%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM706^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:16:54 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 71 ( 6 ~; 2 |; 1 &; 57 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 33 ( 26 ^; 7 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_24,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_26,type,
in: $i > $i > $o ).
thf(decl_78,type,
e_is: $i > $i > $i > $o ).
thf(decl_124,type,
nat: $i ).
thf(decl_125,type,
n_is: $i > $i > $o ).
thf(decl_131,type,
n_1: $i ).
thf(decl_163,type,
n_ts: $i > $i > $i ).
thf(decl_165,type,
esk1_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sYsLALt2dR/E---3.1_659729.p',def_e_is) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sYsLALt2dR/E---3.1_659729.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sYsLALt2dR/E---3.1_659729.p',def_is_of) ).
thf(satz28e,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ X1 @ ( n_ts @ X1 @ n_1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sYsLALt2dR/E---3.1_659729.p',satz28e) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sYsLALt2dR/E---3.1_659729.p',def_n_is) ).
thf(satz28a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( n_ts @ X1 @ n_1 ) @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.sYsLALt2dR/E---3.1_659729.p',satz28a) ).
thf(c_0_6,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_7,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_all_of]) ).
thf(c_0_8,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_9,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ X1 @ ( n_ts @ X1 @ n_1 ) ) ),
inference(assume_negation,[status(cth)],[satz28e]) ).
thf(c_0_10,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_6]) ).
thf(c_0_11,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_12,negated_conjecture,
~ ! [X443: $i] :
( ( in @ X443 @ nat )
=> ( X443
= ( n_ts @ X443 @ n_1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_9]),c_0_10]),c_0_11]) ).
thf(c_0_13,plain,
! [X464: $i] :
( ( in @ X464 @ nat )
=> ( ( n_ts @ X464 @ n_1 )
= X464 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz28a]),c_0_10]),c_0_11]) ).
thf(c_0_14,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( esk1_0
!= ( n_ts @ esk1_0 @ n_1 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
thf(c_0_15,plain,
! [X623: $i] :
( ~ ( in @ X623 @ nat )
| ( ( n_ts @ X623 @ n_1 )
= X623 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
thf(c_0_16,negated_conjecture,
( esk1_0
!= ( n_ts @ esk1_0 @ n_1 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,plain,
! [X1: $i] :
( ( ( n_ts @ X1 @ n_1 )
= X1 )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM706^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.16 % Computer : n006.cluster.edu
% 0.06/0.16 % Model : x86_64 x86_64
% 0.06/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.16 % Memory : 8046.5625MB
% 0.06/0.16 % OS : Linux 6.8.0-71-generic
% 0.06/0.16 % CPULimit : 300
% 0.06/0.16 % WCLimit : 300
% 0.06/0.16 % DateTime : Tue Sep 29 12:42:39 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running higher-order theorem proving
% 0.06/0.25 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.sYsLALt2dR/E---3.1_659729.p
% 0.22/0.31 % Version: 3.5.1-ho
% 0.22/0.31 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.22/0.31 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting lpo1_fix with 900s (3) cores
% 0.22/0.31 % Starting full_lambda_9 with 300s (1) cores
% 0.22/0.31 % Starting almost_fo_4 with 300s (1) cores
% 0.22/0.31 % Starting new_ho_9 with 300s (1) cores
% 0.22/0.31 % Starting pre_casc_4 with 300s (1) cores
% 0.22/0.31 % Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.31 % pre_casc_4 with pid 659746 completed with status 0
% 0.22/0.31 % Result found by pre_casc_4
% 0.22/0.31 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.22/0.31 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting lpo1_fix with 900s (3) cores
% 0.22/0.31 % Starting full_lambda_9 with 300s (1) cores
% 0.22/0.31 % Starting almost_fo_4 with 300s (1) cores
% 0.22/0.31 % Starting new_ho_9 with 300s (1) cores
% 0.22/0.31 % Starting pre_casc_4 with 300s (1) cores
% 0.22/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.22/0.31 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.22/0.31 % Search class: HGUSM-FSLM31-DHSMMSBN
% 0.22/0.31 % partial match(2): HGHSM-FSLM31-MHSMMSBN
% 0.22/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.31 % SubtermCWHack with pid 659748 completed with status 0
% 0.22/0.31 % Result found by SubtermCWHack
% 0.22/0.31 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.22/0.31 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting lpo1_fix with 900s (3) cores
% 0.22/0.31 % Starting full_lambda_9 with 300s (1) cores
% 0.22/0.31 % Starting almost_fo_4 with 300s (1) cores
% 0.22/0.31 % Starting new_ho_9 with 300s (1) cores
% 0.22/0.31 % Starting pre_casc_4 with 300s (1) cores
% 0.22/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.22/0.31 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.22/0.31 % Search class: HGUSM-FSLM31-DHSMMSBN
% 0.22/0.31 % partial match(2): HGHSM-FSLM31-MHSMMSBN
% 0.22/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.31 % Preprocessing time : 0.005 s
% 0.22/0.31
% 0.22/0.31 % Proof found!
