%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO433^1 : 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 : n020.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 08:42:59 AM UTC 2026
% Result : Theorem 0.11s 0.25s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 124 ( 19 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 262 ( 60 ~; 37 |; 7 &; 155 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 74 ( 39 ^; 35 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_28,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_43,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
rel_s4: $i > $i > $o ).
thf(decl_55,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_56,type,
mdia_s4: ( $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_1: $i > $i ).
thf(mand,axiom,
( mand
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mnot @ ( mor @ ( mnot @ X6 ) @ ( mnot @ X7 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oILXaHM3XG/E---3.1_1305627.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oILXaHM3XG/E---3.1_1305627.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oILXaHM3XG/E---3.1_1305627.p',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oILXaHM3XG/E---3.1_1305627.p',mimplies) ).
thf(mdia_s4,axiom,
( mdia_s4
= ( ^ [X6: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X6 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oILXaHM3XG/E---3.1_1305627.p',mdia_s4) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( rel_s4 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oILXaHM3XG/E---3.1_1305627.p',mbox_s4) ).
thf(prove,conjecture,
mvalid @ ( mimplies @ ( mand @ ( mdia_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mdia_s4 @ ( mand @ p @ ( mbox_s4 @ q ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oILXaHM3XG/E---3.1_1305627.p',prove) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oILXaHM3XG/E---3.1_1305627.p',mvalid) ).
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.oILXaHM3XG/E---3.1_1305627.p',mtransitive) ).
thf(a2,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/tmp/tmp.oILXaHM3XG/E---3.1_1305627.p',a2) ).
thf(c_0_10,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
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,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_14,plain,
( mdia_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X21: $i] :
( ~ ( rel_s4 @ Z1 @ X21 )
| ~ ( Z0 @ X21 ) ) ) ),
inference(fof_simplification,[status(thm)],[mdia_s4]) ).
thf(c_0_15,plain,
( mbox_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X14: $i] :
( ~ ( rel_s4 @ Z1 @ X14 )
| ( Z0 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s4]) ).
thf(c_0_16,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mand @ ( mdia_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mdia_s4 @ ( mand @ p @ ( mbox_s4 @ q ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove]) ).
thf(c_0_17,plain,
( mand
= ( ^ [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_18,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_13,c_0_11]),c_0_12]) ).
thf(c_0_19,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_20,plain,
( mdia_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X21: $i] :
( ~ ( rel_s4 @ Z1 @ X21 )
| ~ ( Z0 @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_11]),c_0_15]) ).
thf(c_0_21,negated_conjecture,
~ ! [X30: $i] :
( ~ ~ ( ~ ~ ! [X26: $i] :
( ~ ( rel_s4 @ X30 @ X26 )
| ~ ( p @ X26 ) )
| ~ ! [X27: $i] :
( ~ ( rel_s4 @ X30 @ X27 )
| ( q @ X27 ) ) )
| ~ ! [X29: $i] :
( ~ ( rel_s4 @ X30 @ X29 )
| ~ ~ ( ~ ( p @ X29 )
| ~ ! [X28: $i] :
( ~ ( rel_s4 @ X29 @ X28 )
| ( q @ X28 ) ) ) ) ),
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)],[c_0_16,c_0_17]),c_0_18]),c_0_19]),c_0_15]),c_0_20])]) ).
thf(c_0_22,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_23,negated_conjecture,
! [X37: $i,X38: $i] :
( ( rel_s4 @ esk1_0 @ esk2_0 )
& ( p @ esk2_0 )
& ( ~ ( rel_s4 @ esk1_0 @ X37 )
| ( q @ X37 ) )
& ( ( rel_s4 @ X38 @ ( esk3_1 @ X38 ) )
| ~ ( p @ X38 )
| ~ ( rel_s4 @ esk1_0 @ X38 ) )
& ( ~ ( q @ ( esk3_1 @ X38 ) )
| ~ ( p @ X38 )
| ~ ( rel_s4 @ esk1_0 @ X38 ) ) ),
inference(distribute,[status(thm)],[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_24,plain,
! [X23: $i,X24: $i,X25: $i] :
( ( ( rel_s4 @ X23 @ X24 )
& ( rel_s4 @ X24 @ X25 ) )
=> ( rel_s4 @ X23 @ X25 ) ),
inference(apply_def,[status(thm)],[a2,c_0_22]) ).
