%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO016^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:42:08 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 232 ( 2 equ; 0 cnn)
% Maximal formula atoms : 172 ( 15 avg)
% Number of connectives : 320 ( 87 ~; 83 |; 30 &; 116 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 7 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 4 ^; 6 !; 2 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
leibeq: $o > $o > $o ).
thf(decl_24,type,
h: $o > $o ).
thf(decl_25,type,
epred1_0: $o > $o ).
thf(conj,conjecture,
leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ ~ $true ) ) ) @ ( h @ ~ $true ),
file('/export/starexec/sandbox/tmp/tmp.0KQwC6QCqd/E---3.1_7560.p',conj) ).
thf(leibeq,axiom,
( leibeq
= ( ^ [X1: $o,X2: $o] :
! [X3: $o > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0KQwC6QCqd/E---3.1_7560.p',leibeq) ).
thf(c_0_2,negated_conjecture,
~ ( leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ ~ $true ) ) ) @ ( h @ ~ $true ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_3,plain,
( leibeq
= ( ^ [Z0: $o,Z1: $o] :
! [X3: $o > $o] :
( ( X3 @ Z0 )
=> ( X3 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[leibeq]) ).
thf(c_0_4,negated_conjecture,
~ ! [X5: $o > $o] :
( ( X5
@ ( h
@ ! [X4: $o > $o] :
( ( X4 @ ( h @ $true ) )
=> ( X4 @ ( h @ ~ $true ) ) ) ) )
=> ( X5 @ ( h @ ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_2,c_0_3]) ).
thf(c_0_5,negated_conjecture,
( ( ? [X4: $o > $o] :
( ( X4 @ ( h @ $true ) )
& ~ ( X4 @ ( h @ ~ $true ) ) )
| ~ ( h @ $true )
| ( epred1_0 @ $true ) )
& ( ! [X4: $o > $o] :
( ~ ( X4 @ ( h @ $true ) )
| ( X4 @ ( h @ ~ $true ) ) )
| ~ ( h @ $false )
| ( epred1_0 @ $true ) )
& ( ? [X4: $o > $o] :
( ( X4 @ ( h @ $true ) )
& ~ ( X4 @ ( h @ ~ $true ) ) )
| ( h @ $true )
| ( epred1_0 @ $false ) )
& ( ! [X4: $o > $o] :
( ~ ( X4 @ ( h @ $true ) )
| ( X4 @ ( h @ ~ $true ) ) )
| ( h @ $false )
| ( epred1_0 @ $false ) )
& ( $true
| ~ $true
| $true
| ~ $true )
& ( ~ ( h @ $false )
| ~ $true
| $true
| ~ $true )
& ( $true
| ~ ( h @ $true )
| $true
| ~ $true )
& ( ~ ( h @ $false )
| ~ ( h @ $true )
| $true
| ~ $true )
& ( ~ ( epred1_0 @ $false )
| $true
| ~ $true )
& ( $true
| ~ $true
| ( h @ $false )
| ~ $true )
& ( ~ ( h @ $false )
| ~ $true
| ( h @ $false )
| ~ $true )
& ( $true
| ~ ( h @ $true )
| ( h @ $false )
| ~ $true )
& ( ~ ( h @ $false )
| ~ ( h @ $true )
| ( h @ $false )
| ~ $true )
& ( ~ ( epred1_0 @ $false )
| ( h @ $false )
| ~ $true )
& ( $true
| ~ $true
| $true
| ( h @ $true ) )
& ( ~ ( h @ $false )
| ~ $true
| $true
| ( h @ $true ) )
& ( $true
| ~ ( h @ $true )
| $true
| ( h @ $true ) )
& ( ~ ( h @ $false )
| ~ ( h @ $true )
| $true
| ( h @ $true ) )
& ( ~ ( epred1_0 @ $false )
| $true
| ( h @ $true ) )
& ( $true
| ~ $true
| ( h @ $false )
| ( h @ $true ) )
& ( ~ ( h @ $false )
| ~ $true
| ( h @ $false )
| ( h @ $true ) )
& ( $true
| ~ ( h @ $true )
| ( h @ $false )
| ( h @ $true ) )
& ( ~ ( h @ $false )
| ~ ( h @ $true )
| ( h @ $false )
| ( h @ $true ) )
& ( ~ ( epred1_0 @ $false )
| ( h @ $false )
| ( h @ $true ) )
& ( $true
| ~ $true
| ~ ( epred1_0 @ $true ) )
& ( ~ ( h @ $false )
| ~ $true
| ~ ( epred1_0 @ $true ) )
& ( $true
| ~ ( h @ $true )
| ~ ( epred1_0 @ $true ) )
& ( ~ ( h @ $false )
| ~ ( h @ $true )
| ~ ( epred1_0 @ $true ) )
& ( ~ ( epred1_0 @ $false )
| ~ ( epred1_0 @ $true ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).
