%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO053^2 : 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 : n018.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 08:42:14 AM UTC 2026
% Result : Theorem 0.12s 0.25s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 11 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 60 ( 18 ~; 5 |; 1 &; 36 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 37 ( 22 ^; 12 !; 3 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_36,type,
mtrue: $i > $o ).
thf(decl_38,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_39,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
esk1_2: ( $i > $i > $o ) > $i > $i ).
thf(mdia,axiom,
( mdia
= ( ^ [X13: $i > $i > $o,X6: $i > $o] : ( mnot @ ( mbox @ X13 @ ( mnot @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ArrHTHxIrQ/E---3.1_291803.p',mdia) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ArrHTHxIrQ/E---3.1_291803.p',mnot) ).
thf(mbox,axiom,
( mbox
= ( ^ [X13: $i > $i > $o,X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( X13 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ArrHTHxIrQ/E---3.1_291803.p',mbox) ).
thf(conj,conjecture,
? [X13: $i > $i > $o] :
~ ( mvalid @ ( mdia @ X13 @ mtrue ) ),
file('/export/starexec/sandbox/tmp/tmp.ArrHTHxIrQ/E---3.1_291803.p',conj) ).
thf(mtrue,axiom,
( mtrue
= ( ^ [X3: $i] : $true ) ),
file('/export/starexec/sandbox/tmp/tmp.ArrHTHxIrQ/E---3.1_291803.p',mtrue) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ArrHTHxIrQ/E---3.1_291803.p',mvalid) ).
thf(c_0_6,plain,
( mdia
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
~ ! [X21: $i] :
( ~ ( Z0 @ Z2 @ X21 )
| ~ ( Z1 @ X21 ) ) ) ),
inference(fof_simplification,[status(thm)],[mdia]) ).
thf(c_0_7,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_8,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X14: $i] :
( ~ ( Z0 @ Z2 @ X14 )
| ( Z1 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_9,negated_conjecture,
~ ? [X13: $i > $i > $o] :
~ ( mvalid @ ( mdia @ X13 @ mtrue ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_10,plain,
( mtrue
= ( ^ [Z0: $i] : $true ) ),
inference(fof_simplification,[status(thm)],[mtrue]) ).
thf(c_0_11,plain,
( mdia
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
~ ! [X21: $i] :
( ~ ( Z0 @ Z2 @ X21 )
| ~ ( Z1 @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
thf(c_0_12,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_13,negated_conjecture,
~ ? [X13: $i > $i > $o] :
~ ! [X23: $i] :
~ ! [X22: $i] :
( ~ ( X13 @ X23 @ X22 )
| ~ $true ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X24: $i > $i > $o,X25: $i] :
( ( X24 @ X25 @ ( esk1_2 @ X24 @ X25 ) )
& $true ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])])]) ).
thf(c_0_15,negated_conjecture,
! [X13: $i > $i > $o,X3: $i] : ( X13 @ X3 @ ( esk1_2 @ X13 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_16,negated_conjecture,
$false,
inference(flex_resolve,[status(thm)],[c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO053^2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.17 % Computer : n018.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Sep 29 16:27:11 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.21 Running higher-order theorem proving
% 0.12/0.23 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.ArrHTHxIrQ/E---3.1_291803.p
% 0.12/0.25 % Version: 3.5.1-ho
% 0.12/0.25 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.12/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.12/0.25 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.12/0.25 % Starting almost_fo_3_lam with 300s (1) cores
% 0.12/0.25 % Starting post_as_ho1 with 300s (1) cores
% 0.12/0.25 % ehoh_best2_full_lfho with pid 291817 completed with status 0
% 0.12/0.25 % Result found by ehoh_best2_full_lfho
% 0.12/0.25 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.12/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.12/0.25 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.12/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.25 % No SInE strategy applied
% 0.12/0.25 % Search class: HUUNF-FFSF22-SHSSMMBN
% 0.12/0.25 % partial match(1): HGUNF-FFSF22-SHSSMMBN
% 0.12/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.25 % SubtermCWHack with pid 291820 completed with status 0
% 0.12/0.25 % Result found by SubtermCWHack
% 0.12/0.25 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.12/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.12/0.25 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.12/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.25 % No SInE strategy applied
% 0.12/0.25 % Search class: HUUNF-FFSF22-SHSSMMBN
% 0.12/0.25 % partial match(1): HGUNF-FFSF22-SHSSMMBN
% 0.12/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.25 % Preprocessing time : 0.001 s
% 0.12/0.25
% 0.12/0.25 % Proof found!
