%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM809^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:17:10 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 137 ( 13 ~; 11 |; 12 &; 90 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 2 ^; 29 !; 3 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
c0: $i ).
thf(decl_24,type,
cS: $i > $i ).
thf(decl_25,type,
r: $i > $i > $o ).
thf(decl_26,type,
cIND: $o ).
thf(decl_27,type,
esk1_1: ( $i > $o ) > $i ).
thf(decl_28,type,
esk2_0: $i ).
thf(cTHM130,conjecture,
( ( cIND
& ( r @ c0 @ c0 )
& ! [X2: $i,X3: $i] :
( ( r @ X2 @ X3 )
=> ( r @ ( cS @ X2 ) @ ( cS @ X3 ) ) ) )
=> ! [X2: $i] :
? [X3: $i] : ( r @ X2 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.O1j0pgrtra/E---3.1_3481191.p',cTHM130) ).
thf(cIND_def,axiom,
( cIND
<=> ! [X1: $i > $o] :
( ( ( X1 @ c0 )
& ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ X2 ) ) ) )
=> ! [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.O1j0pgrtra/E---3.1_3481191.p',cIND_def) ).
thf(c_0_2,negated_conjecture,
~ ( ( cIND
& ( r @ c0 @ c0 )
& ! [X2: $i,X3: $i] :
( ( r @ X2 @ X3 )
=> ( r @ ( cS @ X2 ) @ ( cS @ X3 ) ) ) )
=> ! [X2: $i] :
? [X3: $i] : ( r @ X2 @ X3 ) ),
inference(assume_negation,[status(cth)],[cTHM130]) ).
thf(c_0_3,negated_conjecture,
~ ( ( ! [X11: $i > $o] :
( ( ( X11 @ c0 )
& ! [X12: $i] :
( ( X11 @ X12 )
=> ( X11 @ ( cS @ X12 ) ) ) )
=> ! [X13: $i] : ( X11 @ X13 ) )
& ( r @ c0 @ c0 )
& ! [X2: $i,X3: $i] :
( ( r @ X2 @ X3 )
=> ( r @ ( cS @ X2 ) @ ( cS @ X3 ) ) ) )
=> ! [X2: $i] :
? [X3: $i] : ( r @ X2 @ X3 ) ),
inference(apply_def,[status(thm)],[c_0_2,cIND_def]) ).
thf(c_0_4,negated_conjecture,
! [X14: $i > $o,X16: $i,X17: $i,X18: $i,X20: $i] :
( ( ( X14 @ ( esk1_1 @ X14 ) )
| ~ ( X14 @ c0 )
| ( X14 @ X16 ) )
& ( ~ ( X14 @ ( cS @ ( esk1_1 @ X14 ) ) )
| ~ ( X14 @ c0 )
| ( X14 @ X16 ) )
& ( r @ c0 @ c0 )
& ( ~ ( r @ X17 @ X18 )
| ( r @ ( cS @ X17 ) @ ( cS @ X18 ) ) )
& ~ ( r @ esk2_0 @ X20 ) ),
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_3])])])])])]) ).
thf(c_0_5,negated_conjecture,
! [X2: $i,X1: $i > $o] :
( ( X1 @ X2 )
| ~ ( X1 @ ( cS @ ( esk1_1 @ X1 ) ) )
| ~ ( X1 @ c0 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_6,negated_conjecture,
! [X2: $i,X3: $i] :
( ( r @ ( cS @ X2 ) @ ( cS @ X3 ) )
| ~ ( r @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_7,negated_conjecture,
r @ c0 @ c0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_8,negated_conjecture,
! [X2: $i,X1: $i > $o] :
( ( X1 @ ( esk1_1 @ X1 ) )
| ( X1 @ X2 )
| ~ ( X1 @ c0 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_9,negated_conjecture,
! [X2: $i] :
( ( r @ X2 @ X2 )
| ~ ( r
@ ( esk1_1
@ ^ [Z0: $i] : ( r @ Z0 @ Z0 ) )
@ ( esk1_1
@ ^ [Z0: $i] : ( r @ Z0 @ Z0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7])]) ).
