%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM642^4 : 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 : n018.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 08:17:17 AM UTC 2026
% Result : Theorem 0.34s 0.50s
% Output : CNFRefutation 0.34s
% 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 : 138 ( 8 ~; 4 |; 2 &; 117 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 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_144,type,
esk1_0: $i ).
thf(decl_145,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.uu0PcQm9tY/E---3.1_10712.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.uu0PcQm9tY/E---3.1_10712.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uu0PcQm9tY/E---3.1_10712.p',def_is_of) ).
thf(satz4h,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X191: $i] : ( in @ X191 @ nat )
@ ^ [X192: $i] : ( n_is @ ( ordsucc @ ( n_pl @ X1 @ X192 ) ) @ ( n_pl @ ( ordsucc @ X1 ) @ X192 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uu0PcQm9tY/E---3.1_10712.p',satz4h) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uu0PcQm9tY/E---3.1_10712.p',def_n_is) ).
thf(satz4d,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X187: $i] : ( in @ X187 @ nat )
@ ^ [X188: $i] : ( n_is @ ( n_pl @ ( ordsucc @ X1 ) @ X188 ) @ ( ordsucc @ ( n_pl @ X1 @ X188 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uu0PcQm9tY/E---3.1_10712.p',satz4d) ).
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
@ ^ [X191: $i] : ( in @ X191 @ nat )
@ ^ [X192: $i] : ( n_is @ ( ordsucc @ ( n_pl @ X1 @ X192 ) ) @ ( n_pl @ ( ordsucc @ X1 ) @ X192 ) ) ) ),
inference(assume_negation,[status(cth)],[satz4h]) ).
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,
~ ! [X282: $i] :
( ( in @ X282 @ nat )
=> ! [X281: $i] :
( ( in @ X281 @ nat )
=> ( ( ordsucc @ ( n_pl @ X282 @ X281 ) )
= ( n_pl @ ( ordsucc @ X282 ) @ X281 ) ) ) ),
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,
! [X290: $i] :
( ( in @ X290 @ nat )
=> ! [X289: $i] :
( ( in @ X289 @ nat )
=> ( ( n_pl @ ( ordsucc @ X290 ) @ X289 )
= ( ordsucc @ ( n_pl @ X290 @ X289 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz4d]),c_0_10]),c_0_11]) ).
thf(c_0_14,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( ( ordsucc @ ( n_pl @ esk1_0 @ esk2_0 ) )
!= ( n_pl @ ( 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,
! [X355: $i,X356: $i] :
( ~ ( in @ X355 @ nat )
| ~ ( in @ X356 @ nat )
| ( ( n_pl @ ( ordsucc @ X355 ) @ X356 )
= ( ordsucc @ ( n_pl @ X355 @ X356 ) ) ) ),
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,
( ( ordsucc @ ( n_pl @ esk1_0 @ esk2_0 ) )
!= ( n_pl @ ( ordsucc @ esk1_0 ) @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,plain,
! [X1: $i,X4: $i] :
( ( ( n_pl @ ( ordsucc @ X1 ) @ X4 )
= ( ordsucc @ ( n_pl @ X1 @ 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
% 0.00/0.04 % Problem : NUM642^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.28 % Computer : n018.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Tue Sep 29 12:33:26 UTC 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.29/0.36 Running higher-order theorem proving
% 0.34/0.41 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.uu0PcQm9tY/E---3.1_10712.p
% 0.34/0.50 % Version: 3.5.1-ho
% 0.34/0.50 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.34/0.50 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.50 % Starting lpo1_fix with 900s (3) cores
% 0.34/0.50 % Starting full_lambda_9 with 300s (1) cores
% 0.34/0.50 % Starting almost_fo_4 with 300s (1) cores
% 0.34/0.50 % Starting new_ho_9 with 300s (1) cores
% 0.34/0.50 % Starting pre_casc_4 with 300s (1) cores
% 0.34/0.50 % Starting ho_unfolding_6 with 300s (1) cores
% 0.34/0.50 % pre_casc_4 with pid 10729 completed with status 0
% 0.34/0.50 % Result found by pre_casc_4
% 0.34/0.50 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.34/0.50 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.50 % Starting lpo1_fix with 900s (3) cores
% 0.34/0.50 % Starting full_lambda_9 with 300s (1) cores
% 0.34/0.50 % Starting almost_fo_4 with 300s (1) cores
% 0.34/0.50 % Starting new_ho_9 with 300s (1) cores
% 0.34/0.50 % Starting pre_casc_4 with 300s (1) cores
% 0.34/0.50 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.34/0.50 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.34/0.50 % Search class: HGUSM-FFMM31-DHSMMSBN
% 0.34/0.50 % partial match(3): HGHSM-FFMM31-SHSSMSBN
% 0.34/0.50 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.34/0.50 % Starting SubtermCWHack with 28s (1) cores
% 0.34/0.50 % SubtermCWHack with pid 10731 completed with status 0
% 0.34/0.50 % Result found by SubtermCWHack
% 0.34/0.50 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.34/0.50 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.50 % Starting lpo1_fix with 900s (3) cores
% 0.34/0.50 % Starting full_lambda_9 with 300s (1) cores
% 0.34/0.50 % Starting almost_fo_4 with 300s (1) cores
% 0.34/0.50 % Starting new_ho_9 with 300s (1) cores
% 0.34/0.50 % Starting pre_casc_4 with 300s (1) cores
% 0.34/0.50 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.34/0.50 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.34/0.50 % Search class: HGUSM-FFMM31-DHSMMSBN
% 0.34/0.50 % partial match(3): HGHSM-FFMM31-SHSSMSBN
% 0.34/0.50 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.34/0.50 % Starting SubtermCWHack with 28s (1) cores
% 0.34/0.50 % Preprocessing time : 0.005 s
% 0.34/0.50
% 0.34/0.50 % Proof found!