% 0.22/0.31 % SZS status Theorem
% 0.22/0.31 % SZS output start CNFRefutation
% See solution above
% 0.22/0.31 % Parsed axioms : 436
% 0.22/0.31 % Removed by relevancy pruning/SinE : 325
% 0.22/0.31 % Initial clauses : 152
% 0.22/0.31 % Removed in clause preprocessing : 9
% 0.22/0.31 % Initial clauses in saturation : 143
% 0.22/0.31 % Processed clauses : 30
% 0.22/0.31 % ...of these trivial : 2
% 0.22/0.31 % ...subsumed : 1
% 0.22/0.31 % ...remaining for further processing : 27
% 0.22/0.31 % Other redundant clauses eliminated : 0
% 0.22/0.31 % Clauses deleted for lack of memory : 0
% 0.22/0.31 % Backward-subsumed : 0
% 0.22/0.31 % Backward-rewritten : 0
% 0.22/0.31 % Generated clauses : 9
% 0.22/0.31 % ...of the previous two non-redundant : 6
% 0.22/0.31 % ...aggressively subsumed : 0
% 0.22/0.31 % Contextual simplify-reflections : 0
% 0.22/0.31 % Paramodulations : 6
% 0.22/0.31 % Factorizations : 0
% 0.22/0.31 % NegExts : 0
% 0.22/0.31 % Equation resolutions : 1
% 0.22/0.31 % Disequality decompositions : 0
% 0.22/0.31 % Total rewrite steps : 5
% 0.22/0.31 % ...of those cached : 0
% 0.22/0.31 % Propositional unsat checks : 0
% 0.22/0.31 % Propositional check models : 0
% 0.22/0.31 % Propositional check unsatisfiable : 0
% 0.22/0.31 % Propositional clauses : 0
% 0.22/0.31 % Propositional clauses after purity: 0
% 0.22/0.31 % Propositional unsat core size : 0
% 0.22/0.31 % Propositional preprocessing time : 0.000
% 0.22/0.31 % Propositional encoding time : 0.000
% 0.22/0.31 % Propositional solver time : 0.000
% 0.22/0.31 % Success case prop preproc time : 0.000
% 0.22/0.31 % Success case prop encoding time : 0.000
% 0.22/0.31 % Success case prop solver time : 0.000
% 0.22/0.31 % Current number of processed clauses : 27
% 0.22/0.31 % Positive orientable unit clauses : 15
% 0.22/0.31 % Positive unorientable unit clauses: 0
% 0.22/0.31 % Negative unit clauses : 4
% 0.22/0.31 % Non-unit-clauses : 8
% 0.22/0.31 % Current number of unprocessed clauses: 119
% 0.22/0.31 % ...number of literals in the above : 422
% 0.22/0.31 % Current number of archived formulas : 0
% 0.22/0.31 % Current number of archived clauses : 0
% 0.22/0.31 % Clause-clause subsumption calls (NU) : 14
% 0.22/0.31 % Rec. Clause-clause subsumption calls : 14
% 0.22/0.31 % Non-unit clause-clause subsumptions : 1
% 0.22/0.31 % Unit Clause-clause subsumption calls : 2
% 0.22/0.31 % Rewrite failures with RHS unbound : 0
% 0.22/0.31 % BW rewrite match attempts : 0
% 0.22/0.31 % BW rewrite match successes : 0
% 0.22/0.31 % Condensation attempts : 0
% 0.22/0.31 % Condensation successes : 0
% 0.22/0.31 % Termbank termtop insertions : 28430
% 0.22/0.31 % Search garbage collected termcells : 10806
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.023 s
% 0.22/0.31 % System time : 0.007 s
% 0.22/0.31 % Total time : 0.030 s
% 0.22/0.31 % Maximum resident set size: 6168 pages
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.034 s
% 0.22/0.31 % System time : 0.013 s
% 0.22/0.31 % Total time : 0.047 s
% 0.22/0.31 % Maximum resident set size: 5632 pages
% 0.22/0.31 % E exiting
%------------------------------------------------------------------------------