%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : MSC020^5 : 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 : 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 08:15:34 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 0 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 251 ( 19 ~; 18 |; 16 &; 188 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 37 ( 4 ^; 33 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cHALF: $i > $i > $o ).
thf(decl_24,type,
cDOUBLE: $i > $i > $o ).
thf(decl_25,type,
cS: $i > $i ).
thf(decl_26,type,
c0: $i ).
thf(decl_27,type,
esk1_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_28,type,
esk2_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_29,type,
esk3_0: $i ).
thf(decl_30,type,
esk4_0: $i ).
thf(cTHM301,conjecture,
( ( ! [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( ( cDOUBLE @ X2 @ X3 )
& ( X1 @ c0 @ c0 )
& ! [X4: $i,X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X1 @ ( cS @ X4 ) @ ( cS @ ( cS @ X5 ) ) ) ) )
=> ( X1 @ X2 @ X3 ) )
& ( cHALF @ c0 @ c0 )
& ( cHALF @ ( cS @ c0 ) @ c0 )
& ! [X4: $i,X5: $i] :
( ( cHALF @ X4 @ X5 )
=> ( cHALF @ ( cS @ ( cS @ X4 ) ) @ ( cS @ X5 ) ) ) )
=> ! [X2: $i,X3: $i] :
( ( cDOUBLE @ X2 @ X3 )
=> ( cHALF @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9gC5ITooWa/E---3.1_2535109.p',cTHM301) ).
thf(c_0_1,negated_conjecture,
~ ( ( ! [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( ( cDOUBLE @ X2 @ X3 )
& ( X1 @ c0 @ c0 )
& ! [X4: $i,X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X1 @ ( cS @ X4 ) @ ( cS @ ( cS @ X5 ) ) ) ) )
=> ( X1 @ X2 @ X3 ) )
& ( cHALF @ c0 @ c0 )
& ( cHALF @ ( cS @ c0 ) @ c0 )
& ! [X4: $i,X5: $i] :
( ( cHALF @ X4 @ X5 )
=> ( cHALF @ ( cS @ ( cS @ X4 ) ) @ ( cS @ X5 ) ) ) )
=> ! [X2: $i,X3: $i] :
( ( cDOUBLE @ X2 @ X3 )
=> ( cHALF @ X3 @ X2 ) ) ),
inference(assume_negation,[status(cth)],[cTHM301]) ).
thf(c_0_2,negated_conjecture,
! [X15: $i > $i > $o,X16: $i,X17: $i,X20: $i,X21: $i] :
( ( ( X15 @ ( esk1_3 @ X15 @ X16 @ X17 ) @ ( esk2_3 @ X15 @ X16 @ X17 ) )
| ~ ( cDOUBLE @ X16 @ X17 )
| ~ ( X15 @ c0 @ c0 )
| ( X15 @ X16 @ X17 ) )
& ( ~ ( X15 @ ( cS @ ( esk1_3 @ X15 @ X16 @ X17 ) ) @ ( cS @ ( cS @ ( esk2_3 @ X15 @ X16 @ X17 ) ) ) )
| ~ ( cDOUBLE @ X16 @ X17 )
| ~ ( X15 @ c0 @ c0 )
| ( X15 @ X16 @ X17 ) )
& ( cHALF @ c0 @ c0 )
& ( cHALF @ ( cS @ c0 ) @ c0 )
& ( ~ ( cHALF @ X20 @ X21 )
| ( cHALF @ ( cS @ ( cS @ X20 ) ) @ ( cS @ X21 ) ) )
& ( cDOUBLE @ esk3_0 @ esk4_0 )
& ~ ( cHALF @ esk4_0 @ 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_1])])])])])]) ).