% 0.34/0.50 % SZS status Theorem
% 0.34/0.50 % SZS output start CNFRefutation
% See solution above
% 0.34/0.50 % Parsed axioms : 314
% 0.34/0.50 % Removed by relevancy pruning/SinE : 244
% 0.34/0.50 % Initial clauses : 110
% 0.34/0.50 % Removed in clause preprocessing : 3
% 0.34/0.50 % Initial clauses in saturation : 107
% 0.34/0.50 % Processed clauses : 143
% 0.34/0.50 % ...of these trivial : 16
% 0.34/0.50 % ...subsumed : 16
% 0.34/0.50 % ...remaining for further processing : 111
% 0.34/0.50 % Other redundant clauses eliminated : 5
% 0.34/0.50 % Clauses deleted for lack of memory : 0
% 0.34/0.50 % Backward-subsumed : 0
% 0.34/0.50 % Backward-rewritten : 1
% 0.34/0.50 % Generated clauses : 242
% 0.34/0.50 % ...of the previous two non-redundant : 222
% 0.34/0.50 % ...aggressively subsumed : 0
% 0.34/0.50 % Contextual simplify-reflections : 1
% 0.34/0.50 % Paramodulations : 233
% 0.34/0.50 % Factorizations : 0
% 0.34/0.50 % NegExts : 0
% 0.34/0.50 % Equation resolutions : 6
% 0.34/0.50 % Disequality decompositions : 0
% 0.34/0.50 % Total rewrite steps : 40
% 0.34/0.50 % ...of those cached : 18
% 0.34/0.50 % Propositional unsat checks : 0
% 0.34/0.50 % Propositional check models : 0
% 0.34/0.50 % Propositional check unsatisfiable : 0
% 0.34/0.50 % Propositional clauses : 0
% 0.34/0.50 % Propositional clauses after purity: 0
% 0.34/0.50 % Propositional unsat core size : 0
% 0.34/0.50 % Propositional preprocessing time : 0.000
% 0.34/0.50 % Propositional encoding time : 0.000
% 0.34/0.50 % Propositional solver time : 0.000
% 0.34/0.50 % Success case prop preproc time : 0.000
% 0.34/0.50 % Success case prop encoding time : 0.000
% 0.34/0.50 % Success case prop solver time : 0.000
% 0.34/0.50 % Current number of processed clauses : 109
% 0.34/0.50 % Positive orientable unit clauses : 37
% 0.34/0.50 % Positive unorientable unit clauses: 2
% 0.34/0.50 % Negative unit clauses : 12
% 0.34/0.50 % Non-unit-clauses : 58
% 0.34/0.50 % Current number of unprocessed clauses: 183
% 0.34/0.50 % ...number of literals in the above : 500
% 0.34/0.50 % Current number of archived formulas : 0
% 0.34/0.50 % Current number of archived clauses : 1
% 0.34/0.50 % Clause-clause subsumption calls (NU) : 668
% 0.34/0.50 % Rec. Clause-clause subsumption calls : 585
% 0.34/0.50 % Non-unit clause-clause subsumptions : 15
% 0.34/0.50 % Unit Clause-clause subsumption calls : 75
% 0.34/0.50 % Rewrite failures with RHS unbound : 0
% 0.34/0.50 % BW rewrite match attempts : 7
% 0.34/0.50 % BW rewrite match successes : 1
% 0.34/0.50 % Condensation attempts : 0
% 0.34/0.50 % Condensation successes : 0
% 0.34/0.50 % Termbank termtop insertions : 16417
% 0.34/0.50 % Search garbage collected termcells : 4601
% 0.34/0.50
% 0.34/0.50 % -------------------------------------------------
% 0.34/0.50 % User time : 0.034 s
% 0.34/0.50 % System time : 0.009 s
% 0.34/0.50 % Total time : 0.043 s
% 0.34/0.50 % Maximum resident set size: 4516 pages
% 0.34/0.50
% 0.34/0.50 % -------------------------------------------------
% 0.34/0.50 % User time : 0.046 s
% 0.34/0.50 % System time : 0.018 s
% 0.34/0.50 % Total time : 0.064 s
% 0.34/0.50 % Maximum resident set size: 5376 pages
% 0.34/0.50 % E exiting
%------------------------------------------------------------------------------