%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO448^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:43:01 AM UTC 2026
% Result : Theorem 0.11s 0.26s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 115 ( 15 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 229 ( 32 ~; 26 |; 10 &; 155 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 69 ( 28 ^; 41 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
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_41,type,
msymmetric: ( $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,
p: $i > $o ).
thf(decl_58,type,
q: $i > $o ).
thf(decl_59,type,
esk1_0: $i ).
thf(decl_60,type,
esk2_0: $i ).
thf(decl_61,type,
esk3_0: $i ).
thf(decl_62,type,
esk4_0: $i ).
thf(decl_63,type,
esk5_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OZyCN9gEtz/E---3.1_3637032.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OZyCN9gEtz/E---3.1_3637032.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OZyCN9gEtz/E---3.1_3637032.p',mor) ).
thf(prove,conjecture,
mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ ( mbox_s5 @ p ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OZyCN9gEtz/E---3.1_3637032.p',prove) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OZyCN9gEtz/E---3.1_3637032.p',mvalid) ).
thf(mbox_s5,axiom,
( mbox_s5
= ( ^ [X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( rel_s5 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OZyCN9gEtz/E---3.1_3637032.p',mbox_s5) ).
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/sandbox/tmp/tmp.OZyCN9gEtz/E---3.1_3637032.p',mtransitive) ).
thf(msymmetric,axiom,
( msymmetric
= ( ^ [X13: $i > $i > $o] :
! [X15: $i,X16: $i] :
( ( X13 @ X15 @ X16 )
=> ( X13 @ X16 @ X15 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OZyCN9gEtz/E---3.1_3637032.p',msymmetric) ).
thf(a2,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/tmp/tmp.OZyCN9gEtz/E---3.1_3637032.p',a2) ).
thf(a3,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/tmp/tmp.OZyCN9gEtz/E---3.1_3637032.p',a3) ).
thf(c_0_10,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_11,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_12,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_13,negated_conjecture,
~ ( mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ ( mbox_s5 @ p ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove]) ).
thf(c_0_14,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_10,c_0_11]),c_0_12]) ).
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_s5
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X14: $i] :
( ~ ( rel_s5 @ Z1 @ X14 )
| ( Z0 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s5]) ).
thf(c_0_17,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_18,plain,
( msymmetric
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i,X16: $i] :
( ( Z0 @ X15 @ X16 )
=> ( Z0 @ X16 @ X15 ) ) ) ),
inference(fof_simplification,[status(thm)],[msymmetric]) ).
thf(c_0_19,negated_conjecture,
~ ! [X34: $i] :
( ! [X30: $i] :
( ~ ( rel_s5 @ X34 @ X30 )
| ~ ! [X28: $i] :
( ~ ( rel_s5 @ X30 @ X28 )
| ( p @ X28 ) )
| ! [X29: $i] :
( ~ ( rel_s5 @ X30 @ X29 )
| ( q @ X29 ) ) )
| ! [X33: $i] :
( ~ ( rel_s5 @ X34 @ X33 )
| ~ ! [X31: $i] :
( ~ ( rel_s5 @ X33 @ X31 )
| ( q @ X31 ) )
| ! [X32: $i] :
( ~ ( rel_s5 @ X33 @ X32 )
| ( p @ 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)],[c_0_13,c_0_12]),c_0_14]),c_0_15]),c_0_16])]) ).
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_17]) ).
thf(c_0_21,plain,
! [X26: $i,X27: $i] :
( ( rel_s5 @ X26 @ X27 )
=> ( rel_s5 @ X27 @ X26 ) ),
inference(apply_def,[status(thm)],[a3,c_0_18]) ).
thf(c_0_22,negated_conjecture,
! [X43: $i,X46: $i] :
( ( rel_s5 @ esk1_0 @ esk2_0 )
& ( ~ ( rel_s5 @ esk2_0 @ X43 )
| ( p @ X43 ) )
& ( rel_s5 @ esk2_0 @ esk3_0 )
& ~ ( q @ esk3_0 )
& ( rel_s5 @ esk1_0 @ esk4_0 )
& ( ~ ( rel_s5 @ esk4_0 @ X46 )
| ( q @ X46 ) )
& ( rel_s5 @ esk4_0 @ esk5_0 )
& ~ ( p @ 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_19])])])])]) ).
thf(c_0_23,plain,
! [X36: $i,X37: $i,X38: $i] :
( ~ ( rel_s5 @ X36 @ X37 )
| ~ ( rel_s5 @ X37 @ X38 )
| ( rel_s5 @ X36 @ X38 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
thf(c_0_24,plain,
! [X39: $i,X40: $i] :
( ~ ( rel_s5 @ X39 @ X40 )
| ( rel_s5 @ X40 @ X39 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
thf(c_0_25,negated_conjecture,
~ ( p @ esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_26,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ~ ( rel_s5 @ esk2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_27,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_28,negated_conjecture,
rel_s5 @ esk4_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_29,negated_conjecture,
rel_s5 @ esk1_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_30,plain,
! [X3: $i,X14: $i] :
( ( rel_s5 @ X14 @ X3 )
| ~ ( rel_s5 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_31,negated_conjecture,
rel_s5 @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_32,negated_conjecture,
~ ( rel_s5 @ esk2_0 @ esk5_0 ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_33,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ X3 @ esk5_0 )
| ~ ( rel_s5 @ X3 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_34,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ X3 @ esk4_0 )
| ~ ( rel_s5 @ X3 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_29]) ).
