%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL623^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 0.22s 0.29s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 11 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 266 ( 32 ~; 39 |; 5 &; 182 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 66 ( 26 ^; 40 !; 0 ?; 66 :)
% 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_38,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_42,type,
r: $i > $i > $o ).
thf(decl_43,type,
esk1_2: ( $i > $o ) > $i > $i ).
thf(decl_44,type,
epred1_0: $i > $o ).
thf(decl_45,type,
esk2_0: $i ).
thf(decl_46,type,
esk3_1: $i > $i ).
thf(decl_47,type,
esk4_0: $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Q4NaAHnpKl/E---3.1_107394.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Q4NaAHnpKl/E---3.1_107394.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Q4NaAHnpKl/E---3.1_107394.p',mor) ).
thf(mbox,axiom,
( mbox
= ( ^ [X10: $i > $i > $o,X11: $i > $o,X1: $i] :
! [X12: $i] :
( ( X10 @ X1 @ X12 )
=> ( X11 @ X12 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Q4NaAHnpKl/E---3.1_107394.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Q4NaAHnpKl/E---3.1_107394.p',mvalid) ).
thf(loeb,conjecture,
! [X11: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ X11 ) @ X11 ) ) @ ( mbox @ r @ X11 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Q4NaAHnpKl/E---3.1_107394.p',loeb) ).
thf(gl,axiom,
! [X19: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ X19 ) @ X19 ) ) @ ( mbox @ r @ X19 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Q4NaAHnpKl/E---3.1_107394.p',gl) ).
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,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_11,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_12,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_13,negated_conjecture,
~ ! [X11: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ X11 ) @ X11 ) ) @ ( mbox @ r @ X11 ) ) ),
inference(assume_negation,[status(cth)],[loeb]) ).
thf(c_0_14,plain,
! [X19: $i > $o,X25: $i] :
( ~ ! [X23: $i] :
( ( r @ X25 @ X23 )
=> ( ~ ! [X22: $i] :
( ( r @ X23 @ X22 )
=> ( X19 @ X22 ) )
| ( X19 @ X23 ) ) )
| ! [X24: $i] :
( ( r @ X25 @ X24 )
=> ( X19 @ X24 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[gl,c_0_10]),c_0_11]),c_0_12]) ).
thf(c_0_15,negated_conjecture,
~ ! [X11: $i > $o,X29: $i] :
( ~ ! [X27: $i] :
( ( r @ X29 @ X27 )
=> ( ~ ! [X26: $i] :
( ( r @ X27 @ X26 )
=> ( X11 @ X26 ) )
| ( X11 @ X27 ) ) )
| ! [X28: $i] :
( ( r @ X29 @ X28 )
=> ( X11 @ X28 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_10]),c_0_11]),c_0_12]) ).
thf(c_0_16,plain,
! [X30: $i > $o,X31: $i,X33: $i,X34: $i] :
( ( ( r @ X31 @ ( esk1_2 @ X30 @ X31 ) )
| ~ ( r @ X31 @ X34 )
| ( X30 @ X34 ) )
& ( ~ ( r @ ( esk1_2 @ X30 @ X31 ) @ X33 )
| ( X30 @ X33 )
| ~ ( r @ X31 @ X34 )
| ( X30 @ X34 ) )
& ( ~ ( X30 @ ( esk1_2 @ X30 @ X31 ) )
| ~ ( r @ X31 @ X34 )
| ( X30 @ X34 ) ) ),
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_14])])])])])]) ).
thf(c_0_17,negated_conjecture,
! [X37: $i] :
( ( ( r @ X37 @ ( esk3_1 @ X37 ) )
| ( epred1_0 @ X37 )
| ~ ( r @ esk2_0 @ X37 ) )
& ( ~ ( epred1_0 @ ( esk3_1 @ X37 ) )
| ( epred1_0 @ X37 )
| ~ ( r @ esk2_0 @ X37 ) )
& ( r @ esk2_0 @ esk4_0 )
& ~ ( epred1_0 @ esk4_0 ) ),
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_15])])])])])]) ).
