%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO495^6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:43:14 AM UTC 2026
% Result : Theorem 0.23s 0.28s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 17 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 216 ( 26 ~; 26 |; 6 &; 155 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 78 ( 36 ^; 42 !; 0 ?; 78 :)
% 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_28,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_40,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(decl_43,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
rel_s5: $i > $i > $o ).
thf(decl_55,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(decl_57,type,
f: mu > $i > $o ).
thf(decl_58,type,
g: mu > $i > $o ).
thf(decl_59,type,
esk1_0: $i ).
thf(decl_60,type,
esk2_0: $i ).
thf(decl_61,type,
esk3_0: mu ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8BfGVcfHGE/E---3.1_1035018.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8BfGVcfHGE/E---3.1_1035018.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8BfGVcfHGE/E---3.1_1035018.p',mor) ).
thf(mtransitive,axiom,
( mtransitive
= ( ^ [X13: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( ( X13 @ X15 @ X16 )
& ( X13 @ X16 @ X17 ) )
=> ( X13 @ X15 @ X17 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8BfGVcfHGE/E---3.1_1035018.p',mtransitive) ).
thf(prove,conjecture,
( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X1: mu] : ( mor @ ( mbox_s5 @ ( f @ X1 ) ) @ ( mbox_s5 @ ( g @ X1 ) ) ) )
@ ( mbox_s5
@ ( mforall_ind
@ ^ [X1: mu] : ( mor @ ( f @ X1 ) @ ( g @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8BfGVcfHGE/E---3.1_1035018.p',prove) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X8: mu > $i > $o,X3: $i] :
! [X1: mu] : ( X8 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8BfGVcfHGE/E---3.1_1035018.p',mforall_ind) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8BfGVcfHGE/E---3.1_1035018.p',mvalid) ).
thf(mbox_s5,axiom,
( mbox_s5
= ( ^ [X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( rel_s5 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8BfGVcfHGE/E---3.1_1035018.p',mbox_s5) ).
thf(a2,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/tmp/tmp.8BfGVcfHGE/E---3.1_1035018.p',a2) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X13: $i > $i > $o] :
! [X15: $i] : ( X13 @ X15 @ X15 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8BfGVcfHGE/E---3.1_1035018.p',mreflexive) ).
thf(a1,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox2/tmp/tmp.8BfGVcfHGE/E---3.1_1035018.p',a1) ).
thf(c_0_11,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_12,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_13,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_14,plain,
( mtransitive
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( ( Z0 @ X15 @ X16 )
& ( Z0 @ X16 @ X17 ) )
=> ( Z0 @ X15 @ X17 ) ) ) ),
inference(fof_simplification,[status(thm)],[mtransitive]) ).
thf(c_0_15,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X1: mu] : ( mor @ ( mbox_s5 @ ( f @ X1 ) ) @ ( mbox_s5 @ ( g @ X1 ) ) ) )
@ ( mbox_s5
@ ( mforall_ind
@ ^ [X1: mu] : ( mor @ ( f @ X1 ) @ ( g @ X1 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove]) ).
thf(c_0_16,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_11,c_0_12]),c_0_13]) ).
thf(c_0_17,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X1: mu] : ( Z0 @ X1 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_18,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_19,plain,
( mbox_s5
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X14: $i] :
( ~ ( rel_s5 @ Z1 @ X14 )
| ( Z0 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s5]) ).
thf(c_0_20,plain,
! [X23: $i,X24: $i,X25: $i] :
( ( ( rel_s5 @ X23 @ X24 )
& ( rel_s5 @ X24 @ X25 ) )
=> ( rel_s5 @ X23 @ X25 ) ),
inference(apply_def,[status(thm)],[a2,c_0_14]) ).
thf(c_0_21,negated_conjecture,
~ ! [X33: $i] :
( ~ ! [X30: mu] :
( ! [X28: $i] :
( ~ ( rel_s5 @ X33 @ X28 )
| ( f @ X30 @ X28 ) )
| ! [X29: $i] :
( ~ ( rel_s5 @ X33 @ X29 )
| ( g @ X30 @ X29 ) ) )
| ! [X32: $i] :
( ~ ( rel_s5 @ X33 @ X32 )
| ! [X31: mu] :
( ( f @ X31 @ X32 )
| ( g @ X31 @ X32 ) ) ) ),
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(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_15]),c_0_13]),c_0_16]),c_0_17]),c_0_18]),c_0_19])]) ).