thf(c_0_35,negated_conjecture,
rel_s5 @ esk2_0 @ esk1_0,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_36,negated_conjecture,
~ ( rel_s5 @ esk2_0 @ esk4_0 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO448^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n007.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 16:50:10 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.23 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.OZyCN9gEtz/E---3.1_3637032.p
% 0.11/0.26 % Version: 3.5.1-ho
% 0.11/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.11/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.11/0.26 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.11/0.26 % Starting almost_fo_3_lam with 300s (1) cores
% 0.11/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.11/0.26 % ehoh_best2_full_lfho with pid 3637072 completed with status 0
% 0.11/0.26 % Result found by ehoh_best2_full_lfho
% 0.11/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.11/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.11/0.26 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.11/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.26 % No SInE strategy applied
% 0.11/0.26 % Search class: HHUNF-FFSS00-SHSSMFNN
% 0.11/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.26 % SubtermCWHack with pid 3637079 completed with status 0
% 0.11/0.26 % Result found by SubtermCWHack
% 0.11/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.11/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.11/0.26 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.11/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.26 % No SInE strategy applied
% 0.11/0.26 % Search class: HHUNF-FFSS00-SHSSMFNN
% 0.11/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.26 % Preprocessing time : 0.001 s
% 0.11/0.26
% 0.11/0.26 % Proof found!
% 0.11/0.26 % SZS status Theorem
% 0.11/0.26 % SZS output start CNFRefutation
% See solution above
% 0.11/0.26 % Parsed axioms : 74
% 0.11/0.26 % Removed by relevancy pruning/SinE : 0
% 0.11/0.26 % Initial clauses : 48
% 0.11/0.26 % Removed in clause preprocessing : 37
% 0.11/0.26 % Initial clauses in saturation : 11
% 0.11/0.26 % Processed clauses : 26
% 0.11/0.26 % ...of these trivial : 0
% 0.11/0.26 % ...subsumed : 0
% 0.11/0.26 % ...remaining for further processing : 26
% 0.11/0.26 % Other redundant clauses eliminated : 0
% 0.11/0.26 % Clauses deleted for lack of memory : 0
% 0.11/0.26 % Backward-subsumed : 0
% 0.11/0.26 % Backward-rewritten : 0
% 0.11/0.26 % Generated clauses : 41
% 0.11/0.26 % ...of the previous two non-redundant : 24
% 0.11/0.26 % ...aggressively subsumed : 0
% 0.11/0.26 % Contextual simplify-reflections : 0
% 0.11/0.26 % Paramodulations : 41
% 0.11/0.26 % Factorizations : 0
% 0.11/0.26 % NegExts : 0
% 0.11/0.26 % Equation resolutions : 0
% 0.11/0.26 % Disequality decompositions : 0
% 0.11/0.26 % Total rewrite steps : 10
% 0.11/0.26 % ...of those cached : 1
% 0.11/0.26 % Propositional unsat checks : 0
% 0.11/0.26 % Propositional check models : 0
% 0.11/0.26 % Propositional check unsatisfiable : 0
% 0.11/0.26 % Propositional clauses : 0
% 0.11/0.26 % Propositional clauses after purity: 0
% 0.11/0.26 % Propositional unsat core size : 0
% 0.11/0.26 % Propositional preprocessing time : 0.000
% 0.11/0.26 % Propositional encoding time : 0.000
% 0.11/0.26 % Propositional solver time : 0.000
% 0.11/0.26 % Success case prop preproc time : 0.000
% 0.11/0.26 % Success case prop encoding time : 0.000
% 0.11/0.26 % Success case prop solver time : 0.000
% 0.11/0.26 % Current number of processed clauses : 26
% 0.11/0.26 % Positive orientable unit clauses : 9
% 0.11/0.26 % Positive unorientable unit clauses: 0
% 0.11/0.26 % Negative unit clauses : 6
% 0.11/0.26 % Non-unit-clauses : 11
% 0.11/0.26 % Current number of unprocessed clauses: 9
% 0.11/0.26 % ...number of literals in the above : 22
% 0.11/0.26 % Current number of archived formulas : 0
% 0.11/0.26 % Current number of archived clauses : 0
% 0.11/0.26 % Clause-clause subsumption calls (NU) : 13
% 0.11/0.26 % Rec. Clause-clause subsumption calls : 13
% 0.11/0.26 % Non-unit clause-clause subsumptions : 0
% 0.11/0.26 % Unit Clause-clause subsumption calls : 7
% 0.11/0.26 % Rewrite failures with RHS unbound : 0
% 0.11/0.26 % BW rewrite match attempts : 4
% 0.11/0.26 % BW rewrite match successes : 0
% 0.11/0.26 % Condensation attempts : 0
% 0.11/0.26 % Condensation successes : 0
% 0.11/0.26 % Termbank termtop insertions : 3066
% 0.11/0.26 % Search garbage collected termcells : 605
% 0.11/0.26
% 0.11/0.26 % -------------------------------------------------
% 0.11/0.26 % User time : 0.006 s
% 0.11/0.26 % System time : 0.002 s
% 0.11/0.26 % Total time : 0.008 s
% 0.11/0.26 % Maximum resident set size: 3700 pages
% 0.11/0.26
% 0.11/0.26 % -------------------------------------------------
% 0.11/0.26 % User time : 0.009 s
% 0.11/0.26 % System time : 0.006 s
% 0.11/0.26 % Total time : 0.015 s
% 0.11/0.26 % Maximum resident set size: 4608 pages
% 0.11/0.26 % E exiting
%------------------------------------------------------------------------------