thf(c_0_18,plain,
! [X1: $i,X3: $i,X2: $i > $o,X12: $i] :
( ( X2 @ X3 )
| ( X2 @ X12 )
| ~ ( r @ ( esk1_2 @ X2 @ X1 ) @ X3 )
| ~ ( r @ X1 @ X12 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i] :
( ( r @ X1 @ ( esk3_1 @ X1 ) )
| ( epred1_0 @ X1 )
| ~ ( r @ esk2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,plain,
! [X1: $i,X2: $i > $o,X3: $i] :
( ( r @ X1 @ ( esk1_2 @ X2 @ X1 ) )
| ( X2 @ X3 )
| ~ ( r @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_21,negated_conjecture,
r @ esk2_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i,X2: $i > $o,X3: $i] :
( ( X2 @ ( esk3_1 @ ( esk1_2 @ X2 @ X1 ) ) )
| ( epred1_0 @ ( esk1_2 @ X2 @ X1 ) )
| ( X2 @ X3 )
| ~ ( r @ esk2_0 @ ( esk1_2 @ X2 @ X1 ) )
| ~ ( r @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_23,negated_conjecture,
! [X2: $i > $o] :
( ( r @ esk2_0 @ ( esk1_2 @ X2 @ esk2_0 ) )
| ( X2 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ X1 )
| ~ ( epred1_0 @ ( esk3_1 @ X1 ) )
| ~ ( r @ esk2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_25,negated_conjecture,
! [X2: $i > $o] :
( ( X2 @ ( esk3_1 @ ( esk1_2 @ X2 @ esk2_0 ) ) )
| ( epred1_0 @ ( esk1_2 @ X2 @ esk2_0 ) )
| ( X2 @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_21]),c_0_23]) ).
thf(c_0_26,negated_conjecture,
~ ( epred1_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_27,negated_conjecture,
( ( epred1_0 @ ( esk1_2 @ epred1_0 @ esk2_0 ) )
| ~ ( r @ esk2_0 @ ( esk1_2 @ epred1_0 @ esk2_0 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
thf(c_0_28,plain,
! [X1: $i,X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
| ~ ( X2 @ ( esk1_2 @ X2 @ X1 ) )
| ~ ( r @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_29,negated_conjecture,
epred1_0 @ ( esk1_2 @ epred1_0 @ esk2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_23]),c_0_26]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ X1 )
| ~ ( r @ esk2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_21]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL623^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n017.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 09:23:51 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.Q4NaAHnpKl/E---3.1_107394.p
% 0.22/0.29 % Version: 3.5.1-ho
% 0.22/0.29 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.22/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29 % Starting new_ho_9 with 1500s (5) cores
% 0.22/0.29 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.29 % Starting sh1l with 300s (1) cores
% 0.22/0.29 % Starting post_as_ho10 with 300s (1) cores
% 0.22/0.29 % post_as_ho1 with pid 107408 completed with status 0
% 0.22/0.29 % Result found by post_as_ho1
% 0.22/0.29 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.22/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29 % Starting new_ho_9 with 1500s (5) cores
% 0.22/0.29 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.29 % No SInE strategy applied
% 0.22/0.29 % Search class: HGUNF-FFSF21-SHSSMSBN
% 0.22/0.29 % partial match(2): HGHNF-FFMF21-SHSSMSBN
% 0.22/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.29 % SubtermCWHack with pid 107412 completed with status 0
% 0.22/0.29 % Result found by SubtermCWHack
% 0.22/0.29 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.22/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29 % Starting new_ho_9 with 1500s (5) cores
% 0.22/0.29 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.29 % No SInE strategy applied
% 0.22/0.29 % Search class: HGUNF-FFSF21-SHSSMSBN
% 0.22/0.29 % partial match(2): HGHNF-FFMF21-SHSSMSBN
% 0.22/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.29 % Preprocessing time : 0.002 s
% 0.22/0.29
% 0.22/0.29 % Proof found!
