSS00-SHSSMFNN
% 0.07/0.22 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.22 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.22 % Preprocessing time : 0.001 s
% 0.07/0.22
% 0.07/0.22 % Proof found!
% 0.07/0.22 % SZS status Theorem
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22 % Parsed axioms : 36
% 0.07/0.22 % Removed by relevancy pruning/SinE : 0
% 0.07/0.22 % Initial clauses : 29
% 0.07/0.22 % Removed in clause preprocessing : 20
% 0.07/0.22 % Initial clauses in saturation : 9
% 0.07/0.22 % Processed clauses : 15
% 0.07/0.22 % ...of these trivial : 0
% 0.07/0.22 % ...subsumed : 1
% 0.07/0.22 % ...remaining for further processing : 14
% 0.07/0.22 % Other redundant clauses eliminated : 0
% 0.07/0.22 % Clauses deleted for lack of memory : 0
% 0.07/0.22 % Backward-subsumed : 2
% 0.07/0.22 % Backward-rewritten : 7
% 0.07/0.22 % Generated clauses : 12
% 0.07/0.22 % ...of the previous two non-redundant : 8
% 0.07/0.22 % ...aggressively subsumed : 0
% 0.07/0.22 % Contextual simplify-reflections : 1
% 0.07/0.22 % Paramodulations : 12
% 0.07/0.22 % Factorizations : 0
% 0.07/0.22 % NegExts : 0
% 0.07/0.22 % Equation resolutions : 0
% 0.07/0.22 % Disequality decompositions : 0
% 0.07/0.22 % Total rewrite steps : 15
% 0.07/0.22 % ...of those cached : 11
% 0.07/0.22 % Propositional unsat checks : 0
% 0.07/0.22 % Propositional check models : 0
% 0.07/0.22 % Propositional check unsatisfiable : 0
% 0.07/0.22 % Propositional clauses : 0
% 0.07/0.22 % Propositional clauses after purity: 0
% 0.07/0.22 % Propositional unsat core size : 0
% 0.07/0.22 % Propositional preprocessing time : 0.000
% 0.07/0.22 % Propositional encoding time : 0.000
% 0.07/0.22 % Propositional solver time : 0.000
% 0.07/0.22 % Success case prop preproc time : 0.000
% 0.07/0.22 % Success case prop encoding time : 0.000
% 0.07/0.22 % Success case prop solver time : 0.000
% 0.07/0.22 % Current number of processed clauses : 5
% 0.07/0.22 % Positive orientable unit clauses : 4
% 0.07/0.22 % Positive unorientable unit clauses: 0
% 0.07/0.22 % Negative unit clauses : 0
% 0.07/0.22 % Non-unit-clauses : 1
% 0.07/0.22 % Current number of unprocessed clauses: 1
% 0.07/0.22 % ...number of literals in the above : 2
% 0.07/0.22 % Current number of archived formulas : 0
% 0.07/0.22 % Current number of archived clauses : 9
% 0.07/0.22 % Clause-clause subsumption calls (NU) : 5
% 0.07/0.22 % Rec. Clause-clause subsumption calls : 5
% 0.07/0.22 % Non-unit clause-clause subsumptions : 3
% 0.07/0.22 % Unit Clause-clause subsumption calls : 2
% 0.07/0.22 % Rewrite failures with RHS unbound : 0
% 0.07/0.22 % BW rewrite match attempts : 4
% 0.07/0.22 % BW rewrite match successes : 4
% 0.07/0.22 % Condensation attempts : 0
% 0.07/0.22 % Condensation successes : 0
% 0.07/0.22 % Termbank termtop insertions : 1526
% 0.07/0.22 % Search garbage collected termcells : 304
% 0.07/0.22
% 0.07/0.22 % -------------------------------------------------
% 0.07/0.22 % User time : 0.004 s
% 0.07/0.22 % System time : 0.001 s
% 0.07/0.22 % Total time : 0.005 s
% 0.07/0.22 % Maximum resident set size: 3668 pages
% 0.07/0.22
% 0.07/0.22 % -------------------------------------------------
% 0.07/0.22 % User time : 0.006 s
% 0.07/0.22 % System time : 0.005 s
% 0.07/0.22 % Total time : 0.011 s
% 0.07/0.22 % Maximum resident set size: 4608 pages
% 0.07/0.22 % E exiting
%------------------------------------------------------------------------------