%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM709^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:16:55 AM UTC 2026
% Result : Theorem 0.25s 0.34s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 19 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 147 ( 8 ~; 4 |; 2 &; 126 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 43 ( 32 ^; 11 !; 0 ?; 43 :)
% 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_48,type,
ordsucc: $i > $i ).
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_143,type,
n_pl: $i > $i > $i ).
thf(decl_163,type,
n_ts: $i > $i > $i ).
thf(decl_164,type,
esk1_0: $i ).
thf(decl_165,type,
esk2_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.P4k7o7zWom/E---3.1_1610283.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/sandbox2/tmp/tmp.P4k7o7zWom/E---3.1_1610283.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.P4k7o7zWom/E---3.1_1610283.p',def_is_of) ).
thf(satz28h,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X360: $i] : ( in @ X360 @ nat )
@ ^ [X361: $i] : ( n_is @ ( n_pl @ ( n_ts @ X1 @ X361 ) @ X361 ) @ ( n_ts @ ( ordsucc @ X1 ) @ X361 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.P4k7o7zWom/E---3.1_1610283.p',satz28h) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.P4k7o7zWom/E---3.1_1610283.p',def_n_is) ).
thf(satz28d,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X356: $i] : ( in @ X356 @ nat )
@ ^ [X357: $i] : ( n_is @ ( n_ts @ ( ordsucc @ X1 ) @ X357 ) @ ( n_pl @ ( n_ts @ X1 @ X357 ) @ X357 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.P4k7o7zWom/E---3.1_1610283.p',satz28d) ).
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] :
( all_of
@ ^ [X360: $i] : ( in @ X360 @ nat )
@ ^ [X361: $i] : ( n_is @ ( n_pl @ ( n_ts @ X1 @ X361 ) @ X361 ) @ ( n_ts @ ( ordsucc @ X1 ) @ X361 ) ) ) ),
inference(assume_negation,[status(cth)],[satz28h]) ).
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,
~ ! [X451: $i] :
( ( in @ X451 @ nat )
=> ! [X450: $i] :
( ( in @ X450 @ nat )
=> ( ( n_pl @ ( n_ts @ X451 @ X450 ) @ X450 )
= ( n_ts @ ( ordsucc @ X451 ) @ X450 ) ) ) ),
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,
! [X477: $i] :
( ( in @ X477 @ nat )
=> ! [X476: $i] :
( ( in @ X476 @ nat )
=> ( ( n_ts @ ( ordsucc @ X477 ) @ X476 )
= ( n_pl @ ( n_ts @ X477 @ X476 ) @ X476 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz28d]),c_0_10]),c_0_11]) ).
thf(c_0_14,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( ( n_pl @ ( n_ts @ esk1_0 @ esk2_0 ) @ esk2_0 )
!= ( n_ts @ ( ordsucc @ esk1_0 ) @ esk2_0 ) ) ),
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,
! [X639: $i,X640: $i] :
( ~ ( in @ X639 @ nat )
| ~ ( in @ X640 @ nat )
| ( ( n_ts @ ( ordsucc @ X639 ) @ X640 )
= ( n_pl @ ( n_ts @ X639 @ X640 ) @ X640 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
thf(c_0_16,negated_conjecture,
( ( n_pl @ ( n_ts @ esk1_0 @ esk2_0 ) @ esk2_0 )
!= ( n_ts @ ( ordsucc @ esk1_0 ) @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,plain,
! [X1: $i,X4: $i] :
( ( ( n_ts @ ( ordsucc @ X1 ) @ X4 )
= ( n_pl @ ( n_ts @ X1 @ X4 ) @ X4 ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM709^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n005.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 12:43:16 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.27 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.P4k7o7zWom/E---3.1_1610283.p
% 0.25/0.34 % Version: 3.5.1-ho
% 0.25/0.34 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.25/0.34 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.34 % Starting lpo1_fix with 900s (3) cores
% 0.25/0.34 % Starting full_lambda_9 with 300s (1) cores
% 0.25/0.34 % Starting almost_fo_4 with 300s (1) cores
% 0.25/0.34 % Starting new_ho_9 with 300s (1) cores
% 0.25/0.34 % Starting pre_casc_4 with 300s (1) cores
% 0.25/0.34 % Starting ho_unfolding_6 with 300s (1) cores
% 0.25/0.34 % pre_casc_4 with pid 1610339 completed with status 0
% 0.25/0.34 % Result found by pre_casc_4
% 0.25/0.34 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.25/0.34 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.34 % Starting lpo1_fix with 900s (3) cores
% 0.25/0.34 % Starting full_lambda_9 with 300s (1) cores
% 0.25/0.34 % Starting almost_fo_4 with 300s (1) cores
% 0.25/0.34 % Starting new_ho_9 with 300s (1) cores
% 0.25/0.34 % Starting pre_casc_4 with 300s (1) cores
% 0.25/0.34 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.25/0.34 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.25/0.34 % Search class: HGUSM-FSLM31-DHSMMSBN
% 0.25/0.34 % partial match(2): HGHSM-FSLM31-MHSMMSBN
% 0.25/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.34 % SubtermCWHack with pid 1610349 completed with status 0
% 0.25/0.34 % Result found by SubtermCWHack
% 0.25/0.34 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.25/0.34 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.34 % Starting lpo1_fix with 900s (3) cores
% 0.25/0.34 % Starting full_lambda_9 with 300s (1) cores
% 0.25/0.34 % Starting almost_fo_4 with 300s (1) cores
% 0.25/0.34 % Starting new_ho_9 with 300s (1) cores
% 0.25/0.34 % Starting pre_casc_4 with 300s (1) cores
% 0.25/0.34 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.25/0.34 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.25/0.34 % Search class: HGUSM-FSLM31-DHSMMSBN
% 0.25/0.34 % partial match(2): HGHSM-FSLM31-MHSMMSBN
% 0.25/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.34 % Preprocessing time : 0.005 s
% 0.25/0.34
% 0.25/0.34 % Proof found!
