%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO570^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 08:43:25 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 13 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 190 ( 25 ~; 20 |; 5 &; 133 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 65 ( 36 ^; 29 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_37,type,
exists_in_world: mu > $i > $o ).
thf(decl_38,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_51,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_55,type,
rel_s4: $i > $i > $o ).
thf(decl_56,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_58,type,
r: mu > mu > $i > $o ).
thf(decl_60,type,
esk2_0: $i ).
thf(decl_61,type,
esk3_0: mu ).
thf(decl_62,type,
esk4_0: mu ).
thf(decl_63,type,
esk5_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hr7JbJb2D5/E---3.1_3455713.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hr7JbJb2D5/E---3.1_3455713.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hr7JbJb2D5/E---3.1_3455713.p',mor) ).
thf(con,conjecture,
( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X20: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X21: mu] : ( r @ X20 @ X21 ) ) ) )
@ ( mforall_ind
@ ^ [X22: mu] :
( mforall_ind
@ ^ [X23: mu] : ( mbox_s4 @ ( r @ X22 @ X23 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hr7JbJb2D5/E---3.1_3455713.p',con) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X11: mu > $i > $o,X3: $i] :
! [X12: mu] :
( ( exists_in_world @ X12 @ X3 )
=> ( X11 @ X12 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hr7JbJb2D5/E---3.1_3455713.p',mforall_ind) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hr7JbJb2D5/E---3.1_3455713.p',mvalid) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X4: $i > $o,X3: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ( X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hr7JbJb2D5/E---3.1_3455713.p',mbox_s4) ).
thf(cumulative_ax,axiom,
! [X19: mu,X7: $i,X3: $i] :
( ( ( exists_in_world @ X19 @ X7 )
& ( rel_s4 @ X7 @ X3 ) )
=> ( exists_in_world @ X19 @ X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.hr7JbJb2D5/E---3.1_3455713.p',cumulative_ax) ).
thf(c_0_8,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
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,
~ ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X20: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X21: mu] : ( r @ X20 @ X21 ) ) ) )
@ ( mforall_ind
@ ^ [X22: mu] :
( mforall_ind
@ ^ [X23: mu] : ( mbox_s4 @ ( r @ X22 @ X23 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_12,plain,
( mimplies
= ( ^ [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_13,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X12: mu] :
( ( exists_in_world @ X12 @ Z1 )
=> ( Z0 @ X12 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_14,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_15,plain,
( mbox_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ Z1 @ X7 )
| ( Z0 @ X7 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s4]) ).
thf(c_0_16,negated_conjecture,
~ ! [X43: $i] :
( ~ ! [X39: mu] :
( ( exists_in_world @ X39 @ X43 )
=> ! [X38: $i] :
( ~ ( rel_s4 @ X43 @ X38 )
| ! [X37: mu] :
( ( exists_in_world @ X37 @ X38 )
=> ( r @ X39 @ X37 @ X38 ) ) ) )
| ! [X42: mu] :
( ( exists_in_world @ X42 @ X43 )
=> ! [X41: mu] :
( ( exists_in_world @ X41 @ X43 )
=> ! [X40: $i] :
( ~ ( rel_s4 @ X43 @ X40 )
| ( r @ X42 @ X41 @ X40 ) ) ) ) ),
inference(fof_simplification,[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_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]) ).
thf(c_0_17,negated_conjecture,
! [X54: mu,X55: $i,X56: mu] :
( ( ~ ( exists_in_world @ X54 @ esk2_0 )
| ~ ( rel_s4 @ esk2_0 @ X55 )
| ~ ( exists_in_world @ X56 @ X55 )
| ( r @ X54 @ X56 @ X55 ) )
& ( exists_in_world @ esk3_0 @ esk2_0 )
& ( exists_in_world @ esk4_0 @ esk2_0 )
& ( rel_s4 @ esk2_0 @ esk5_0 )
& ~ ( r @ esk3_0 @ esk4_0 @ esk5_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_16])])])])]) ).
thf(c_0_18,plain,
! [X50: mu,X51: $i,X52: $i] :
( ~ ( exists_in_world @ X50 @ X51 )
| ~ ( rel_s4 @ X51 @ X52 )
| ( exists_in_world @ X50 @ X52 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cumulative_ax])])]) ).
thf(c_0_19,negated_conjecture,
~ ( r @ esk3_0 @ esk4_0 @ esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X12: mu,X10: mu,X3: $i] :
( ( r @ X10 @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ esk2_0 )
| ~ ( rel_s4 @ esk2_0 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_21,negated_conjecture,
exists_in_world @ esk3_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,negated_conjecture,
rel_s4 @ esk2_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,plain,
! [X3: $i,X10: mu,X7: $i] :
( ( exists_in_world @ X10 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,negated_conjecture,
~ ( exists_in_world @ esk4_0 @ esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).