thf(c_0_22,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i] : ( Z0 @ X15 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_23,plain,
! [X35: $i,X36: $i,X37: $i] :
( ~ ( rel_s5 @ X35 @ X36 )
| ~ ( rel_s5 @ X36 @ X37 )
| ( rel_s5 @ X35 @ X37 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
thf(c_0_24,negated_conjecture,
! [X41: mu,X42: $i,X43: $i] :
( ( ~ ( rel_s5 @ esk1_0 @ X42 )
| ( f @ X41 @ X42 )
| ~ ( rel_s5 @ esk1_0 @ X43 )
| ( g @ X41 @ X43 ) )
& ( rel_s5 @ esk1_0 @ esk2_0 )
& ~ ( f @ 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_21])])])])]) ).
thf(c_0_25,plain,
! [X22: $i] : ( rel_s5 @ X22 @ X22 ),
inference(apply_def,[status(thm)],[a1,c_0_22]) ).
thf(c_0_26,plain,
! [X3: $i,X14: $i,X15: $i] :
( ( rel_s5 @ X3 @ X15 )
| ~ ( rel_s5 @ X3 @ X14 )
| ~ ( rel_s5 @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_27,negated_conjecture,
rel_s5 @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_28,plain,
! [X34: $i] : ( rel_s5 @ X34 @ X34 ),
inference(variable_rename,[status(thm)],[c_0_25]) ).
thf(c_0_29,negated_conjecture,
! [X3: $i,X1: mu,X14: $i] :
( ( f @ X1 @ X3 )
| ( g @ X1 @ X14 )
| ~ ( rel_s5 @ esk1_0 @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_30,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ X3 @ esk2_0 )
| ~ ( rel_s5 @ X3 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_31,plain,
! [X3: $i] : ( rel_s5 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_32,negated_conjecture,
! [X1: mu,X3: $i] :
( ( g @ X1 @ esk2_0 )
| ( f @ X1 @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
thf(c_0_33,negated_conjecture,
~ ( g @ esk3_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_34,negated_conjecture,
! [X1: mu] :
( ( f @ X1 @ esk2_0 )
| ( g @ X1 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_30]),c_0_31])]) ).
thf(c_0_35,negated_conjecture,
~ ( f @ esk3_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO495^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n006.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 17:09:40 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 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.8BfGVcfHGE/E---3.1_1035018.p
% 0.23/0.28 % Version: 3.5.1-ho
% 0.23/0.28 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.23/0.28 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.23/0.28 % Starting almost_fo_3_lam with 300s (1) cores
% 0.23/0.28 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.28 % ho_unfolding_3 with pid 1035054 completed with status 0
% 0.23/0.28 % Result found by ho_unfolding_3
% 0.23/0.28 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.23/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.28 % No SInE strategy applied
% 0.23/0.28 % Search class: HGUNF-FFSF00-SHSSMFNN
% 0.23/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.28 % Starting ho_unfolding_3 with 151s (1) cores
% 0.23/0.28 % Starting sh5l with 136s (1) cores
% 0.23/0.28 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.23/0.28 % Starting lpo1_def_fix with 136s (1) cores
% 0.23/0.28 % SubtermCWHack with pid 1035058 completed with status 0
% 0.23/0.28 % Result found by SubtermCWHack
% 0.23/0.28 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.23/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.28 % No SInE strategy applied
% 0.23/0.28 % Search class: HGUNF-FFSF00-SHSSMFNN
% 0.23/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.28 % Preprocessing time : 0.001 s
% 0.23/0.28
% 0.23/0.28 % Proof found!