% 0.25/0.34 % SZS status Theorem
% 0.25/0.34 % SZS output start CNFRefutation
% See solution above
% 0.25/0.34 % Parsed axioms : 439
% 0.25/0.34 % Removed by relevancy pruning/SinE : 326
% 0.25/0.34 % Initial clauses : 150
% 0.25/0.34 % Removed in clause preprocessing : 7
% 0.25/0.34 % Initial clauses in saturation : 143
% 0.25/0.34 % Processed clauses : 220
% 0.25/0.34 % ...of these trivial : 16
% 0.25/0.34 % ...subsumed : 63
% 0.25/0.34 % ...remaining for further processing : 141
% 0.25/0.34 % Other redundant clauses eliminated : 5
% 0.25/0.34 % Clauses deleted for lack of memory : 0
% 0.25/0.34 % Backward-subsumed : 2
% 0.25/0.34 % Backward-rewritten : 1
% 0.25/0.34 % Generated clauses : 375
% 0.25/0.34 % ...of the previous two non-redundant : 354
% 0.25/0.34 % ...aggressively subsumed : 0
% 0.25/0.34 % Contextual simplify-reflections : 1
% 0.25/0.34 % Paramodulations : 365
% 0.25/0.34 % Factorizations : 0
% 0.25/0.34 % NegExts : 0
% 0.25/0.34 % Equation resolutions : 6
% 0.25/0.34 % Disequality decompositions : 0
% 0.25/0.34 % Total rewrite steps : 54
% 0.25/0.34 % ...of those cached : 30
% 0.25/0.34 % Propositional unsat checks : 0
% 0.25/0.34 % Propositional check models : 0
% 0.25/0.34 % Propositional check unsatisfiable : 0
% 0.25/0.34 % Propositional clauses : 0
% 0.25/0.34 % Propositional clauses after purity: 0
% 0.25/0.34 % Propositional unsat core size : 0
% 0.25/0.34 % Propositional preprocessing time : 0.000
% 0.25/0.34 % Propositional encoding time : 0.000
% 0.25/0.34 % Propositional solver time : 0.000
% 0.25/0.34 % Success case prop preproc time : 0.000
% 0.25/0.34 % Success case prop encoding time : 0.000
% 0.25/0.34 % Success case prop solver time : 0.000
% 0.25/0.34 % Current number of processed clauses : 137
% 0.25/0.34 % Positive orientable unit clauses : 39
% 0.25/0.34 % Positive unorientable unit clauses: 2
% 0.25/0.34 % Negative unit clauses : 27
% 0.25/0.34 % Non-unit-clauses : 69
% 0.25/0.34 % Current number of unprocessed clauses: 272
% 0.25/0.34 % ...number of literals in the above : 786
% 0.25/0.34 % Current number of archived formulas : 0
% 0.25/0.34 % Current number of archived clauses : 3
% 0.25/0.34 % Clause-clause subsumption calls (NU) : 860
% 0.25/0.34 % Rec. Clause-clause subsumption calls : 707
% 0.25/0.34 % Non-unit clause-clause subsumptions : 25
% 0.25/0.34 % Unit Clause-clause subsumption calls : 320
% 0.25/0.34 % Rewrite failures with RHS unbound : 0
% 0.25/0.34 % BW rewrite match attempts : 8
% 0.25/0.34 % BW rewrite match successes : 1
% 0.25/0.34 % Condensation attempts : 0
% 0.25/0.34 % Condensation successes : 0
% 0.25/0.34 % Termbank termtop insertions : 31928
% 0.25/0.34 % Search garbage collected termcells : 10518
% 0.25/0.34
% 0.25/0.34 % -------------------------------------------------
% 0.25/0.34 % User time : 0.035 s
% 0.25/0.34 % System time : 0.011 s
% 0.25/0.34 % Total time : 0.046 s
% 0.25/0.34 % Maximum resident set size: 5920 pages
% 0.25/0.34
% 0.25/0.34 % -------------------------------------------------
% 0.25/0.34 % User time : 0.048 s
% 0.25/0.34 % System time : 0.016 s
% 0.25/0.34 % Total time : 0.064 s
% 0.25/0.34 % Maximum resident set size: 5632 pages
% 0.25/0.34 % E exiting
%------------------------------------------------------------------------------