thf(c_0_3,negated_conjecture,
! [X3: $i,X2: $i,X1: $i > $i > $o] :
( ( X1 @ X2 @ X3 )
| ~ ( X1 @ ( cS @ ( esk1_3 @ X1 @ X2 @ X3 ) ) @ ( cS @ ( cS @ ( esk2_3 @ X1 @ X2 @ X3 ) ) ) )
| ~ ( cDOUBLE @ X2 @ X3 )
| ~ ( X1 @ c0 @ c0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
cDOUBLE @ esk3_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,negated_conjecture,
! [X3: $i,X2: $i,X1: $i > $i > $o] :
( ( X1 @ ( esk1_3 @ X1 @ X2 @ X3 ) @ ( esk2_3 @ X1 @ X2 @ X3 ) )
| ( X1 @ X2 @ X3 )
| ~ ( cDOUBLE @ X2 @ X3 )
| ~ ( X1 @ c0 @ c0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i > $i > $o] :
( ( X1 @ esk3_0 @ esk4_0 )
| ~ ( X1 @ ( cS @ ( esk1_3 @ X1 @ esk3_0 @ esk4_0 ) ) @ ( cS @ ( cS @ ( esk2_3 @ X1 @ esk3_0 @ esk4_0 ) ) ) )
| ~ ( X1 @ c0 @ c0 ) ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_7,negated_conjecture,
! [X2: $i,X3: $i] :
( ( cHALF @ ( cS @ ( cS @ X2 ) ) @ ( cS @ X3 ) )
| ~ ( cHALF @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_8,negated_conjecture,
cHALF @ c0 @ c0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_9,negated_conjecture,
~ ( cHALF @ esk4_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i > $i > $o] :
( ( X1 @ ( esk1_3 @ X1 @ esk3_0 @ esk4_0 ) @ ( esk2_3 @ X1 @ esk3_0 @ esk4_0 ) )
| ( X1 @ esk3_0 @ esk4_0 )
| ~ ( X1 @ c0 @ c0 ) ),
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
thf(c_0_11,negated_conjecture,
~ ( cHALF
@ ( esk2_3
@ ^ [Z0: $i,Z1: $i] : ( cHALF @ Z1 @ Z0 )
@ esk3_0
@ esk4_0 )
@ ( esk1_3
@ ^ [Z0: $i,Z1: $i] : ( cHALF @ Z1 @ Z0 )
@ esk3_0
@ esk4_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]),c_0_9]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_8]),c_0_11]),c_0_9]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MSC020^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/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 11:21:15 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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.9gC5ITooWa/E---3.1_2535109.p
% 0.08/0.27 % Version: 3.5.1-ho
% 0.08/0.27 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.08/0.27 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.27 % Starting post_as_ho12 with 300s (1) cores
% 0.08/0.27 % Starting new_bool_9 with 300s (1) cores
% 0.08/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.27 % Starting post_as_ho4 with 300s (1) cores
% 0.08/0.27 % Starting post_as_ho2 with 300s (1) cores
% 0.08/0.27 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.08/0.27 % Starting full_lambda_10 with 300s (1) cores
% 0.08/0.27 % Starting new_ho_8 with 300s (1) cores
% 0.08/0.27 % post_as_ho12 with pid 2535122 completed with status 0
% 0.08/0.27 % Result found by post_as_ho12
% 0.08/0.27 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.08/0.27 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.27 % Starting post_as_ho12 with 300s (1) cores
% 0.08/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.27 % No SInE strategy applied
% 0.08/0.27 % Search class: HGUNF-FFSS32-MSSFFSBN
% 0.08/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.27 % SubtermCWHack with pid 2535132 completed with status 10
% 0.08/0.27 % Starting post_as_ho12 with 181s (1) cores
% 0.08/0.27 % post_as_ho12 with pid 2535139 completed with status 0
% 0.08/0.27 % Result found by post_as_ho12
% 0.08/0.27 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.08/0.27 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.27 % Starting post_as_ho12 with 300s (1) cores
% 0.08/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.27 % No SInE strategy applied
% 0.08/0.27 % Search class: HGUNF-FFSS32-MSSFFSBN
% 0.08/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.27 % SubtermCWHack with pid 2535132 completed with status 10
% 0.08/0.27 % Starting post_as_ho12 with 181s (1) cores
% 0.08/0.27 % Preprocessing time : 0.001 s
% 0.08/0.27 % Presaturation interreduction done
% 0.08/0.27
% 0.08/0.27 % Proof found!
