%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PLA053^5 : 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 08:20:23 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 101 ( 12 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 208 ( 20 ~; 16 |; 8 &; 154 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 69 ( 32 ^; 33 !; 4 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mworld: $tType ).
thf(decl_23,type,
mrel: mworld > mworld > $o ).
thf(decl_24,type,
mactual: mworld ).
thf(decl_25,type,
mlocal: ( mworld > $o ) > $o ).
thf(decl_27,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_29,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_31,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(decl_33,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_34,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_35,type,
h: $i > mworld > $o ).
thf(decl_36,type,
bomb: $i > mworld > $o ).
thf(decl_37,type,
defused: $i > mworld > $o ).
thf(decl_40,type,
esk3_2: mworld > $i > $i ).
thf(decl_41,type,
esk4_0: mworld ).
thf(decl_42,type,
esk5_0: $i ).
thf(con,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X8: $i] :
( mexists_di
@ ^ [X12: $i] : ( mimplies @ ( mand @ ( bomb @ X8 ) @ ( h @ X12 ) ) @ ( defused @ X8 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VNxe4QXRhi/E---3.1_3966624.p',con) ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VNxe4QXRhi/E---3.1_3966624.p',mlocal_def) ).
thf(mand_def,axiom,
( mand
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
& ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VNxe4QXRhi/E---3.1_3966624.p',mand_def) ).
thf(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VNxe4QXRhi/E---3.1_3966624.p',mimplies_def) ).
thf(mbox_def,axiom,
( mbox
= ( ^ [X1: mworld > $o,X3: mworld] :
! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VNxe4QXRhi/E---3.1_3966624.p',mbox_def) ).
thf(mforall_di_def,axiom,
( mforall_di
= ( ^ [X7: $i > mworld > $o,X3: mworld] :
! [X8: $i] : ( X7 @ X8 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VNxe4QXRhi/E---3.1_3966624.p',mforall_di_def) ).
thf(mexists_di_def,axiom,
( mexists_di
= ( ^ [X9: $i > mworld > $o,X3: mworld] :
? [X8: $i] : ( X9 @ X8 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VNxe4QXRhi/E---3.1_3966624.p',mexists_di_def) ).
thf(ax3,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X8: $i] :
( mexists_di
@ ^ [X12: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X8 ) @ ( h @ X12 ) ) @ ( defused @ X8 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VNxe4QXRhi/E---3.1_3966624.p',ax3) ).
thf(mrel_euclidean,axiom,
! [X3: mworld,X5: mworld,X6: mworld] :
( ( ( mrel @ X3 @ X6 )
& ( mrel @ X3 @ X5 ) )
=> ( mrel @ X6 @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VNxe4QXRhi/E---3.1_3966624.p',mrel_euclidean) ).
thf(mrel_reflexive,axiom,
! [X3: mworld] : ( mrel @ X3 @ X3 ),
file('/export/starexec/sandbox2/tmp/tmp.VNxe4QXRhi/E---3.1_3966624.p',mrel_reflexive) ).
thf(c_0_10,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X8: $i] :
( mexists_di
@ ^ [X12: $i] : ( mimplies @ ( mand @ ( bomb @ X8 ) @ ( h @ X12 ) ) @ ( defused @ X8 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_11,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_12,plain,
( mand
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand_def]) ).
thf(c_0_13,plain,
( mimplies
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies_def]) ).
thf(c_0_14,plain,
( mbox
= ( ^ [Z0: mworld > $o,Z1: mworld] :
! [X5: mworld] :
( ( mrel @ Z1 @ X5 )
=> ( Z0 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_def]) ).
thf(c_0_15,plain,
( mforall_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
! [X8: $i] : ( Z0 @ X8 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_di_def]) ).
thf(c_0_16,plain,
( mexists_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
? [X8: $i] : ( Z0 @ X8 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mexists_di_def]) ).
thf(c_0_17,negated_conjecture,
~ ! [X29: mworld] :
( ( mrel @ mactual @ X29 )
=> ! [X28: $i] :
? [X27: $i] :
( ( ( bomb @ X28 @ X29 )
& ( h @ X27 @ X29 ) )
=> ( defused @ X28 @ X29 ) ) ),
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)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_10]),c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16]) ).
thf(c_0_18,plain,
! [X26: mworld] :
( ( mrel @ mactual @ X26 )
=> ! [X25: $i] :
? [X24: $i] :
! [X23: mworld] :
( ( mrel @ X26 @ X23 )
=> ( ( ( bomb @ X25 @ X23 )
& ( h @ X24 @ X23 ) )
=> ( defused @ X25 @ X23 ) ) ) ),
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)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[ax3]),c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16]) ).
thf(c_0_19,plain,
! [X31: mworld,X32: mworld,X33: mworld] :
( ~ ( mrel @ X31 @ X33 )
| ~ ( mrel @ X31 @ X32 )
| ( mrel @ X33 @ X32 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mrel_euclidean])])]) ).
thf(c_0_20,negated_conjecture,
! [X46: $i] :
( ( mrel @ mactual @ esk4_0 )
& ( bomb @ esk5_0 @ esk4_0 )
& ( h @ X46 @ esk4_0 )
& ~ ( defused @ esk5_0 @ esk4_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_17])])])])]) ).
thf(c_0_21,plain,
! [X40: mworld,X41: $i,X43: mworld] :
( ~ ( mrel @ mactual @ X40 )
| ~ ( mrel @ X40 @ X43 )
| ~ ( bomb @ X41 @ X43 )
| ~ ( h @ ( esk3_2 @ X40 @ X41 ) @ X43 )
| ( defused @ X41 @ X43 ) ),
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_18])])])])]) ).