thf(c_0_25,negated_conjecture,
! [X3: $i] :
( ~ ( q @ ( esk3_1 @ X3 ) )
| ~ ( p @ X3 )
| ~ ( rel_s4 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_26,negated_conjecture,
! [X3: $i] :
( ( q @ X3 )
| ~ ( rel_s4 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_27,plain,
! [X32: $i,X33: $i,X34: $i] :
( ~ ( rel_s4 @ X32 @ X33 )
| ~ ( rel_s4 @ X33 @ X34 )
| ( rel_s4 @ X32 @ X34 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
thf(c_0_28,negated_conjecture,
! [X3: $i] :
( ~ ( rel_s4 @ esk1_0 @ ( esk3_1 @ X3 ) )
| ~ ( rel_s4 @ esk1_0 @ X3 )
| ~ ( p @ X3 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_29,plain,
! [X3: $i,X14: $i,X15: $i] :
( ( rel_s4 @ X3 @ X15 )
| ~ ( rel_s4 @ X3 @ X14 )
| ~ ( rel_s4 @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_30,negated_conjecture,
! [X3: $i,X14: $i] :
( ~ ( rel_s4 @ X3 @ ( esk3_1 @ X14 ) )
| ~ ( rel_s4 @ esk1_0 @ X14 )
| ~ ( rel_s4 @ esk1_0 @ X3 )
| ~ ( p @ X14 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_31,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ ( esk3_1 @ X3 ) )
| ~ ( p @ X3 )
| ~ ( rel_s4 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_32,negated_conjecture,
! [X3: $i] :
( ~ ( rel_s4 @ esk1_0 @ X3 )
| ~ ( p @ X3 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_33,negated_conjecture,
p @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_34,negated_conjecture,
rel_s4 @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO433^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.16 % Computer : n020.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Sep 29 16:52:34 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.22 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.oILXaHM3XG/E---3.1_1305627.p
% 0.11/0.25 % Version: 3.5.1-ho
% 0.11/0.25 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.11/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.11/0.25 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.11/0.25 % Starting almost_fo_3_lam with 300s (1) cores
% 0.11/0.25 % Starting post_as_ho1 with 300s (1) cores
% 0.11/0.25 % ho_unfolding_3 with pid 1305655 completed with status 0
% 0.11/0.25 % Result found by ho_unfolding_3
% 0.11/0.25 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.11/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.11/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.25 % No SInE strategy applied
% 0.11/0.25 % Search class: HHHNF-FFSF11-SHSSMFNN
% 0.11/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.25 % Starting ho_unfolding_3 with 151s (1) cores
% 0.11/0.25 % Starting lpo1_def_fix with 136s (1) cores
% 0.11/0.25 % Starting lpo1_lambda_fix with 136s (1) cores
% 0.11/0.25 % Starting new_ho_7 with 136s (1) cores
% 0.11/0.25 % new_ho_7 with pid 1305664 completed with status 0
% 0.11/0.25 % Result found by new_ho_7
% 0.11/0.25 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.11/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.11/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.25 % No SInE strategy applied
% 0.11/0.25 % Search class: HHHNF-FFSF11-SHSSMFNN
% 0.11/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.25 % Starting ho_unfolding_3 with 151s (1) cores
% 0.11/0.25 % Starting lpo1_def_fix with 136s (1) cores
% 0.11/0.25 % Starting lpo1_lambda_fix with 136s (1) cores
% 0.11/0.25 % Starting new_ho_7 with 136s (1) cores
% 0.11/0.25 % Preprocessing time : 0.001 s
% 0.11/0.25
% 0.11/0.25 % Proof found!
