%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV085^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:39:41 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 100 ( 14 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 258 ( 39 ~; 28 |; 6 &; 185 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 46 ( 32 ^; 14 !; 0 ?; 46 :)
% 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_31,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $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_62,type,
leq: mu > mu > $i > $o ).
thf(decl_82,type,
minus: mu > mu > mu ).
thf(decl_83,type,
pv68: mu ).
thf(decl_86,type,
n5: mu ).
thf(decl_87,type,
n1: mu ).
thf(decl_90,type,
n0: mu ).
thf(decl_92,type,
esk1_0: $i ).
thf(decl_93,type,
esk2_0: $i ).
thf(decl_94,type,
esk3_0: $i ).
thf(decl_95,type,
esk4_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bbIDXZFKjk/E---3.1_2849986.p',mimplies) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bbIDXZFKjk/E---3.1_2849986.p',mor) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bbIDXZFKjk/E---3.1_2849986.p',mnot) ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bbIDXZFKjk/E---3.1_2849986.p',mand) ).
thf(cl5_nebula_array_0026,conjecture,
mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv68 ) ) @ ( mbox_s4 @ ( leq @ pv68 @ ( minus @ n5 @ n1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv68 ) ) @ ( mbox_s4 @ ( leq @ pv68 @ ( minus @ n5 @ n1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bbIDXZFKjk/E---3.1_2849986.p',cl5_nebula_array_0026) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bbIDXZFKjk/E---3.1_2849986.p',mvalid) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X4: $i > $o,X3: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ( X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bbIDXZFKjk/E---3.1_2849986.p',mbox_s4) ).
thf(c_0_7,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_8,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_9,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
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,negated_conjecture,
~ ( mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv68 ) ) @ ( mbox_s4 @ ( leq @ pv68 @ ( minus @ n5 @ n1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv68 ) ) @ ( mbox_s4 @ ( leq @ pv68 @ ( minus @ n5 @ n1 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_array_0026]) ).
thf(c_0_12,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_13,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_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_7,c_0_8]),c_0_9]) ).
thf(c_0_15,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_8]),c_0_9]) ).
thf(c_0_16,negated_conjecture,
~ ! [X127: $i,X126: $i] :
( ~ ( rel_s4 @ X127 @ X126 )
| ~ ~ ( ~ ! [X122: $i] :
( ~ ( rel_s4 @ X126 @ X122 )
| ( leq @ n0 @ pv68 @ X122 ) )
| ~ ! [X123: $i] :
( ~ ( rel_s4 @ X126 @ X123 )
| ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X123 ) ) )
| ~ ( ~ ! [X124: $i] :
( ~ ( rel_s4 @ X126 @ X124 )
| ( leq @ n0 @ pv68 @ X124 ) )
| ~ ! [X125: $i] :
( ~ ( rel_s4 @ X126 @ X125 )
| ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X125 ) ) ) ),
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_11,c_0_12]),c_0_13]),c_0_14]),c_0_15])]) ).
thf(c_0_17,negated_conjecture,
! [X130: $i,X131: $i] :
( ( rel_s4 @ esk1_0 @ esk2_0 )
& ( ~ ( rel_s4 @ esk2_0 @ X130 )
| ( leq @ n0 @ pv68 @ X130 ) )
& ( ~ ( rel_s4 @ esk2_0 @ X131 )
| ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X131 ) )
& ( ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ~ ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk4_0 )
| ~ ( leq @ n0 @ pv68 @ esk3_0 ) )
& ( ~ ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ esk4_0 )
| ~ ( leq @ n0 @ pv68 @ esk3_0 ) ) ),
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_16])])])])])]) ).
thf(c_0_18,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk4_0 )
| ~ ( leq @ n0 @ pv68 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_19,negated_conjecture,
! [X3: $i] :
( ( leq @ n0 @ pv68 @ X3 )
| ~ ( rel_s4 @ esk2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_21,negated_conjecture,
( ~ ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ esk4_0 )
| ~ ( leq @ n0 @ pv68 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,negated_conjecture,
! [X3: $i] :
( ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X3 )
| ~ ( rel_s4 @ esk2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,negated_conjecture,
rel_s4 @ esk2_0 @ esk4_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
thf(c_0_24,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk3_0 )
| ~ ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_25,negated_conjecture,
~ ( leq @ n0 @ pv68 @ esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
thf(c_0_26,negated_conjecture,
rel_s4 @ esk2_0 @ esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_23])]) ).
thf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV085^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:59:59 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.22/0.27 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.bbIDXZFKjk/E---3.1_2849986.p
% 0.22/0.31 % Version: 3.5.1-ho
% 0.22/0.31 % Preprocessing class: HSLSSMSMMLLNHSN.
% 0.22/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting new_ho_10 with 900s (3) cores
% 0.22/0.31 % Starting ehoh_best8_lambda with 900s (3) cores
% 0.22/0.31 % Starting ho_unfolding_3 with 300s (1) cores
% 0.22/0.31 % Starting new_ho_16 with 300s (1) cores
% 0.22/0.31 % new_ho_16 with pid 2850002 completed with status 0
% 0.22/0.31 % Result found by new_ho_16
% 0.22/0.31 % Preprocessing class: HSLSSMSMMLLNHSN.
