%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL962^16 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:12:54 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 101 ( 8 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 240 ( 33 ~; 25 |; 2 &; 168 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 44 ( 18 ^; 26 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mindex: $tType ).
thf(decl_sort2,type,
mworld: $tType ).
thf(decl_23,type,
mrel: mindex > mworld > mworld > $o ).
thf(decl_24,type,
'#b': mindex ).
thf(decl_25,type,
'#a': mindex ).
thf(decl_26,type,
mactual: mworld ).
thf(decl_27,type,
mlocal: ( mworld > $o ) > $o ).
thf(decl_28,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(decl_31,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_33,type,
mbox: mindex > ( mworld > $o ) > mworld > $o ).
thf(decl_35,type,
p: mworld > $o ).
thf(decl_36,type,
esk1_1: mworld > mworld ).
thf(decl_37,type,
esk2_0: mworld ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.k4UeMqV5wa/E---3.1_3860000.p',mlocal_def) ).
thf(mnot_def,axiom,
( mnot
= ( ^ [X2: mworld > $o,X3: mworld] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.k4UeMqV5wa/E---3.1_3860000.p',mnot_def) ).
thf(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.k4UeMqV5wa/E---3.1_3860000.p',mimplies_def) ).
thf(mbox_def,axiom,
( mbox
= ( ^ [X5: mindex,X1: mworld > $o,X3: mworld] :
! [X6: mworld] :
( ( mrel @ X5 @ X3 @ X6 )
=> ( X1 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.k4UeMqV5wa/E---3.1_3860000.p',mbox_def) ).
thf(ab_axiom_2,axiom,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.k4UeMqV5wa/E---3.1_3860000.p',ab_axiom_2) ).
thf(not_a_axiom_1,axiom,
mlocal @ ( mnot @ p ),
file('/export/starexec/sandbox2/tmp/tmp.k4UeMqV5wa/E---3.1_3860000.p',not_a_axiom_1) ).
thf(ab_axiom_1,axiom,
mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.k4UeMqV5wa/E---3.1_3860000.p',ab_axiom_1) ).
thf('mrel_#b_reflexive',axiom,
! [X3: mworld] : ( mrel @ '#b' @ X3 @ X3 ),
file('/export/starexec/sandbox2/tmp/tmp.k4UeMqV5wa/E---3.1_3860000.p','mrel_#b_reflexive') ).
thf(conj,conjecture,
mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ),
file('/export/starexec/sandbox2/tmp/tmp.k4UeMqV5wa/E---3.1_3860000.p',conj) ).
thf(c_0_9,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_10,plain,
( mnot
= ( ^ [Z0: mworld > $o,Z1: mworld] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot_def]) ).
thf(c_0_11,plain,
( mimplies
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies_def]) ).
thf(c_0_12,plain,
( mbox
= ( ^ [Z0: mindex,Z1: mworld > $o,Z2: mworld] :
! [X6: mworld] :
( ( mrel @ Z0 @ Z2 @ X6 )
=> ( Z1 @ X6 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_def]) ).
thf(c_0_13,plain,
( ~ ! [X18: mworld] :
( ( mrel @ '#b' @ mactual @ X18 )
=> ( p @ X18 ) )
=> ! [X20: mworld] :
( ( mrel @ '#a' @ mactual @ X20 )
=> ~ ! [X19: mworld] :
( ( mrel @ '#b' @ X20 @ X19 )
=> ( p @ X19 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[ab_axiom_2,c_0_9]),c_0_10]),c_0_11]),c_0_12]) ).
thf(c_0_14,plain,
~ ( p @ mactual ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[not_a_axiom_1,c_0_9]),c_0_10])]) ).
thf(c_0_15,plain,
! [X17: mworld] :
( ( mrel @ '#a' @ mactual @ X17 )
=> ( ( p @ X17 )
=> ! [X16: mworld] :
( ( mrel @ '#b' @ X17 @ X16 )
=> ( p @ X16 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[ab_axiom_1,c_0_9]),c_0_11]),c_0_12]) ).