% 0.08/0.27 % SZS status Theorem
% 0.08/0.27 % SZS output start CNFRefutation
% See solution above
% 0.08/0.27 % Parsed axioms : 5
% 0.08/0.27 % Removed by relevancy pruning/SinE : 0
% 0.08/0.27 % Initial clauses : 11
% 0.08/0.27 % Removed in clause preprocessing : 4
% 0.08/0.27 % Initial clauses in saturation : 7
% 0.08/0.27 % Processed clauses : 18
% 0.08/0.27 % ...of these trivial : 0
% 0.08/0.27 % ...subsumed : 0
% 0.08/0.27 % ...remaining for further processing : 18
% 0.08/0.27 % Other redundant clauses eliminated : 0
% 0.08/0.27 % Clauses deleted for lack of memory : 0
% 0.08/0.27 % Backward-subsumed : 0
% 0.08/0.27 % Backward-rewritten : 0
% 0.08/0.27 % Generated clauses : 16
% 0.08/0.27 % ...of the previous two non-redundant : 7
% 0.08/0.27 % ...aggressively subsumed : 0
% 0.08/0.27 % Contextual simplify-reflections : 0
% 0.08/0.27 % Paramodulations : 8
% 0.08/0.27 % Factorizations : 0
% 0.08/0.27 % NegExts : 0
% 0.08/0.27 % Equation resolutions : 2
% 0.08/0.27 % Disequality decompositions : 0
% 0.08/0.27 % Total rewrite steps : 2
% 0.08/0.27 % ...of those cached : 1
% 0.08/0.27 % Propositional unsat checks : 0
% 0.08/0.27 % Propositional check models : 0
% 0.08/0.27 % Propositional check unsatisfiable : 0
% 0.08/0.27 % Propositional clauses : 0
% 0.08/0.27 % Propositional clauses after purity: 0
% 0.08/0.27 % Propositional unsat core size : 0
% 0.08/0.27 % Propositional preprocessing time : 0.000
% 0.08/0.27 % Propositional encoding time : 0.000
% 0.08/0.27 % Propositional solver time : 0.000
% 0.08/0.27 % Success case prop preproc time : 0.000
% 0.08/0.27 % Success case prop encoding time : 0.000
% 0.08/0.27 % Success case prop solver time : 0.000
% 0.08/0.27 % Current number of processed clauses : 11
% 0.08/0.27 % Positive orientable unit clauses : 3
% 0.08/0.27 % Positive unorientable unit clauses: 0
% 0.08/0.27 % Negative unit clauses : 2
% 0.08/0.27 % Non-unit-clauses : 6
% 0.08/0.27 % Current number of unprocessed clauses: 2
% 0.08/0.27 % ...number of literals in the above : 8
% 0.08/0.27 % Current number of archived formulas : 0
% 0.08/0.27 % Current number of archived clauses : 7
% 0.08/0.27 % Clause-clause subsumption calls (NU) : 1
% 0.08/0.27 % Rec. Clause-clause subsumption calls : 1
% 0.08/0.27 % Non-unit clause-clause subsumptions : 0
% 0.08/0.27 % Unit Clause-clause subsumption calls : 0
% 0.08/0.27 % Rewrite failures with RHS unbound : 0
% 0.08/0.27 % BW rewrite match attempts : 0
% 0.08/0.27 % BW rewrite match successes : 0
% 0.08/0.27 % Condensation attempts : 0
% 0.08/0.27 % Condensation successes : 0
% 0.08/0.27 % Termbank termtop insertions : 2607
% 0.08/0.27 % Search garbage collected termcells : 278
% 0.08/0.27
% 0.08/0.27 % -------------------------------------------------
% 0.08/0.27 % User time : 0.006 s
% 0.08/0.27 % System time : 0.002 s
% 0.08/0.27 % Total time : 0.008 s
% 0.08/0.27 % Maximum resident set size: 3636 pages
% 0.08/0.27
% 0.08/0.27 % -------------------------------------------------
% 0.08/0.27 % User time : 0.006 s
% 0.08/0.27 % System time : 0.009 s
% 0.08/0.27 % Total time : 0.014 s
% 0.08/0.27 % Maximum resident set size: 4608 pages
% 0.08/0.27 % E exiting
%------------------------------------------------------------------------------