thf(c_0_6,negated_conjecture,
( ( h @ ~ $true )
| ~ ( epred1_0 @ ~ $true )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
( ( h @ ~ $true )
| ~ ( epred1_0 @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
( ( h @ ~ $true )
| ( epred1_0 @ ~ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
( ~ ( h @ ~ $true )
| ~ $true
| ~ ( epred1_0 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,negated_conjecture,
( ( epred1_0 @ $true )
| ~ ( h @ ~ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_11,negated_conjecture,
h @ ~ $true,
inference(csr,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_12,negated_conjecture,
( ~ ( epred1_0 @ $true )
| ~ ( h @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
epred1_0 @ $true,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO016^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n009.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:21:30 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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.0KQwC6QCqd/E---3.1_7560.p
% 0.09/0.26 % Version: 3.5.1-ho
% 0.09/0.26 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.26 % Starting post_as_ho5 with 300s (1) cores
% 0.09/0.26 % Starting sh4l with 300s (1) cores
% 0.09/0.26 % Starting ho_unfolding_2 with 300s (1) cores
% 0.09/0.26 % sh4l with pid 7595 completed with status 0
% 0.09/0.26 % Result found by sh4l
% 0.09/0.26 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.26 % Starting post_as_ho5 with 300s (1) cores
% 0.09/0.26 % Starting sh4l with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HGHNF-FFSF00-SSFFMFNN
% 0.09/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.26 % SubtermCWHack with pid 7600 completed with status 0
% 0.09/0.26 % Result found by SubtermCWHack
% 0.09/0.26 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.26 % Starting post_as_ho5 with 300s (1) cores
% 0.09/0.26 % Starting sh4l with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HGHNF-FFSF00-SSFFMFNN
% 0.09/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.26 % Preprocessing time : 0.001 s
% 0.09/0.26
% 0.09/0.26 % Proof found!
% 0.09/0.26 % SZS status Theorem
% 0.09/0.26 % SZS output start CNFRefutation
% See solution above
% 0.09/0.26 % Parsed axioms : 4
% 0.09/0.26 % Removed by relevancy pruning/SinE : 0
% 0.09/0.26 % Initial clauses : 31
% 0.09/0.26 % Removed in clause preprocessing : 22
% 0.09/0.26 % Initial clauses in saturation : 9
% 0.09/0.26 % Processed clauses : 7
% 0.09/0.26 % ...of these trivial : 0
% 0.09/0.26 % ...subsumed : 0
% 0.09/0.26 % ...remaining for further processing : 6
% 0.09/0.26 % Other redundant clauses eliminated : 0
% 0.09/0.26 % Clauses deleted for lack of memory : 0
% 0.09/0.26 % Backward-subsumed : 1
% 0.09/0.26 % Backward-rewritten : 2
% 0.09/0.26 % Generated clauses : 2
% 0.09/0.26 % ...of the previous two non-redundant : 3
% 0.09/0.26 % ...aggressively subsumed : 0
% 0.09/0.26 % Contextual simplify-reflections : 1
% 0.09/0.26 % Paramodulations : 2
% 0.09/0.26 % Factorizations : 0
% 0.09/0.26 % NegExts : 0
% 0.09/0.26 % Equation resolutions : 0
% 0.09/0.26 % Disequality decompositions : 0
% 0.09/0.26 % Total rewrite steps : 4
% 0.09/0.26 % ...of those cached : 2
% 0.09/0.26 % Propositional unsat checks : 0
% 0.09/0.26 % Propositional check models : 0
% 0.09/0.26 % Propositional check unsatisfiable : 0
% 0.09/0.26 % Propositional clauses : 0
% 0.09/0.26 % Propositional clauses after purity: 0
% 0.09/0.26 % Propositional unsat core size : 0
% 0.09/0.26 % Propositional preprocessing time : 0.000
% 0.09/0.26 % Propositional encoding time : 0.000
% 0.09/0.26 % Propositional solver time : 0.000
% 0.09/0.26 % Success case prop preproc time : 0.000
% 0.09/0.26 % Success case prop encoding time : 0.000
% 0.09/0.26 % Success case prop solver time : 0.000
% 0.09/0.26 % Current number of processed clauses : 3
% 0.09/0.26 % Positive orientable unit clauses : 2
% 0.09/0.26 % Positive unorientable unit clauses: 0
% 0.09/0.26 % Negative unit clauses : 0
% 0.09/0.26 % Non-unit-clauses : 1
% 0.09/0.26 % Current number of unprocessed clauses: 5
% 0.09/0.26 % ...number of literals in the above : 12
% 0.09/0.26 % Current number of archived formulas : 0
% 0.09/0.26 % Current number of archived clauses : 3
% 0.09/0.26 % Clause-clause subsumption calls (NU) : 2
% 0.09/0.26 % Rec. Clause-clause subsumption calls : 2
% 0.09/0.26 % Non-unit clause-clause subsumptions : 1
% 0.09/0.26 % Unit Clause-clause subsumption calls : 3
% 0.09/0.26 % Rewrite failures with RHS unbound : 0
% 0.09/0.26 % BW rewrite match attempts : 2
% 0.09/0.26 % BW rewrite match successes : 2
% 0.09/0.26 % Condensation attempts : 0
% 0.09/0.26 % Condensation successes : 0
% 0.09/0.26 % Termbank termtop insertions : 997
% 0.09/0.26 % Search garbage collected termcells : 215
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.001 s
% 0.09/0.26 % System time : 0.004 s
% 0.09/0.26 % Total time : 0.005 s
% 0.09/0.26 % Maximum resident set size: 3628 pages
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.002 s
% 0.09/0.26 % System time : 0.006 s
% 0.09/0.26 % Total time : 0.009 s
% 0.09/0.26 % Maximum resident set size: 4864 pages
% 0.09/0.26 % E exiting
%------------------------------------------------------------------------------