%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO435^1 : 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 : n012.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 0.08s 0.15s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 39 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 117 ( 18 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 256 ( 49 ~; 33 |; 7 &; 164 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 78 ( 33 ^; 45 !; 0 ?; 78 :)
% 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_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_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,
esk1_0: $i ).
thf(decl_59,type,
esk2_1: $i > $i ).
thf(decl_60,type,
esk3_0: $i ).
thf(decl_61,type,
esk4_1: $i > $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a0m7JHpvp3/E---3.1_370887.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a0m7JHpvp3/E---3.1_370887.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a0m7JHpvp3/E---3.1_370887.p',mor) ).
thf(mdia_s4,axiom,
( mdia_s4
= ( ^ [X6: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a0m7JHpvp3/E---3.1_370887.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/sandbox/tmp/tmp.a0m7JHpvp3/E---3.1_370887.p',mbox_s4) ).
thf(prove,conjecture,
mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ p ) ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a0m7JHpvp3/E---3.1_370887.p',prove) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a0m7JHpvp3/E---3.1_370887.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/sandbox/tmp/tmp.a0m7JHpvp3/E---3.1_370887.p',mtransitive) ).
thf(a2,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/tmp/tmp.a0m7JHpvp3/E---3.1_370887.p',a2) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X13: $i > $i > $o] :
! [X15: $i] : ( X13 @ X15 @ X15 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a0m7JHpvp3/E---3.1_370887.p',mreflexive) ).
thf(a1,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/tmp/tmp.a0m7JHpvp3/E---3.1_370887.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,
( 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 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove]) ).
thf(c_0_17,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_18,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_19,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_12]),c_0_15]) ).
thf(c_0_20,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_21,negated_conjecture,
~ ! [X32: $i] :
( ~ ! [X27: $i] :
( ~ ( rel_s4 @ X32 @ X27 )
| ~ ! [X26: $i] :
( ~ ( rel_s4 @ X27 @ X26 )
| ~ ( p @ X26 ) ) )
| ! [X31: $i] :
( ~ ( rel_s4 @ X32 @ X31 )
| ~ ! [X30: $i] :
( ~ ( rel_s4 @ X31 @ X30 )
| ~ ! [X29: $i] :
( ~ ( rel_s4 @ X30 @ X29 )
| ~ ! [X28: $i] :
( ~ ( rel_s4 @ X29 @ X28 )
| ~ ( p @ 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)],[c_0_16,c_0_17]),c_0_18]),c_0_15]),c_0_19])]) ).
thf(c_0_22,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_20]) ).
thf(c_0_23,negated_conjecture,
! [X38: $i,X41: $i,X43: $i] :
( ( ( rel_s4 @ X38 @ ( esk2_1 @ X38 ) )
| ~ ( rel_s4 @ esk1_0 @ X38 ) )
& ( ( p @ ( esk2_1 @ X38 ) )
| ~ ( rel_s4 @ esk1_0 @ X38 ) )
& ( rel_s4 @ esk1_0 @ esk3_0 )
& ( ( rel_s4 @ X41 @ ( esk4_1 @ X41 ) )
| ~ ( rel_s4 @ esk3_0 @ X41 ) )
& ( ~ ( rel_s4 @ ( esk4_1 @ X41 ) @ X43 )
| ~ ( p @ X43 )
| ~ ( rel_s4 @ esk3_0 @ X41 ) ) ),
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,
! [X34: $i,X35: $i,X36: $i] :
( ~ ( rel_s4 @ X34 @ X35 )
| ~ ( rel_s4 @ X35 @ X36 )
| ( rel_s4 @ X34 @ X36 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
thf(c_0_25,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i] : ( Z0 @ X15 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_26,negated_conjecture,
! [X14: $i,X3: $i] :
( ~ ( rel_s4 @ ( esk4_1 @ X3 ) @ X14 )
| ~ ( p @ X14 )
| ~ ( rel_s4 @ esk3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_27,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ ( esk2_1 @ X3 ) )
| ~ ( rel_s4 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_28,negated_conjecture,
! [X3: $i] :
( ( p @ ( esk2_1 @ X3 ) )
| ~ ( rel_s4 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
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_24]) ).
thf(c_0_30,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ ( esk4_1 @ X3 ) )
| ~ ( rel_s4 @ esk3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_31,plain,
! [X22: $i] : ( rel_s4 @ X22 @ X22 ),
inference(apply_def,[status(thm)],[a1,c_0_25]) ).
thf(c_0_32,negated_conjecture,
! [X3: $i] :
( ~ ( rel_s4 @ esk1_0 @ ( esk4_1 @ X3 ) )
| ~ ( rel_s4 @ esk3_0 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_33,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_s4 @ X3 @ ( esk4_1 @ X14 ) )
| ~ ( rel_s4 @ esk3_0 @ X14 )
| ~ ( rel_s4 @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_34,plain,
! [X33: $i] : ( rel_s4 @ X33 @ X33 ),
inference(variable_rename,[status(thm)],[c_0_31]) ).
