%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO566^7 : 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 : n001.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 0.12s 0.27s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 15 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 169 ( 23 ~; 18 |; 3 &; 120 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 58 ( 36 ^; 22 !; 0 ?; 58 :)
% 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_41,type,
mreflexive: ( $i > $i > $o ) > $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,
g: mu > $i > $o ).
thf(decl_59,type,
f: mu > $i > $o ).
thf(decl_61,type,
esk2_0: $i ).
thf(decl_62,type,
esk3_0: mu ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52tceHLONl/E---3.1_1544595.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52tceHLONl/E---3.1_1544595.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52tceHLONl/E---3.1_1544595.p',mor) ).
thf(con,conjecture,
( mvalid
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X20: mu] : ( mimplies @ ( f @ X20 ) @ ( g @ X20 ) ) ) )
@ ( mimplies
@ ( mforall_ind
@ ^ [X21: mu] : ( f @ X21 ) )
@ ( mforall_ind
@ ^ [X22: mu] : ( g @ X22 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52tceHLONl/E---3.1_1544595.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.52tceHLONl/E---3.1_1544595.p',mforall_ind) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52tceHLONl/E---3.1_1544595.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.52tceHLONl/E---3.1_1544595.p',mbox_s4) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X6: $i > $i > $o] :
! [X16: $i] : ( X6 @ X16 @ X16 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52tceHLONl/E---3.1_1544595.p',mreflexive) ).
thf(a1,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/tmp/tmp.52tceHLONl/E---3.1_1544595.p',a1) ).
thf(c_0_9,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
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,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X20: mu] : ( mimplies @ ( f @ X20 ) @ ( g @ X20 ) ) ) )
@ ( mimplies
@ ( mforall_ind
@ ^ [X21: mu] : ( f @ X21 ) )
@ ( mforall_ind
@ ^ [X22: mu] : ( g @ X22 ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_13,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_9,c_0_10]),c_0_11]) ).
thf(c_0_14,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_15,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_16,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_17,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X16: $i] : ( Z0 @ X16 @ X16 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_18,negated_conjecture,
~ ! [X40: $i] :
( ~ ! [X37: $i] :
( ~ ( rel_s4 @ X40 @ X37 )
| ! [X36: mu] :
( ( exists_in_world @ X36 @ X37 )
=> ( ~ ( f @ X36 @ X37 )
| ( g @ X36 @ X37 ) ) ) )
| ~ ! [X38: mu] :
( ( exists_in_world @ X38 @ X40 )
=> ( f @ X38 @ X40 ) )
| ! [X39: mu] :
( ( exists_in_world @ X39 @ X40 )
=> ( g @ X39 @ 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_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16])]) ).
thf(c_0_19,plain,
! [X32: $i] : ( rel_s4 @ X32 @ X32 ),
inference(apply_def,[status(thm)],[a1,c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X51: $i,X52: mu,X53: mu] :
( ( ~ ( rel_s4 @ esk2_0 @ X51 )
| ~ ( exists_in_world @ X52 @ X51 )
| ~ ( f @ X52 @ X51 )
| ( g @ X52 @ X51 ) )
& ( ~ ( exists_in_world @ X53 @ esk2_0 )
| ( f @ X53 @ esk2_0 ) )
& ( exists_in_world @ esk3_0 @ esk2_0 )
& ~ ( g @ esk3_0 @ esk2_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_18])])])])]) ).
thf(c_0_21,plain,
! [X43: $i] : ( rel_s4 @ X43 @ X43 ),
inference(variable_rename,[status(thm)],[c_0_19]) ).
thf(c_0_22,negated_conjecture,
~ ( g @ esk3_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_23,negated_conjecture,
! [X10: mu,X3: $i] :
( ( g @ X10 @ X3 )
| ~ ( rel_s4 @ esk2_0 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( f @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,plain,
! [X3: $i] : ( rel_s4 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,negated_conjecture,
exists_in_world @ esk3_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,negated_conjecture,
~ ( f @ esk3_0 @ esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
thf(c_0_27,negated_conjecture,
! [X10: mu] :
( ( f @ X10 @ esk2_0 )
| ~ ( exists_in_world @ X10 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO566^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.18 % Computer : n001.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Sep 29 17:20:50 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running higher-order theorem proving
% 0.12/0.24 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.52tceHLONl/E---3.1_1544595.p
% 0.12/0.27 % Version: 3.5.1-ho
% 0.12/0.27 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.12/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.12/0.27 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.12/0.27 % Starting almost_fo_3_lam with 300s (1) cores
% 0.12/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.12/0.27 % ehoh_best2_full_lfho with pid 1544609 completed with status 0
% 0.12/0.27 % Result found by ehoh_best2_full_lfho
% 0.12/0.27 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.12/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.12/0.27 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.12/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.27 % No SInE strategy applied
% 0.12/0.27 % Search class: HHUNS-FFSF11-SHSSMFNN
% 0.12/0.27 % partial match(1): HHHNS-FFSF11-SHSSMFNN
% 0.12/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.27 % SubtermCWHack with pid 1544613 completed with status 0
% 0.12/0.27 % Result found by SubtermCWHack
% 0.12/0.27 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.12/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.27 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.12/0.27 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.12/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.27 % No SInE strategy applied
% 0.12/0.27 % Search class: HHUNS-FFSF11-SHSSMFNN
% 0.12/0.27 % partial match(1): HHHNS-FFSF11-SHSSMFNN
% 0.12/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.27 % Preprocessing time : 0.001 s
% 0.12/0.27
% 0.12/0.27 % Proof found!
