%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM802^5 : 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 : n020.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 08:17:09 AM UTC 2026
% Result : Theorem 0.26s 0.38s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 7 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 80 ( 15 ~; 4 |; 5 &; 47 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 1 ^; 16 !; 3 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
c_2: $i ).
thf(decl_24,type,
absval: $i > $i ).
thf(decl_25,type,
c0: $i ).
thf(decl_26,type,
c_less_: $i > $i > $o ).
thf(decl_27,type,
esk1_1: ( $i > $o ) > $i ).
thf(cBLEDSOE_FENG_8,conjecture,
( ( c_less_ @ c_2 @ c0 )
=> ( ! [X1: $i,X2: $i] :
( ( c_less_ @ X1 @ c0 )
=> ( X1
!= ( absval @ X2 ) ) )
=> ? [X3: $i > $o] :
( ! [X4: $i] :
~ ( X3 @ ( absval @ X4 ) )
& ( X3 @ c_2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ki3KrTwJnX/E---3.1_1012168.p',cBLEDSOE_FENG_8) ).
thf(c_0_1,negated_conjecture,
~ ( ( c_less_ @ c_2 @ c0 )
=> ( ! [X1: $i,X2: $i] :
( ( c_less_ @ X1 @ c0 )
=> ( X1
!= ( absval @ X2 ) ) )
=> ? [X3: $i > $o] :
( ! [X4: $i] :
~ ( X3 @ ( absval @ X4 ) )
& ( X3 @ c_2 ) ) ) ),
inference(assume_negation,[status(cth)],[cBLEDSOE_FENG_8]) ).
thf(c_0_2,negated_conjecture,
~ ( ( c_less_ @ c_2 @ c0 )
=> ( ! [X1: $i,X2: $i] :
( ( c_less_ @ X1 @ c0 )
=> ( X1
!= ( absval @ X2 ) ) )
=> ? [X3: $i > $o] :
( ! [X4: $i] :
~ ( X3 @ ( absval @ X4 ) )
& ( X3 @ c_2 ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X9: $i,X10: $i,X11: $i > $o] :
( ( c_less_ @ c_2 @ c0 )
& ( ~ ( c_less_ @ X9 @ c0 )
| ( X9
!= ( absval @ X10 ) ) )
& ( ( X11 @ ( absval @ ( esk1_1 @ X11 ) ) )
| ~ ( X11 @ c_2 ) ) ),
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_2])])])])]) ).
thf(c_0_4,negated_conjecture,
! [X1: $i,X2: $i] :
( ~ ( c_less_ @ X1 @ c0 )
| ( X1
!= ( absval @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X3: $i > $o] :
( ( X3 @ ( absval @ ( esk1_1 @ X3 ) ) )
| ~ ( X3 @ c_2 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i] :
~ ( c_less_ @ ( absval @ X1 ) @ c0 ),
inference(er,[status(thm)],[c_0_4]) ).
thf(c_0_7,negated_conjecture,
( ( absval
@ ( esk1_1
@ ^ [Z0: $i] : ( Z0 = c_2 ) ) )
= c_2 ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_5]) ).
thf(c_0_8,negated_conjecture,
c_less_ @ c_2 @ c0,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_9,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM802^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.27 % Computer : n020.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8046.5625MB
% 0.08/0.27 % OS : Linux 6.8.0-71-generic
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Tue Sep 29 13:01:34 UTC 2026
% 0.08/0.27 % CPUTime :
% 0.08/0.27 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.34 Running higher-order theorem proving
% 0.26/0.35 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.Ki3KrTwJnX/E---3.1_1012168.p
% 0.26/0.38 % Version: 3.5.1-ho
% 0.26/0.38 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.26/0.38 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.38 % Starting post_as_ho12 with 300s (1) cores
% 0.26/0.38 % Starting new_bool_9 with 300s (1) cores
% 0.26/0.38 % Starting post_as_ho1 with 300s (1) cores
% 0.26/0.38 % Starting post_as_ho4 with 300s (1) cores
% 0.26/0.38 % Starting post_as_ho2 with 300s (1) cores
% 0.26/0.38 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.26/0.38 % Starting full_lambda_10 with 300s (1) cores
% 0.26/0.38 % Starting new_ho_8 with 300s (1) cores
% 0.26/0.38 % ehoh_best2_full_lfho with pid 1012187 completed with status 0
% 0.26/0.38 % Result found by ehoh_best2_full_lfho
% 0.26/0.38 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.26/0.38 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.38 % Starting post_as_ho12 with 300s (1) cores
% 0.26/0.38 % Starting new_bool_9 with 300s (1) cores
% 0.26/0.38 % Starting post_as_ho1 with 300s (1) cores
% 0.26/0.38 % Starting post_as_ho4 with 300s (1) cores
% 0.26/0.38 % Starting post_as_ho2 with 300s (1) cores
% 0.26/0.38 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.26/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.38 % No SInE strategy applied
% 0.26/0.38 % Search class: HHHSF-FFSF11-SSSFFSBN
% 0.26/0.38 % partial match(1): HGHSF-FFSF11-SSSFFSBN
% 0.26/0.38 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.38 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.38 % SubtermCWHack with pid 1012192 completed with status 10
% 0.26/0.38 % Starting ehoh_best2_full_lfho with 181s (1) cores
% 0.26/0.38 % ehoh_best2_full_lfho with pid 1012198 completed with status 0
% 0.26/0.38 % Result found by ehoh_best2_full_lfho
% 0.26/0.38 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.26/0.38 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.38 % Starting post_as_ho12 with 300s (1) cores
% 0.26/0.38 % Starting new_bool_9 with 300s (1) cores
% 0.26/0.38 % Starting post_as_ho1 with 300s (1) cores
% 0.26/0.38 % Starting post_as_ho4 with 300s (1) cores
% 0.26/0.38 % Starting post_as_ho2 with 300s (1) cores
% 0.26/0.38 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.26/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.38 % No SInE strategy applied
% 0.26/0.38 % Search class: HHHSF-FFSF11-SSSFFSBN
% 0.26/0.38 % partial match(1): HGHSF-FFSF11-SSSFFSBN
% 0.26/0.38 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.38 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.38 % SubtermCWHack with pid 1012192 completed with status 10
% 0.26/0.38 % Starting ehoh_best2_full_lfho with 181s (1) cores
% 0.26/0.38 % Preprocessing time : 0.001 s
% 0.26/0.38
% 0.26/0.38 % Proof found!