thf(c_0_22,plain,
! [X3: mworld,X5: mworld,X6: mworld] :
( ( mrel @ X5 @ X6 )
| ~ ( mrel @ X3 @ X5 )
| ~ ( mrel @ X3 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_23,negated_conjecture,
mrel @ mactual @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,plain,
! [X8: $i,X3: mworld,X5: mworld] :
( ( defused @ X8 @ X5 )
| ~ ( mrel @ mactual @ X3 )
| ~ ( mrel @ X3 @ X5 )
| ~ ( bomb @ X8 @ X5 )
| ~ ( h @ ( esk3_2 @ X3 @ X8 ) @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,negated_conjecture,
! [X8: $i] : ( h @ X8 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,negated_conjecture,
! [X3: mworld] :
( ( mrel @ X3 @ esk4_0 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_27,plain,
! [X30: mworld] : ( mrel @ X30 @ X30 ),
inference(variable_rename,[status(thm)],[mrel_reflexive]) ).
thf(c_0_28,negated_conjecture,
! [X3: mworld,X8: $i] :
( ( defused @ X8 @ esk4_0 )
| ~ ( mrel @ mactual @ X3 )
| ~ ( bomb @ X8 @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
thf(c_0_29,plain,
! [X3: mworld] : ( mrel @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_30,negated_conjecture,
~ ( defused @ esk5_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_31,negated_conjecture,
! [X8: $i] :
( ( defused @ X8 @ esk4_0 )
| ~ ( bomb @ X8 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_32,negated_conjecture,
bomb @ esk5_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PLA053^5 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n009.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 13:21:00 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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.VNxe4QXRhi/E---3.1_3966624.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.07/0.25 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.07/0.25 % Starting almost_fo_3_lam with 300s (1) cores
% 0.07/0.25 % Starting post_as_ho1 with 300s (1) cores
% 0.07/0.25 % ehoh_best2_full_lfho with pid 3966638 completed with status 0
% 0.07/0.25 % Result found by ehoh_best2_full_lfho
% 0.07/0.25 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.07/0.25 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HHUNS-FFSF21-SHSSMFNN
% 0.07/0.25 % partial match(2): HHHNS-FFSF11-SHSSMFNN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 3966641 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.07/0.25 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HHUNS-FFSF21-SHSSMFNN
% 0.07/0.25 % partial match(2): HHHNS-FFSF11-SHSSMFNN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 32
% 0.07/0.25 % Removed by relevancy pruning/SinE : 0
% 0.07/0.25 % Initial clauses : 25
% 0.07/0.25 % Removed in clause preprocessing : 16
% 0.07/0.25 % Initial clauses in saturation : 9
% 0.07/0.25 % Processed clauses : 20
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 2
% 0.07/0.25 % ...remaining for further processing : 18
% 0.07/0.25 % Other redundant clauses eliminated : 0
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 1
% 0.07/0.25 % Backward-rewritten : 0
% 0.07/0.25 % Generated clauses : 19
% 0.07/0.25 % ...of the previous two non-redundant : 12
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 1
% 0.07/0.25 % Paramodulations : 19
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 0
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 11
% 0.07/0.26 % ...of those cached : 5
% 0.07/0.26 % Propositional unsat checks : 0
% 0.07/0.26 % Propositional check models : 0
% 0.07/0.26 % Propositional check unsatisfiable : 0
% 0.07/0.26 % Propositional clauses : 0
% 0.07/0.26 % Propositional clauses after purity: 0
% 0.07/0.26 % Propositional unsat core size : 0
% 0.07/0.26 % Propositional preprocessing time : 0.000
% 0.07/0.26 % Propositional encoding time : 0.000
% 0.07/0.26 % Propositional solver time : 0.000
% 0.07/0.26 % Success case prop preproc time : 0.000
% 0.07/0.26 % Success case prop encoding time : 0.000
% 0.07/0.26 % Success case prop solver time : 0.000
% 0.07/0.26 % Current number of processed clauses : 17
% 0.07/0.26 % Positive orientable unit clauses : 5
% 0.07/0.26 % Positive unorientable unit clauses: 0
% 0.07/0.26 % Negative unit clauses : 1
% 0.07/0.26 % Non-unit-clauses : 11
% 0.07/0.26 % Current number of unprocessed clauses: 1
% 0.07/0.26 % ...number of literals in the above : 2
% 0.07/0.26 % Current number of archived formulas : 0
% 0.07/0.26 % Current number of archived clauses : 1
% 0.07/0.26 % Clause-clause subsumption calls (NU) : 21
% 0.07/0.26 % Rec. Clause-clause subsumption calls : 19
% 0.07/0.26 % Non-unit clause-clause subsumptions : 4
% 0.07/0.26 % Unit Clause-clause subsumption calls : 0
% 0.07/0.26 % Rewrite failures with RHS unbound : 0
% 0.07/0.26 % BW rewrite match attempts : 1
% 0.07/0.26 % BW rewrite match successes : 0
% 0.07/0.26 % Condensation attempts : 0
% 0.07/0.26 % Condensation successes : 0
% 0.07/0.26 % Termbank termtop insertions : 2119
% 0.07/0.26 % Search garbage collected termcells : 656
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.004 s
% 0.07/0.26 % System time : 0.002 s
% 0.07/0.26 % Total time : 0.007 s
% 0.07/0.26 % Maximum resident set size: 3660 pages
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.004 s
% 0.07/0.26 % System time : 0.009 s
% 0.07/0.26 % Total time : 0.014 s
% 0.07/0.26 % Maximum resident set size: 4864 pages
% 0.07/0.26 % E exiting
%------------------------------------------------------------------------------