% 0.12/0.25 % SZS status Theorem
% 0.12/0.25 % SZS output start CNFRefutation
% See solution above
% 0.12/0.25 % Parsed axioms : 64
% 0.12/0.25 % Removed by relevancy pruning/SinE : 0
% 0.12/0.25 % Initial clauses : 34
% 0.12/0.25 % Removed in clause preprocessing : 33
% 0.12/0.25 % Initial clauses in saturation : 1
% 0.12/0.25 % Processed clauses : 1
% 0.12/0.25 % ...of these trivial : 0
% 0.12/0.25 % ...subsumed : 0
% 0.12/0.25 % ...remaining for further processing : 0
% 0.12/0.25 % Other redundant clauses eliminated : 0
% 0.12/0.25 % Clauses deleted for lack of memory : 0
% 0.12/0.25 % Backward-subsumed : 0
% 0.12/0.25 % Backward-rewritten : 0
% 0.12/0.25 % Generated clauses : 0
% 0.12/0.25 % ...of the previous two non-redundant : 0
% 0.12/0.25 % ...aggressively subsumed : 0
% 0.12/0.25 % Contextual simplify-reflections : 0
% 0.12/0.25 % Paramodulations : 0
% 0.12/0.25 % Factorizations : 0
% 0.12/0.25 % NegExts : 0
% 0.12/0.25 % Equation resolutions : 0
% 0.12/0.25 % Disequality decompositions : 0
% 0.12/0.25 % Total rewrite steps : 0
% 0.12/0.25 % ...of those cached : 0
% 0.12/0.25 % Propositional unsat checks : 0
% 0.12/0.25 % Propositional check models : 0
% 0.12/0.25 % Propositional check unsatisfiable : 0
% 0.12/0.25 % Propositional clauses : 0
% 0.12/0.25 % Propositional clauses after purity: 0
% 0.12/0.25 % Propositional unsat core size : 0
% 0.12/0.25 % Propositional preprocessing time : 0.000
% 0.12/0.25 % Propositional encoding time : 0.000
% 0.12/0.25 % Propositional solver time : 0.000
% 0.12/0.25 % Success case prop preproc time : 0.000
% 0.12/0.25 % Success case prop encoding time : 0.000
% 0.12/0.25 % Success case prop solver time : 0.000
% 0.12/0.25 % Current number of processed clauses : 0
% 0.12/0.25 % Positive orientable unit clauses : 0
% 0.12/0.25 % Positive unorientable unit clauses: 0
% 0.12/0.25 % Negative unit clauses : 0
% 0.12/0.25 % Non-unit-clauses : 0
% 0.12/0.25 % Current number of unprocessed clauses: 0
% 0.12/0.25 % ...number of literals in the above : 0
% 0.12/0.25 % Current number of archived formulas : 0
% 0.12/0.25 % Current number of archived clauses : 0
% 0.12/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.12/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.12/0.25 % Non-unit clause-clause subsumptions : 0
% 0.12/0.25 % Unit Clause-clause subsumption calls : 0
% 0.12/0.25 % Rewrite failures with RHS unbound : 0
% 0.12/0.25 % BW rewrite match attempts : 0
% 0.12/0.25 % BW rewrite match successes : 0
% 0.12/0.25 % Condensation attempts : 0
% 0.12/0.25 % Condensation successes : 0
% 0.12/0.25 % Termbank termtop insertions : 1872
% 0.12/0.25 % Search garbage collected termcells : 312
% 0.12/0.25
% 0.12/0.25 % -------------------------------------------------
% 0.12/0.25 % User time : 0.004 s
% 0.12/0.25 % System time : 0.001 s
% 0.12/0.25 % Total time : 0.005 s
% 0.12/0.25 % Maximum resident set size: 3692 pages
% 0.12/0.25
% 0.12/0.25 % -------------------------------------------------
% 0.12/0.25 % User time : 0.008 s
% 0.12/0.25 % System time : 0.004 s
% 0.12/0.25 % Total time : 0.012 s
% 0.12/0.25 % Maximum resident set size: 4864 pages
% 0.12/0.25 % E exiting
%------------------------------------------------------------------------------