% 0.22/0.29 % SZS status Theorem
% 0.22/0.29 % SZS output start CNFRefutation
% See solution above
% 0.22/0.29 % Parsed axioms : 38
% 0.22/0.29 % Removed by relevancy pruning/SinE : 0
% 0.22/0.29 % Initial clauses : 28
% 0.22/0.29 % Removed in clause preprocessing : 21
% 0.22/0.29 % Initial clauses in saturation : 7
% 0.22/0.29 % Processed clauses : 51
% 0.22/0.29 % ...of these trivial : 0
% 0.22/0.29 % ...subsumed : 23
% 0.22/0.29 % ...remaining for further processing : 28
% 0.22/0.29 % Other redundant clauses eliminated : 0
% 0.22/0.29 % Clauses deleted for lack of memory : 0
% 0.22/0.29 % Backward-subsumed : 8
% 0.22/0.29 % Backward-rewritten : 1
% 0.22/0.29 % Generated clauses : 219
% 0.22/0.29 % ...of the previous two non-redundant : 195
% 0.22/0.29 % ...aggressively subsumed : 0
% 0.22/0.29 % Contextual simplify-reflections : 1
% 0.22/0.29 % Paramodulations : 193
% 0.22/0.29 % Factorizations : 26
% 0.22/0.29 % NegExts : 0
% 0.22/0.29 % Equation resolutions : 0
% 0.22/0.29 % Disequality decompositions : 0
% 0.22/0.29 % Total rewrite steps : 11
% 0.22/0.29 % ...of those cached : 9
% 0.22/0.29 % Propositional unsat checks : 0
% 0.22/0.29 % Propositional check models : 0
% 0.22/0.29 % Propositional check unsatisfiable : 0
% 0.22/0.29 % Propositional clauses : 0
% 0.22/0.29 % Propositional clauses after purity: 0
% 0.22/0.29 % Propositional unsat core size : 0
% 0.22/0.29 % Propositional preprocessing time : 0.000
% 0.22/0.29 % Propositional encoding time : 0.000
% 0.22/0.29 % Propositional solver time : 0.000
% 0.22/0.29 % Success case prop preproc time : 0.000
% 0.22/0.29 % Success case prop encoding time : 0.000
% 0.22/0.29 % Success case prop solver time : 0.000
% 0.22/0.29 % Current number of processed clauses : 19
% 0.22/0.29 % Positive orientable unit clauses : 2
% 0.22/0.29 % Positive unorientable unit clauses: 0
% 0.22/0.29 % Negative unit clauses : 1
% 0.22/0.29 % Non-unit-clauses : 16
% 0.22/0.29 % Current number of unprocessed clauses: 141
% 0.22/0.29 % ...number of literals in the above : 855
% 0.22/0.29 % Current number of archived formulas : 0
% 0.22/0.29 % Current number of archived clauses : 9
% 0.22/0.29 % Clause-clause subsumption calls (NU) : 153
% 0.22/0.29 % Rec. Clause-clause subsumption calls : 107
% 0.22/0.29 % Non-unit clause-clause subsumptions : 32
% 0.22/0.29 % Unit Clause-clause subsumption calls : 0
% 0.22/0.29 % Rewrite failures with RHS unbound : 0
% 0.22/0.29 % BW rewrite match attempts : 1
% 0.22/0.29 % BW rewrite match successes : 1
% 0.22/0.29 % Condensation attempts : 0
% 0.22/0.29 % Condensation successes : 0
% 0.22/0.29 % Termbank termtop insertions : 6815
% 0.22/0.29 % Search garbage collected termcells : 482
% 0.22/0.29
% 0.22/0.29 % -------------------------------------------------
% 0.22/0.29 % User time : 0.018 s
% 0.22/0.29 % System time : 0.004 s
% 0.22/0.29 % Total time : 0.023 s
% 0.22/0.29 % Maximum resident set size: 3668 pages
% 0.22/0.29
% 0.22/0.29 % -------------------------------------------------
% 0.22/0.29 % User time : 0.020 s
% 0.22/0.29 % System time : 0.009 s
% 0.22/0.29 % Total time : 0.030 s
% 0.22/0.29 % Maximum resident set size: 4864 pages
% 0.22/0.29 % E exiting
%------------------------------------------------------------------------------