% 0.23/0.28 % SZS status Theorem
% 0.23/0.28 % SZS output start CNFRefutation
% See solution above
% 0.23/0.28 % Parsed axioms : 74
% 0.23/0.28 % Removed by relevancy pruning/SinE : 0
% 0.23/0.28 % Initial clauses : 44
% 0.23/0.28 % Removed in clause preprocessing : 37
% 0.23/0.28 % Initial clauses in saturation : 7
% 0.23/0.28 % Processed clauses : 15
% 0.23/0.28 % ...of these trivial : 0
% 0.23/0.28 % ...subsumed : 1
% 0.23/0.28 % ...remaining for further processing : 14
% 0.23/0.28 % Other redundant clauses eliminated : 0
% 0.23/0.28 % Clauses deleted for lack of memory : 0
% 0.23/0.28 % Backward-subsumed : 0
% 0.23/0.28 % Backward-rewritten : 0
% 0.23/0.28 % Generated clauses : 22
% 0.23/0.28 % ...of the previous two non-redundant : 12
% 0.23/0.28 % ...aggressively subsumed : 0
% 0.23/0.28 % Contextual simplify-reflections : 0
% 0.23/0.28 % Paramodulations : 22
% 0.23/0.28 % Factorizations : 0
% 0.23/0.28 % NegExts : 0
% 0.23/0.28 % Equation resolutions : 0
% 0.23/0.28 % Disequality decompositions : 0
% 0.23/0.28 % Total rewrite steps : 8
% 0.23/0.28 % ...of those cached : 3
% 0.23/0.28 % Propositional unsat checks : 0
% 0.23/0.28 % Propositional check models : 0
% 0.23/0.28 % Propositional check unsatisfiable : 0
% 0.23/0.28 % Propositional clauses : 0
% 0.23/0.28 % Propositional clauses after purity: 0
% 0.23/0.28 % Propositional unsat core size : 0
% 0.23/0.28 % Propositional preprocessing time : 0.000
% 0.23/0.28 % Propositional encoding time : 0.000
% 0.23/0.28 % Propositional solver time : 0.000
% 0.23/0.28 % Success case prop preproc time : 0.000
% 0.23/0.28 % Success case prop encoding time : 0.000
% 0.23/0.28 % Success case prop solver time : 0.000
% 0.23/0.28 % Current number of processed clauses : 14
% 0.23/0.28 % Positive orientable unit clauses : 3
% 0.23/0.28 % Positive unorientable unit clauses: 0
% 0.23/0.28 % Negative unit clauses : 2
% 0.23/0.28 % Non-unit-clauses : 9
% 0.23/0.28 % Current number of unprocessed clauses: 4
% 0.23/0.28 % ...number of literals in the above : 10
% 0.23/0.28 % Current number of archived formulas : 0
% 0.23/0.28 % Current number of archived clauses : 0
% 0.23/0.28 % Clause-clause subsumption calls (NU) : 21
% 0.23/0.28 % Rec. Clause-clause subsumption calls : 21
% 0.23/0.28 % Non-unit clause-clause subsumptions : 1
% 0.23/0.28 % Unit Clause-clause subsumption calls : 0
% 0.23/0.28 % Rewrite failures with RHS unbound : 0
% 0.23/0.28 % BW rewrite match attempts : 1
% 0.23/0.28 % BW rewrite match successes : 0
% 0.23/0.28 % Condensation attempts : 0
% 0.23/0.28 % Condensation successes : 0
% 0.23/0.28 % Termbank termtop insertions : 2881
% 0.23/0.28 % Search garbage collected termcells : 570
% 0.23/0.28
% 0.23/0.28 % -------------------------------------------------
% 0.23/0.28 % User time : 0.005 s
% 0.23/0.28 % System time : 0.006 s
% 0.23/0.28 % Total time : 0.011 s
% 0.23/0.28 % Maximum resident set size: 3904 pages
% 0.23/0.28
% 0.23/0.28 % -------------------------------------------------
% 0.23/0.28 % User time : 0.016 s
% 0.23/0.28 % System time : 0.019 s
% 0.23/0.28 % Total time : 0.035 s
% 0.23/0.28 % Maximum resident set size: 4864 pages
% 0.23/0.28 % E exiting
%------------------------------------------------------------------------------