% 0.11/0.25 % SZS status Theorem
% 0.11/0.25 % SZS output start CNFRefutation
% See solution above
% 0.11/0.25 % Parsed axioms : 73
% 0.11/0.25 % Removed by relevancy pruning/SinE : 0
% 0.11/0.25 % Initial clauses : 44
% 0.11/0.25 % Removed in clause preprocessing : 37
% 0.11/0.25 % Initial clauses in saturation : 7
% 0.11/0.25 % Processed clauses : 11
% 0.11/0.25 % ...of these trivial : 0
% 0.11/0.25 % ...subsumed : 0
% 0.11/0.25 % ...remaining for further processing : 11
% 0.11/0.25 % Other redundant clauses eliminated : 0
% 0.11/0.25 % Clauses deleted for lack of memory : 0
% 0.11/0.25 % Backward-subsumed : 4
% 0.11/0.25 % Backward-rewritten : 0
% 0.11/0.25 % Generated clauses : 14
% 0.11/0.25 % ...of the previous two non-redundant : 11
% 0.11/0.25 % ...aggressively subsumed : 0
% 0.11/0.25 % Contextual simplify-reflections : 0
% 0.11/0.25 % Paramodulations : 14
% 0.11/0.25 % Factorizations : 0
% 0.11/0.25 % NegExts : 0
% 0.11/0.25 % Equation resolutions : 0
% 0.11/0.25 % Disequality decompositions : 0
% 0.11/0.25 % Total rewrite steps : 2
% 0.11/0.25 % ...of those cached : 0
% 0.11/0.25 % Propositional unsat checks : 0
% 0.11/0.25 % Propositional check models : 0
% 0.11/0.25 % Propositional check unsatisfiable : 0
% 0.11/0.25 % Propositional clauses : 0
% 0.11/0.25 % Propositional clauses after purity: 0
% 0.11/0.25 % Propositional unsat core size : 0
% 0.11/0.25 % Propositional preprocessing time : 0.000
% 0.11/0.25 % Propositional encoding time : 0.000
% 0.11/0.25 % Propositional solver time : 0.000
% 0.11/0.25 % Success case prop preproc time : 0.000
% 0.11/0.25 % Success case prop encoding time : 0.000
% 0.11/0.25 % Success case prop solver time : 0.000
% 0.11/0.25 % Current number of processed clauses : 7
% 0.11/0.25 % Positive orientable unit clauses : 3
% 0.11/0.25 % Positive unorientable unit clauses: 0
% 0.11/0.25 % Negative unit clauses : 1
% 0.11/0.25 % Non-unit-clauses : 3
% 0.11/0.25 % Current number of unprocessed clauses: 7
% 0.11/0.25 % ...number of literals in the above : 26
% 0.11/0.25 % Current number of archived formulas : 0
% 0.11/0.25 % Current number of archived clauses : 4
% 0.11/0.25 % Clause-clause subsumption calls (NU) : 12
% 0.11/0.25 % Rec. Clause-clause subsumption calls : 9
% 0.11/0.25 % Non-unit clause-clause subsumptions : 4
% 0.11/0.25 % Unit Clause-clause subsumption calls : 3
% 0.11/0.25 % Rewrite failures with RHS unbound : 0
% 0.11/0.25 % BW rewrite match attempts : 1
% 0.11/0.25 % BW rewrite match successes : 0
% 0.11/0.25 % Condensation attempts : 11
% 0.11/0.25 % Condensation successes : 0
% 0.11/0.25 % Termbank termtop insertions : 3157
% 0.11/0.25 % Search garbage collected termcells : 579
% 0.11/0.25
% 0.11/0.25 % -------------------------------------------------
% 0.11/0.25 % User time : 0.002 s
% 0.11/0.25 % System time : 0.005 s
% 0.11/0.25 % Total time : 0.007 s
% 0.11/0.25 % Maximum resident set size: 3700 pages
% 0.11/0.25
% 0.11/0.25 % -------------------------------------------------
% 0.11/0.25 % User time : 0.015 s
% 0.11/0.25 % System time : 0.015 s
% 0.11/0.25 % Total time : 0.030 s
% 0.11/0.25 % Maximum resident set size: 4864 pages
% 0.11/0.25 % E exiting
%------------------------------------------------------------------------------