% 0.12/0.27 % SZS status Theorem
% 0.12/0.27 % SZS output start CNFRefutation
% See solution above
% 0.12/0.27 % Parsed axioms : 75
% 0.12/0.27 % Removed by relevancy pruning/SinE : 0
% 0.12/0.27 % Initial clauses : 46
% 0.12/0.27 % Removed in clause preprocessing : 38
% 0.12/0.27 % Initial clauses in saturation : 8
% 0.12/0.27 % Processed clauses : 9
% 0.12/0.27 % ...of these trivial : 0
% 0.12/0.27 % ...subsumed : 0
% 0.12/0.27 % ...remaining for further processing : 9
% 0.12/0.27 % Other redundant clauses eliminated : 0
% 0.12/0.27 % Clauses deleted for lack of memory : 0
% 0.12/0.27 % Backward-subsumed : 0
% 0.12/0.27 % Backward-rewritten : 0
% 0.12/0.27 % Generated clauses : 4
% 0.12/0.27 % ...of the previous two non-redundant : 1
% 0.12/0.27 % ...aggressively subsumed : 0
% 0.12/0.27 % Contextual simplify-reflections : 0
% 0.12/0.27 % Paramodulations : 4
% 0.12/0.27 % Factorizations : 0
% 0.12/0.27 % NegExts : 0
% 0.12/0.27 % Equation resolutions : 0
% 0.12/0.27 % Disequality decompositions : 0
% 0.12/0.27 % Total rewrite steps : 3
% 0.12/0.27 % ...of those cached : 1
% 0.12/0.27 % Propositional unsat checks : 0
% 0.12/0.27 % Propositional check models : 0
% 0.12/0.27 % Propositional check unsatisfiable : 0
% 0.12/0.27 % Propositional clauses : 0
% 0.12/0.27 % Propositional clauses after purity: 0
% 0.12/0.27 % Propositional unsat core size : 0
% 0.12/0.27 % Propositional preprocessing time : 0.000
% 0.12/0.27 % Propositional encoding time : 0.000
% 0.12/0.27 % Propositional solver time : 0.000
% 0.12/0.27 % Success case prop preproc time : 0.000
% 0.12/0.27 % Success case prop encoding time : 0.000
% 0.12/0.27 % Success case prop solver time : 0.000
% 0.12/0.27 % Current number of processed clauses : 9
% 0.12/0.27 % Positive orientable unit clauses : 3
% 0.12/0.27 % Positive unorientable unit clauses: 0
% 0.12/0.27 % Negative unit clauses : 2
% 0.12/0.27 % Non-unit-clauses : 4
% 0.12/0.27 % Current number of unprocessed clauses: 0
% 0.12/0.27 % ...number of literals in the above : 0
% 0.12/0.27 % Current number of archived formulas : 0
% 0.12/0.27 % Current number of archived clauses : 0
% 0.12/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.12/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.12/0.27 % Non-unit clause-clause subsumptions : 0
% 0.12/0.27 % Unit Clause-clause subsumption calls : 0
% 0.12/0.27 % Rewrite failures with RHS unbound : 0
% 0.12/0.27 % BW rewrite match attempts : 0
% 0.12/0.27 % BW rewrite match successes : 0
% 0.12/0.27 % Condensation attempts : 0
% 0.12/0.27 % Condensation successes : 0
% 0.12/0.27 % Termbank termtop insertions : 2769
% 0.12/0.27 % Search garbage collected termcells : 595
% 0.12/0.27
% 0.12/0.27 % -------------------------------------------------
% 0.12/0.27 % User time : 0.004 s
% 0.12/0.27 % System time : 0.004 s
% 0.12/0.27 % Total time : 0.008 s
% 0.12/0.27 % Maximum resident set size: 3704 pages
% 0.12/0.27
% 0.12/0.27 % -------------------------------------------------
% 0.12/0.27 % User time : 0.006 s
% 0.12/0.27 % System time : 0.008 s
% 0.12/0.27 % Total time : 0.015 s
% 0.12/0.27 % Maximum resident set size: 4864 pages
% 0.12/0.27 % E exiting
%------------------------------------------------------------------------------