thf(c_0_16,plain,
! [X32: mworld,X33: mworld] :
( ( ( mrel @ '#b' @ X33 @ ( esk1_1 @ X33 ) )
| ~ ( mrel @ '#a' @ mactual @ X33 )
| ~ ( mrel @ '#b' @ mactual @ X32 )
| ( p @ X32 ) )
& ( ~ ( p @ ( esk1_1 @ X33 ) )
| ~ ( mrel @ '#a' @ mactual @ X33 )
| ~ ( mrel @ '#b' @ mactual @ X32 )
| ( p @ X32 ) ) ),
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_13])])])])])]) ).
thf(c_0_17,plain,
! [X22: mworld] : ( mrel @ '#b' @ X22 @ X22 ),
inference(variable_rename,[status(thm)],['mrel_#b_reflexive']) ).
thf(c_0_18,plain,
~ ( p @ mactual ),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
thf(c_0_19,plain,
! [X30: mworld,X31: mworld] :
( ~ ( mrel @ '#a' @ mactual @ X30 )
| ~ ( p @ X30 )
| ~ ( mrel @ '#b' @ X30 @ X31 )
| ( p @ X31 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
thf(c_0_20,plain,
! [X3: mworld,X6: mworld] :
( ( mrel @ '#b' @ X3 @ ( esk1_1 @ X3 ) )
| ( p @ X6 )
| ~ ( mrel @ '#a' @ mactual @ X3 )
| ~ ( mrel @ '#b' @ mactual @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_21,plain,
! [X3: mworld] : ( mrel @ '#b' @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,plain,
~ ( p @ mactual ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_23,negated_conjecture,
~ ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_24,plain,
! [X3: mworld,X6: mworld] :
( ( p @ X6 )
| ~ ( mrel @ '#a' @ mactual @ X3 )
| ~ ( p @ X3 )
| ~ ( mrel @ '#b' @ X3 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_25,plain,
! [X3: mworld] :
( ( mrel @ '#b' @ X3 @ ( esk1_1 @ X3 ) )
| ~ ( mrel @ '#a' @ mactual @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
thf(c_0_26,negated_conjecture,
~ ! [X21: mworld] :
( ( mrel @ '#a' @ mactual @ X21 )
=> ~ ( p @ X21 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_23,c_0_9]),c_0_10]),c_0_12])]) ).
thf(c_0_27,plain,
! [X3: mworld,X6: mworld] :
( ( p @ X6 )
| ~ ( p @ ( esk1_1 @ X3 ) )
| ~ ( mrel @ '#a' @ mactual @ X3 )
| ~ ( mrel @ '#b' @ mactual @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_28,plain,
! [X3: mworld] :
( ( p @ ( esk1_1 @ X3 ) )
| ~ ( mrel @ '#a' @ mactual @ X3 )
| ~ ( p @ X3 ) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_29,negated_conjecture,
( ( mrel @ '#a' @ mactual @ esk2_0 )
& ( p @ esk2_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
thf(c_0_30,plain,
! [X3: mworld,X6: mworld] :
( ( p @ X3 )
| ~ ( mrel @ '#b' @ mactual @ X3 )
| ~ ( mrel @ '#a' @ mactual @ X6 )
| ~ ( p @ X6 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_31,negated_conjecture,
p @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_32,negated_conjecture,
mrel @ '#a' @ mactual @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_33,negated_conjecture,
! [X3: mworld] :
( ( p @ X3 )
| ~ ( mrel @ '#b' @ mactual @ X3 ) ),
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_22,c_0_33]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL962^16 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n009.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 11:01:00 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.22 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.k4UeMqV5wa/E---3.1_3860000.p
% 0.09/0.25 % Version: 3.5.1-ho
% 0.09/0.25 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.25 % Starting post_as_ho11 with 300s (1) cores
% 0.09/0.25 % Starting full_lambda_8 with 300s (1) cores
% 0.09/0.25 % post_as_ho11 with pid 3860029 completed with status 0
% 0.09/0.25 % Result found by post_as_ho11
% 0.09/0.25 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.25 % Starting post_as_ho11 with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.25 % No SInE strategy applied
% 0.09/0.25 % Search class: HGUNS-FFSF11-SHSSMFNN
% 0.09/0.25 % partial match(1): HGUNF-FFSF11-SHSSMFNN
% 0.09/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.25 % SubtermCWHack with pid 3860034 completed with status 0
% 0.09/0.25 % Result found by SubtermCWHack
% 0.09/0.25 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.25 % Starting post_as_ho11 with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.25 % No SInE strategy applied
% 0.09/0.25 % Search class: HGUNS-FFSF11-SHSSMFNN
% 0.09/0.25 % partial match(1): HGUNF-FFSF11-SHSSMFNN
% 0.09/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.25 % Preprocessing time : 0.001 s
% 0.09/0.25
% 0.09/0.25 % Proof found!