thf(c_0_25,negated_conjecture,
! [X10: mu] :
( ( exists_in_world @ X10 @ esk5_0 )
| ~ ( exists_in_world @ X10 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
thf(c_0_26,negated_conjecture,
exists_in_world @ esk4_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO570^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:16:09 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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.hr7JbJb2D5/E---3.1_3455713.p
% 0.22/0.27 % Version: 3.5.1-ho
% 0.22/0.27 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.27 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.22/0.27 % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.27 % ehoh_best2_full_lfho with pid 3455745 completed with status 0
% 0.22/0.27 % Result found by ehoh_best2_full_lfho
% 0.22/0.27 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.27 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HHUNS-FFSS11-SHSSMFNN
% 0.22/0.27 % partial match(2): HHHNS-FFSF11-SHSSMFNN
% 0.22/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.27 % SubtermCWHack with pid 3455749 completed with status 0
% 0.22/0.27 % Result found by SubtermCWHack
% 0.22/0.27 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.27 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HHUNS-FFSS11-SHSSMFNN
% 0.22/0.27 % partial match(2): HHHNS-FFSF11-SHSSMFNN
% 0.22/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.27 % Preprocessing time : 0.001 s
% 0.22/0.27
% 0.22/0.27 % Proof found!
% 0.22/0.27 % SZS status Theorem
% 0.22/0.27 % SZS output start CNFRefutation
% See solution above
% 0.22/0.27 % Parsed axioms : 74
% 0.22/0.27 % Removed by relevancy pruning/SinE : 0
% 0.22/0.27 % Initial clauses : 46
% 0.22/0.27 % Removed in clause preprocessing : 37
% 0.22/0.27 % Initial clauses in saturation : 9
% 0.22/0.27 % Processed clauses : 12
% 0.22/0.27 % ...of these trivial : 0
% 0.22/0.27 % ...subsumed : 0
% 0.22/0.27 % ...remaining for further processing : 12
% 0.22/0.27 % Other redundant clauses eliminated : 0
% 0.22/0.27 % Clauses deleted for lack of memory : 0
% 0.22/0.27 % Backward-subsumed : 0
% 0.22/0.27 % Backward-rewritten : 0
% 0.22/0.27 % Generated clauses : 8
% 0.22/0.27 % ...of the previous two non-redundant : 5
% 0.22/0.27 % ...aggressively subsumed : 0
% 0.22/0.27 % Contextual simplify-reflections : 0
% 0.22/0.27 % Paramodulations : 8
% 0.22/0.27 % Factorizations : 0
% 0.22/0.27 % NegExts : 0
% 0.22/0.27 % Equation resolutions : 0
% 0.22/0.27 % Disequality decompositions : 0
% 0.22/0.27 % Total rewrite steps : 3
% 0.22/0.27 % ...of those cached : 0
% 0.22/0.27 % Propositional unsat checks : 0
% 0.22/0.27 % Propositional check models : 0
% 0.22/0.27 % Propositional check unsatisfiable : 0
% 0.22/0.27 % Propositional clauses : 0
% 0.22/0.27 % Propositional clauses after purity: 0
% 0.22/0.27 % Propositional unsat core size : 0
% 0.22/0.27 % Propositional preprocessing time : 0.000
% 0.22/0.27 % Propositional encoding time : 0.000
% 0.22/0.27 % Propositional solver time : 0.000
% 0.22/0.27 % Success case prop preproc time : 0.000
% 0.22/0.27 % Success case prop encoding time : 0.000
% 0.22/0.27 % Success case prop solver time : 0.000
% 0.22/0.27 % Current number of processed clauses : 12
% 0.22/0.27 % Positive orientable unit clauses : 5
% 0.22/0.27 % Positive unorientable unit clauses: 0
% 0.22/0.27 % Negative unit clauses : 2
% 0.22/0.27 % Non-unit-clauses : 5
% 0.22/0.27 % Current number of unprocessed clauses: 2
% 0.22/0.27 % ...number of literals in the above : 6
% 0.22/0.27 % Current number of archived formulas : 0
% 0.22/0.27 % Current number of archived clauses : 0
% 0.22/0.27 % Clause-clause subsumption calls (NU) : 2
% 0.22/0.27 % Rec. Clause-clause subsumption calls : 2
% 0.22/0.27 % Non-unit clause-clause subsumptions : 0
% 0.22/0.27 % Unit Clause-clause subsumption calls : 3
% 0.22/0.27 % Rewrite failures with RHS unbound : 0
% 0.22/0.27 % BW rewrite match attempts : 1
% 0.22/0.27 % BW rewrite match successes : 0
% 0.22/0.27 % Condensation attempts : 0
% 0.22/0.27 % Condensation successes : 0
% 0.22/0.27 % Termbank termtop insertions : 2873
% 0.22/0.27 % Search garbage collected termcells : 648
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.006 s
% 0.22/0.27 % System time : 0.001 s
% 0.22/0.27 % Total time : 0.007 s
% 0.22/0.27 % Maximum resident set size: 3704 pages
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.007 s
% 0.22/0.27 % System time : 0.004 s
% 0.22/0.27 % Total time : 0.011 s
% 0.22/0.27 % Maximum resident set size: 4864 pages
% 0.22/0.27 % E exiting
%------------------------------------------------------------------------------