thf(c_0_35,negated_conjecture,
! [X3: $i] :
( ~ ( rel_s4 @ esk3_0 @ X3 )
| ~ ( rel_s4 @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_36,plain,
! [X3: $i] : ( rel_s4 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_37,negated_conjecture,
rel_s4 @ esk1_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO435^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 16:51:18 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.14 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.a0m7JHpvp3/E---3.1_370887.p
% 0.08/0.15 % Version: 3.5.1-ho
% 0.08/0.15 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.08/0.15 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.08/0.15 % Starting almost_fo_3_lam with 300s (1) cores
% 0.08/0.15 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.15 % ehoh_best2_full_lfho with pid 370901 completed with status 0
% 0.08/0.15 % Result found by ehoh_best2_full_lfho
% 0.08/0.15 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.08/0.15 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.08/0.15 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.15 % No SInE strategy applied
% 0.08/0.15 % Search class: HHHNF-FFSF11-SHSSMFNN
% 0.08/0.15 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.15 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.15 % SubtermCWHack with pid 370905 completed with status 0
% 0.08/0.15 % Result found by SubtermCWHack
% 0.08/0.15 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.08/0.15 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.08/0.15 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.15 % No SInE strategy applied
% 0.08/0.15 % Search class: HHHNF-FFSF11-SHSSMFNN
% 0.08/0.15 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.15 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.15 % Preprocessing time : 0.001 s
% 0.08/0.15
% 0.08/0.15 % Proof found!
% 0.08/0.15 % SZS status Theorem
% 0.08/0.15 % SZS output start CNFRefutation
% See solution above
% 0.08/0.15 % Parsed axioms : 72
% 0.08/0.15 % Removed by relevancy pruning/SinE : 0
% 0.08/0.15 % Initial clauses : 43
% 0.08/0.15 % Removed in clause preprocessing : 36
% 0.08/0.15 % Initial clauses in saturation : 7
% 0.08/0.15 % Processed clauses : 18
% 0.08/0.15 % ...of these trivial : 0
% 0.08/0.15 % ...subsumed : 2
% 0.08/0.15 % ...remaining for further processing : 16
% 0.08/0.15 % Other redundant clauses eliminated : 0
% 0.08/0.15 % Clauses deleted for lack of memory : 0
% 0.08/0.15 % Backward-subsumed : 0
% 0.08/0.15 % Backward-rewritten : 0
% 0.08/0.15 % Generated clauses : 22
% 0.08/0.15 % ...of the previous two non-redundant : 20
% 0.08/0.15 % ...aggressively subsumed : 0
% 0.08/0.15 % Contextual simplify-reflections : 1
% 0.08/0.15 % Paramodulations : 22
% 0.08/0.15 % Factorizations : 0
% 0.08/0.15 % NegExts : 0
% 0.08/0.15 % Equation resolutions : 0
% 0.08/0.15 % Disequality decompositions : 0
% 0.08/0.15 % Total rewrite steps : 4
% 0.08/0.15 % ...of those cached : 2
% 0.08/0.15 % Propositional unsat checks : 0
% 0.08/0.15 % Propositional check models : 0
% 0.08/0.15 % Propositional check unsatisfiable : 0
% 0.08/0.15 % Propositional clauses : 0
% 0.08/0.15 % Propositional clauses after purity: 0
% 0.08/0.15 % Propositional unsat core size : 0
% 0.08/0.15 % Propositional preprocessing time : 0.000
% 0.08/0.15 % Propositional encoding time : 0.000
% 0.08/0.15 % Propositional solver time : 0.000
% 0.08/0.15 % Success case prop preproc time : 0.000
% 0.08/0.15 % Success case prop encoding time : 0.000
% 0.08/0.15 % Success case prop solver time : 0.000
% 0.08/0.15 % Current number of processed clauses : 16
% 0.08/0.15 % Positive orientable unit clauses : 2
% 0.08/0.15 % Positive unorientable unit clauses: 0
% 0.08/0.15 % Negative unit clauses : 1
% 0.08/0.15 % Non-unit-clauses : 13
% 0.08/0.15 % Current number of unprocessed clauses: 4
% 0.08/0.15 % ...number of literals in the above : 16
% 0.08/0.15 % Current number of archived formulas : 0
% 0.08/0.15 % Current number of archived clauses : 0
% 0.08/0.15 % Clause-clause subsumption calls (NU) : 28
% 0.08/0.15 % Rec. Clause-clause subsumption calls : 22
% 0.08/0.15 % Non-unit clause-clause subsumptions : 3
% 0.08/0.15 % Unit Clause-clause subsumption calls : 2
% 0.08/0.15 % Rewrite failures with RHS unbound : 0
% 0.08/0.15 % BW rewrite match attempts : 1
% 0.08/0.15 % BW rewrite match successes : 0
% 0.08/0.15 % Condensation attempts : 0
% 0.08/0.15 % Condensation successes : 0
% 0.08/0.15 % Termbank termtop insertions : 2954
% 0.08/0.15 % Search garbage collected termcells : 597
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.005 s
% 0.08/0.15 % System time : 0.000 s
% 0.08/0.15 % Total time : 0.005 s
% 0.08/0.15 % Maximum resident set size: 3700 pages
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.005 s
% 0.08/0.15 % System time : 0.004 s
% 0.08/0.15 % Total time : 0.009 s
% 0.08/0.15 % Maximum resident set size: 4864 pages
% 0.08/0.15 % E exiting
%------------------------------------------------------------------------------