% 0.09/0.25 % SZS status Theorem
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25 % Parsed axioms : 31
% 0.09/0.25 % Removed by relevancy pruning/SinE : 0
% 0.09/0.25 % Initial clauses : 25
% 0.09/0.25 % Removed in clause preprocessing : 15
% 0.09/0.25 % Initial clauses in saturation : 10
% 0.09/0.25 % Processed clauses : 17
% 0.09/0.25 % ...of these trivial : 0
% 0.09/0.25 % ...subsumed : 1
% 0.09/0.25 % ...remaining for further processing : 16
% 0.09/0.25 % Other redundant clauses eliminated : 0
% 0.09/0.25 % Clauses deleted for lack of memory : 0
% 0.09/0.25 % Backward-subsumed : 3
% 0.09/0.25 % Backward-rewritten : 0
% 0.09/0.25 % Generated clauses : 13
% 0.09/0.25 % ...of the previous two non-redundant : 9
% 0.09/0.25 % ...aggressively subsumed : 0
% 0.09/0.25 % Contextual simplify-reflections : 0
% 0.09/0.25 % Paramodulations : 13
% 0.09/0.25 % Factorizations : 0
% 0.09/0.25 % NegExts : 0
% 0.09/0.25 % Equation resolutions : 0
% 0.09/0.25 % Disequality decompositions : 0
% 0.09/0.25 % Total rewrite steps : 2
% 0.09/0.25 % ...of those cached : 0
% 0.09/0.25 % Propositional unsat checks : 0
% 0.09/0.25 % Propositional check models : 0
% 0.09/0.25 % Propositional check unsatisfiable : 0
% 0.09/0.25 % Propositional clauses : 0
% 0.09/0.25 % Propositional clauses after purity: 0
% 0.09/0.25 % Propositional unsat core size : 0
% 0.09/0.25 % Propositional preprocessing time : 0.000
% 0.09/0.25 % Propositional encoding time : 0.000
% 0.09/0.25 % Propositional solver time : 0.000
% 0.09/0.25 % Success case prop preproc time : 0.000
% 0.09/0.25 % Success case prop encoding time : 0.000
% 0.09/0.25 % Success case prop solver time : 0.000
% 0.09/0.25 % Current number of processed clauses : 13
% 0.09/0.25 % Positive orientable unit clauses : 4
% 0.09/0.25 % Positive unorientable unit clauses: 0
% 0.09/0.25 % Negative unit clauses : 1
% 0.09/0.25 % Non-unit-clauses : 8
% 0.09/0.25 % Current number of unprocessed clauses: 2
% 0.09/0.25 % ...number of literals in the above : 8
% 0.09/0.25 % Current number of archived formulas : 0
% 0.09/0.25 % Current number of archived clauses : 3
% 0.09/0.25 % Clause-clause subsumption calls (NU) : 11
% 0.09/0.25 % Rec. Clause-clause subsumption calls : 10
% 0.09/0.25 % Non-unit clause-clause subsumptions : 4
% 0.09/0.25 % Unit Clause-clause subsumption calls : 0
% 0.09/0.25 % Rewrite failures with RHS unbound : 0
% 0.09/0.25 % BW rewrite match attempts : 1
% 0.09/0.25 % BW rewrite match successes : 0
% 0.09/0.25 % Condensation attempts : 0
% 0.09/0.25 % Condensation successes : 0
% 0.09/0.25 % Termbank termtop insertions : 1819
% 0.09/0.25 % Search garbage collected termcells : 376
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.004 s
% 0.09/0.25 % System time : 0.002 s
% 0.09/0.25 % Total time : 0.006 s
% 0.09/0.25 % Maximum resident set size: 3652 pages
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.007 s
% 0.09/0.25 % System time : 0.005 s
% 0.09/0.25 % Total time : 0.012 s
% 0.09/0.25 % Maximum resident set size: 4608 pages
% 0.09/0.25 % E exiting
%------------------------------------------------------------------------------