thf(c_0_10,negated_conjecture,
! [X2: $i] :
~ ( r @ esk2_0 @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_11,negated_conjecture,
! [X2: $i] : ( r @ X2 @ X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_7]),c_0_9]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_10,c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM809^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n015.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 13:04:33 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 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.O1j0pgrtra/E---3.1_3481191.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSNSFA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting post_as_ho4 with 1200s (4) cores
% 0.07/0.25 % Starting post_as_ho5 with 600s (2) cores
% 0.07/0.25 % Starting new_ho_8 with 300s (1) cores
% 0.07/0.25 % Starting new_ho_4 with 300s (1) cores
% 0.07/0.25 % post_as_ho5 with pid 3481205 completed with status 0
% 0.07/0.25 % Result found by post_as_ho5
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSNSFA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting post_as_ho4 with 1200s (4) cores
% 0.07/0.25 % Starting post_as_ho5 with 600s (2) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.07/0.25 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.07/0.25 % Search class: HGUNF-FFSF11-SSFFMSBN
% 0.07/0.25 % Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 0.07/0.25 % Starting SubtermCWHack with 61s (1) cores
% 0.07/0.25 % Starting post_as_ho12 with 241s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 3481210 completed with status 10
% 0.07/0.25 % Starting new_ho_8 with 91s (1) cores
% 0.07/0.25 % post_as_ho12 with pid 3481212 completed with status 0
% 0.07/0.25 % Result found by post_as_ho12
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSNSFA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting post_as_ho4 with 1200s (4) cores
% 0.07/0.25 % Starting post_as_ho5 with 600s (2) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.07/0.25 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.07/0.25 % Search class: HGUNF-FFSF11-SSFFMSBN
% 0.07/0.25 % Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 0.07/0.25 % Starting SubtermCWHack with 61s (1) cores
% 0.07/0.25 % Starting post_as_ho12 with 241s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25 % Presaturation interreduction done
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 6
% 0.07/0.25 % Removed by relevancy pruning/SinE : 4
% 0.07/0.25 % Initial clauses : 5
% 0.07/0.25 % Removed in clause preprocessing : 0
% 0.07/0.25 % Initial clauses in saturation : 5
% 0.07/0.25 % Processed clauses : 12
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 0
% 0.07/0.25 % ...remaining for further processing : 12
% 0.07/0.25 % Other redundant clauses eliminated : 0
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 0
% 0.07/0.25 % Backward-rewritten : 2
% 0.07/0.25 % Generated clauses : 17
% 0.07/0.25 % ...of the previous two non-redundant : 4
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 1
% 0.07/0.25 % Paramodulations : 9
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 2
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 15
% 0.07/0.25 % ...of those cached : 11
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 5
% 0.07/0.25 % Positive orientable unit clauses : 1
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 1
% 0.07/0.25 % Non-unit-clauses : 3
% 0.07/0.25 % Current number of unprocessed clauses: 2
% 0.07/0.25 % ...number of literals in the above : 6
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 7
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 1
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 1
% 0.07/0.25 % Non-unit clause-clause subsumptions : 1
% 0.07/0.25 % Unit Clause-clause subsumption calls : 1
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 6
% 0.07/0.25 % BW rewrite match successes : 3
% 0.07/0.25 % Condensation attempts : 0
% 0.07/0.25 % Condensation successes : 0
% 0.07/0.25 % Termbank termtop insertions : 1334
% 0.07/0.25 % Search garbage collected termcells : 223
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.005 s
% 0.07/0.25 % System time : 0.004 s
% 0.07/0.25 % Total time : 0.009 s
% 0.07/0.25 % Maximum resident set size: 3632 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.005 s
% 0.07/0.25 % System time : 0.011 s
% 0.07/0.25 % Total time : 0.016 s
% 0.07/0.25 % Maximum resident set size: 4608 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------