%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM721^4 : 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 : n008.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 08:16:56 AM UTC 2026
% Result : Theorem 0.77s 0.44s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 132 ( 12 equ; 0 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 309 ( 16 ~; 12 |; 6 &; 254 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 65 ( 46 ^; 19 !; 0 ?; 65 :)
% 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_73,type,
l_some: $i > ( $i > $o ) > $o ).
thf(decl_124,type,
nat: $i ).
thf(decl_128,type,
n_some: ( $i > $o ) > $o ).
thf(decl_148,type,
diffprop: $i > $i > $i > $o ).
thf(decl_149,type,
d_29_ii: $i > $i > $o ).
thf(decl_150,type,
iii: $i > $i > $o ).
thf(decl_163,type,
n_ts: $i > $i > $i ).
thf(decl_169,type,
esk1_0: $i ).
thf(decl_170,type,
esk2_0: $i ).
thf(decl_171,type,
esk3_0: $i ).
thf(decl_172,type,
esk4_0: $i ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.hLFPGxHzl1/E---3.1_3091617.p',def_iii) ).
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.hLFPGxHzl1/E---3.1_3091617.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.hLFPGxHzl1/E---3.1_3091617.p',def_is_of) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.hLFPGxHzl1/E---3.1_3091617.p',def_d_29_ii) ).
thf(satz34a,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X407: $i] : ( in @ X407 @ nat )
@ ^ [X408: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( iii @ X1 @ X408 )
=> ( ( iii @ X4 @ X13 )
=> ( iii @ ( n_ts @ X1 @ X4 ) @ ( n_ts @ X408 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.hLFPGxHzl1/E---3.1_3091617.p',satz34a) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.hLFPGxHzl1/E---3.1_3091617.p',def_n_some) ).
thf(satz34,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X405: $i] : ( in @ X405 @ nat )
@ ^ [X406: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( d_29_ii @ X1 @ X406 )
=> ( ( d_29_ii @ X4 @ X13 )
=> ( d_29_ii @ ( n_ts @ X1 @ X4 ) @ ( n_ts @ X406 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.hLFPGxHzl1/E---3.1_3091617.p',satz34) ).
thf(c_0_7,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_8,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_9,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_10,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_11,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X407: $i] : ( in @ X407 @ nat )
@ ^ [X408: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( iii @ X1 @ X408 )
=> ( ( iii @ X4 @ X13 )
=> ( iii @ ( n_ts @ X1 @ X4 ) @ ( n_ts @ X408 @ X13 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz34a]) ).
thf(c_0_12,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_7,def_n_some]) ).
thf(c_0_13,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_14,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_10,def_n_some]) ).
thf(c_0_15,negated_conjecture,
~ ! [X447: $i] :
( ( in @ X447 @ nat )
=> ! [X446: $i] :
( ( in @ X446 @ nat )
=> ! [X445: $i] :
( ( in @ X445 @ nat )
=> ! [X444: $i] :
( ( in @ X444 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X446 @ X447 ) )
=> ( ( l_some @ nat @ ( diffprop @ X444 @ X445 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X446 @ X444 ) @ ( n_ts @ X447 @ X445 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_11]),c_0_12]),c_0_13]) ).
thf(c_0_16,plain,
! [X648: $i] :
( ( in @ X648 @ nat )
=> ! [X647: $i] :
( ( in @ X647 @ nat )
=> ! [X646: $i] :
( ( in @ X646 @ nat )
=> ! [X645: $i] :
( ( in @ X645 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X648 @ X647 ) )
=> ( ( l_some @ nat @ ( diffprop @ X646 @ X645 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X648 @ X646 ) @ ( n_ts @ X647 @ X645 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz34]),c_0_14]),c_0_13]) ).
thf(c_0_17,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( in @ esk4_0 @ nat )
& ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) )
& ( l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ) )
& ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ esk2_0 @ esk4_0 ) @ ( n_ts @ esk1_0 @ esk3_0 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
thf(c_0_18,plain,
! [X951: $i,X952: $i,X953: $i,X954: $i] :
( ~ ( in @ X951 @ nat )
| ~ ( in @ X952 @ nat )
| ~ ( in @ X953 @ nat )
| ~ ( in @ X954 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X951 @ X952 ) )
| ~ ( l_some @ nat @ ( diffprop @ X953 @ X954 ) )
| ( l_some @ nat @ ( diffprop @ ( n_ts @ X951 @ X953 ) @ ( n_ts @ X952 @ X954 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
thf(c_0_19,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_ts @ esk2_0 @ esk4_0 ) @ ( n_ts @ esk1_0 @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,plain,
! [X1: $i,X4: $i,X5: $i,X6: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ X5 ) @ ( n_ts @ X4 @ X6 ) ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X6 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) )
| ~ ( l_some @ nat @ ( diffprop @ X5 @ X6 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,negated_conjecture,
l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_24,negated_conjecture,
in @ esk4_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_25,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_26,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM721^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n008.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 12:46:09 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.24 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.hLFPGxHzl1/E---3.1_3091617.p
% 0.77/0.44 % Version: 3.5.1-ho
% 0.77/0.44 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.77/0.44 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.44 % Starting lpo1_fix with 900s (3) cores
% 0.77/0.44 % Starting full_lambda_9 with 300s (1) cores
% 0.77/0.44 % Starting almost_fo_4 with 300s (1) cores
% 0.77/0.44 % Starting new_ho_9 with 300s (1) cores
% 0.77/0.44 % Starting pre_casc_4 with 300s (1) cores
% 0.77/0.44 % Starting ho_unfolding_6 with 300s (1) cores
% 0.77/0.44 % full_lambda_9 with pid 3091631 completed with status 0
% 0.77/0.44 % Result found by full_lambda_9
% 0.77/0.44 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.77/0.44 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.44 % Starting lpo1_fix with 900s (3) cores
% 0.77/0.44 % Starting full_lambda_9 with 300s (1) cores
% 0.77/0.44 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.77/0.44 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.77/0.44 % Search class: HGHSS-FSLM32-MHSMMSBN
% 0.77/0.44 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.77/0.44 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.77/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.77/0.44 % SubtermCWHack with pid 3091636 completed with status 0
% 0.77/0.44 % Result found by SubtermCWHack
% 0.77/0.44 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.77/0.44 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.44 % Starting lpo1_fix with 900s (3) cores
% 0.77/0.44 % Starting full_lambda_9 with 300s (1) cores
% 0.77/0.44 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.77/0.44 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.77/0.44 % Search class: HGHSS-FSLM32-MHSMMSBN
% 0.77/0.44 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.77/0.44 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.77/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.77/0.44 % Preprocessing time : 0.007 s
% 0.77/0.44
% 0.77/0.44 % Proof found!