% 0.22/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting new_ho_10 with 900s (3) cores
% 0.22/0.31 % Starting ehoh_best8_lambda with 900s (3) cores
% 0.22/0.31 % Starting ho_unfolding_3 with 300s (1) cores
% 0.22/0.31 % Starting new_ho_16 with 300s (1) cores
% 0.22/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = LambdaDef)
% 0.22/0.31 % SinE strategy is LambdaDef
% 0.22/0.31 % Search class: HGHNF-FFSF22-SHSSMFNN
% 0.22/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.31 % SubtermCWHack with pid 2850003 completed with status 0
% 0.22/0.31 % Result found by SubtermCWHack
% 0.22/0.31 % Preprocessing class: HSLSSMSMMLLNHSN.
% 0.22/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting new_ho_10 with 900s (3) cores
% 0.22/0.31 % Starting ehoh_best8_lambda with 900s (3) cores
% 0.22/0.31 % Starting ho_unfolding_3 with 300s (1) cores
% 0.22/0.31 % Starting new_ho_16 with 300s (1) cores
% 0.22/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = LambdaDef)
% 0.22/0.31 % SinE strategy is LambdaDef
% 0.22/0.31 % Search class: HGHNF-FFSF22-SHSSMFNN
% 0.22/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.31 % Preprocessing time : 0.002 s
% 0.22/0.31
% 0.22/0.31 % Proof found!
% 0.22/0.31 % SZS status Theorem
% 0.22/0.31 % SZS output start CNFRefutation
% See solution above
% 0.22/0.31 % Parsed axioms : 269
% 0.22/0.31 % Removed by relevancy pruning/SinE : 236
% 0.22/0.31 % Initial clauses : 7
% 0.22/0.31 % Removed in clause preprocessing : 0
% 0.22/0.31 % Initial clauses in saturation : 7
% 0.22/0.31 % Processed clauses : 10
% 0.22/0.31 % ...of these trivial : 0
% 0.22/0.31 % ...subsumed : 0
% 0.22/0.31 % ...remaining for further processing : 10
% 0.22/0.31 % Other redundant clauses eliminated : 0
% 0.22/0.31 % Clauses deleted for lack of memory : 0
% 0.22/0.31 % Backward-subsumed : 2
% 0.22/0.31 % Backward-rewritten : 2
% 0.22/0.31 % Generated clauses : 4
% 0.22/0.31 % ...of the previous two non-redundant : 3
% 0.22/0.31 % ...aggressively subsumed : 0
% 0.22/0.31 % Contextual simplify-reflections : 1
% 0.22/0.31 % Paramodulations : 4
% 0.22/0.31 % Factorizations : 0
% 0.22/0.31 % NegExts : 0
% 0.22/0.31 % Equation resolutions : 0
% 0.22/0.31 % Disequality decompositions : 0
% 0.22/0.31 % Total rewrite steps : 5
% 0.22/0.31 % ...of those cached : 3
% 0.22/0.31 % Propositional unsat checks : 0
% 0.22/0.31 % Propositional check models : 0
% 0.22/0.31 % Propositional check unsatisfiable : 0
% 0.22/0.31 % Propositional clauses : 0
% 0.22/0.31 % Propositional clauses after purity: 0
% 0.22/0.31 % Propositional unsat core size : 0
% 0.22/0.31 % Propositional preprocessing time : 0.000
% 0.22/0.31 % Propositional encoding time : 0.000
% 0.22/0.31 % Propositional solver time : 0.000
% 0.22/0.31 % Success case prop preproc time : 0.000
% 0.22/0.31 % Success case prop encoding time : 0.000
% 0.22/0.31 % Success case prop solver time : 0.000
% 0.22/0.31 % Current number of processed clauses : 6
% 0.22/0.31 % Positive orientable unit clauses : 3
% 0.22/0.31 % Positive unorientable unit clauses: 0
% 0.22/0.31 % Negative unit clauses : 1
% 0.22/0.31 % Non-unit-clauses : 2
% 0.22/0.31 % Current number of unprocessed clauses: 0
% 0.22/0.31 % ...number of literals in the above : 0
% 0.22/0.31 % Current number of archived formulas : 0
% 0.22/0.31 % Current number of archived clauses : 4
% 0.22/0.31 % Clause-clause subsumption calls (NU) : 2
% 0.22/0.31 % Rec. Clause-clause subsumption calls : 2
% 0.22/0.31 % Non-unit clause-clause subsumptions : 1
% 0.22/0.31 % Unit Clause-clause subsumption calls : 2
% 0.22/0.31 % Rewrite failures with RHS unbound : 0
% 0.22/0.31 % BW rewrite match attempts : 2
% 0.22/0.31 % BW rewrite match successes : 2
% 0.22/0.31 % Condensation attempts : 0
% 0.22/0.31 % Condensation successes : 0
% 0.22/0.31 % Termbank termtop insertions : 7373
% 0.22/0.31 % Search garbage collected termcells : 2871
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.008 s
% 0.22/0.31 % System time : 0.002 s
% 0.22/0.31 % Total time : 0.010 s
% 0.22/0.31 % Maximum resident set size: 4376 pages
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.016 s
% 0.22/0.31 % System time : 0.009 s
% 0.22/0.31 % Total time : 0.025 s
% 0.22/0.31 % Maximum resident set size: 5120 pages
% 0.22/0.31 % E exiting
%------------------------------------------------------------------------------