% 0.26/0.38 % SZS status Theorem
% 0.26/0.38 % SZS output start CNFRefutation
% See solution above
% 0.26/0.38 % Parsed axioms : 5
% 0.26/0.38 % Removed by relevancy pruning/SinE : 0
% 0.26/0.38 % Initial clauses : 7
% 0.26/0.38 % Removed in clause preprocessing : 4
% 0.26/0.38 % Initial clauses in saturation : 3
% 0.26/0.38 % Processed clauses : 5
% 0.26/0.38 % ...of these trivial : 0
% 0.26/0.38 % ...subsumed : 0
% 0.26/0.38 % ...remaining for further processing : 5
% 0.26/0.38 % Other redundant clauses eliminated : 1
% 0.26/0.38 % Clauses deleted for lack of memory : 0
% 0.26/0.38 % Backward-subsumed : 0
% 0.26/0.38 % Backward-rewritten : 0
% 0.26/0.38 % Generated clauses : 10
% 0.26/0.38 % ...of the previous two non-redundant : 6
% 0.26/0.38 % ...aggressively subsumed : 0
% 0.26/0.38 % Contextual simplify-reflections : 0
% 0.26/0.38 % Paramodulations : 2
% 0.26/0.38 % Factorizations : 0
% 0.26/0.38 % NegExts : 0
% 0.26/0.38 % Equation resolutions : 1
% 0.26/0.38 % Disequality decompositions : 0
% 0.26/0.38 % Total rewrite steps : 1
% 0.26/0.38 % ...of those cached : 0
% 0.26/0.38 % Propositional unsat checks : 0
% 0.26/0.38 % Propositional check models : 0
% 0.26/0.38 % Propositional check unsatisfiable : 0
% 0.26/0.38 % Propositional clauses : 0
% 0.26/0.38 % Propositional clauses after purity: 0
% 0.26/0.38 % Propositional unsat core size : 0
% 0.26/0.38 % Propositional preprocessing time : 0.000
% 0.26/0.38 % Propositional encoding time : 0.000
% 0.26/0.38 % Propositional solver time : 0.000
% 0.26/0.38 % Success case prop preproc time : 0.000
% 0.26/0.38 % Success case prop encoding time : 0.000
% 0.26/0.38 % Success case prop solver time : 0.000
% 0.26/0.38 % Current number of processed clauses : 4
% 0.26/0.38 % Positive orientable unit clauses : 2
% 0.26/0.38 % Positive unorientable unit clauses: 0
% 0.26/0.38 % Negative unit clauses : 1
% 0.26/0.38 % Non-unit-clauses : 1
% 0.26/0.38 % Current number of unprocessed clauses: 4
% 0.26/0.38 % ...number of literals in the above : 8
% 0.26/0.38 % Current number of archived formulas : 0
% 0.26/0.38 % Current number of archived clauses : 0
% 0.26/0.38 % Clause-clause subsumption calls (NU) : 0
% 0.26/0.38 % Rec. Clause-clause subsumption calls : 0
% 0.26/0.38 % Non-unit clause-clause subsumptions : 0
% 0.26/0.38 % Unit Clause-clause subsumption calls : 0
% 0.26/0.38 % Rewrite failures with RHS unbound : 0
% 0.26/0.38 % BW rewrite match attempts : 0
% 0.26/0.38 % BW rewrite match successes : 0
% 0.26/0.38 % Condensation attempts : 0
% 0.26/0.38 % Condensation successes : 0
% 0.26/0.38 % Termbank termtop insertions : 527
% 0.26/0.38 % Search garbage collected termcells : 112
% 0.26/0.38
% 0.26/0.38 % -------------------------------------------------
% 0.26/0.38 % User time : 0.003 s
% 0.26/0.38 % System time : 0.003 s
% 0.26/0.38 % Total time : 0.006 s
% 0.26/0.38 % Maximum resident set size: 3632 pages
% 0.26/0.38
% 0.26/0.38 % -------------------------------------------------
% 0.26/0.38 % User time : 0.004 s
% 0.26/0.38 % System time : 0.011 s
% 0.26/0.38 % Total time : 0.015 s
% 0.26/0.38 % Maximum resident set size: 4608 pages
% 0.26/0.38 % E exiting
%------------------------------------------------------------------------------