% 0.77/0.44 % SZS status Theorem
% 0.77/0.44 % SZS output start CNFRefutation
% See solution above
% 0.77/0.44 % Parsed axioms : 467
% 0.77/0.44 % Removed by relevancy pruning/SinE : 309
% 0.77/0.44 % Initial clauses : 349
% 0.77/0.44 % Removed in clause preprocessing : 148
% 0.77/0.44 % Initial clauses in saturation : 201
% 0.77/0.44 % Processed clauses : 1529
% 0.77/0.44 % ...of these trivial : 15
% 0.77/0.44 % ...subsumed : 699
% 0.77/0.44 % ...remaining for further processing : 815
% 0.77/0.44 % Other redundant clauses eliminated : 46
% 0.77/0.44 % Clauses deleted for lack of memory : 0
% 0.77/0.44 % Backward-subsumed : 2
% 0.77/0.44 % Backward-rewritten : 0
% 0.77/0.44 % Generated clauses : 4722
% 0.77/0.44 % ...of the previous two non-redundant : 4388
% 0.77/0.44 % ...aggressively subsumed : 0
% 0.77/0.44 % Contextual simplify-reflections : 3
% 0.77/0.44 % Paramodulations : 4670
% 0.77/0.44 % Factorizations : 0
% 0.77/0.44 % NegExts : 0
% 0.77/0.44 % Equation resolutions : 52
% 0.77/0.44 % Disequality decompositions : 0
% 0.77/0.44 % Total rewrite steps : 1757
% 0.77/0.44 % ...of those cached : 1716
% 0.77/0.44 % Propositional unsat checks : 0
% 0.77/0.44 % Propositional check models : 0
% 0.77/0.44 % Propositional check unsatisfiable : 0
% 0.77/0.44 % Propositional clauses : 0
% 0.77/0.44 % Propositional clauses after purity: 0
% 0.77/0.44 % Propositional unsat core size : 0
% 0.77/0.44 % Propositional preprocessing time : 0.000
% 0.77/0.44 % Propositional encoding time : 0.000
% 0.77/0.44 % Propositional solver time : 0.000
% 0.77/0.44 % Success case prop preproc time : 0.000
% 0.77/0.44 % Success case prop encoding time : 0.000
% 0.77/0.44 % Success case prop solver time : 0.000
% 0.77/0.44 % Current number of processed clauses : 788
% 0.77/0.44 % Positive orientable unit clauses : 32
% 0.77/0.44 % Positive unorientable unit clauses: 0
% 0.77/0.44 % Negative unit clauses : 508
% 0.77/0.44 % Non-unit-clauses : 248
% 0.77/0.44 % Current number of unprocessed clauses: 3057
% 0.77/0.44 % ...number of literals in the above : 8987
% 0.77/0.44 % Current number of archived formulas : 0
% 0.77/0.44 % Current number of archived clauses : 2
% 0.77/0.44 % Clause-clause subsumption calls (NU) : 13679
% 0.77/0.44 % Rec. Clause-clause subsumption calls : 6723
% 0.77/0.44 % Non-unit clause-clause subsumptions : 519
% 0.77/0.44 % Unit Clause-clause subsumption calls : 53137
% 0.77/0.44 % Rewrite failures with RHS unbound : 0
% 0.77/0.44 % BW rewrite match attempts : 3
% 0.77/0.44 % BW rewrite match successes : 0
% 0.77/0.44 % Condensation attempts : 0
% 0.77/0.44 % Condensation successes : 0
% 0.77/0.44 % Termbank termtop insertions : 135937
% 0.77/0.44 % Search garbage collected termcells : 24171
% 0.77/0.44
% 0.77/0.44 % -------------------------------------------------
% 0.77/0.44 % User time : 0.134 s
% 0.77/0.44 % System time : 0.021 s
% 0.77/0.44 % Total time : 0.155 s
% 0.77/0.44 % Maximum resident set size: 7792 pages
% 0.77/0.44
% 0.77/0.44 % -------------------------------------------------
% 0.77/0.44 % User time : 0.147 s
% 0.77/0.44 % System time : 0.028 s
% 0.77/0.44 % Total time : 0.175 s
% 0.77/0.44 % Maximum resident set size: 5632 pages
% 0.77/0.44 % E exiting
%------------------------------------------------------------------------------