%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM682^4 : 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 : n016.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 08:16:49 AM UTC 2026
% Result : Theorem 0.59s 0.45s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 105 ( 12 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 238 ( 12 ~; 8 |; 4 &; 200 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 55 ( 40 ^; 15 !; 0 ?; 55 :)
% 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_143,type,
n_pl: $i > $i > $i ).
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_156,type,
esk1_0: $i ).
thf(decl_157,type,
esk2_0: $i ).
thf(decl_158,type,
esk3_0: $i ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jFOHJAjeDQ/E---3.1_286595.p',def_d_29_ii) ).
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.jFOHJAjeDQ/E---3.1_286595.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jFOHJAjeDQ/E---3.1_286595.p',def_is_of) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jFOHJAjeDQ/E---3.1_286595.p',def_iii) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.jFOHJAjeDQ/E---3.1_286595.p',def_n_some) ).
thf(satz20c,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X299: $i] : ( in @ X299 @ nat )
@ ^ [X300: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( iii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X300 @ X4 ) )
=> ( iii @ X1 @ X300 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jFOHJAjeDQ/E---3.1_286595.p',satz20c) ).
thf(satz20a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X295: $i] : ( in @ X295 @ nat )
@ ^ [X296: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( d_29_ii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X296 @ X4 ) )
=> ( d_29_ii @ X1 @ X296 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jFOHJAjeDQ/E---3.1_286595.p',satz20a) ).
thf(c_0_7,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_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,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_11,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_7,def_n_some]) ).
thf(c_0_12,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_13,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X299: $i] : ( in @ X299 @ nat )
@ ^ [X300: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( iii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X300 @ X4 ) )
=> ( iii @ X1 @ X300 ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz20c]) ).
thf(c_0_14,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_10,def_n_some]) ).
thf(c_0_15,plain,
! [X475: $i] :
( ( in @ X475 @ nat )
=> ! [X474: $i] :
( ( in @ X474 @ nat )
=> ! [X473: $i] :
( ( in @ X473 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ ( n_pl @ X475 @ X473 ) @ ( n_pl @ X474 @ X473 ) ) )
=> ( l_some @ nat @ ( diffprop @ X475 @ X474 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz20a]),c_0_11]),c_0_12]) ).
thf(c_0_16,negated_conjecture,
~ ! [X370: $i] :
( ( in @ X370 @ nat )
=> ! [X369: $i] :
( ( in @ X369 @ nat )
=> ! [X368: $i] :
( ( in @ X368 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ ( n_pl @ X369 @ X368 ) @ ( n_pl @ X370 @ X368 ) ) )
=> ( l_some @ nat @ ( diffprop @ X369 @ X370 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_13]),c_0_14]),c_0_12]) ).
thf(c_0_17,plain,
! [X635: $i,X636: $i,X637: $i] :
( ~ ( in @ X635 @ nat )
| ~ ( in @ X636 @ nat )
| ~ ( in @ X637 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ X635 @ X637 ) @ ( n_pl @ X636 @ X637 ) ) )
| ( l_some @ nat @ ( diffprop @ X635 @ X636 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
thf(c_0_18,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk3_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) )
& ~ ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
thf(c_0_19,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( l_some @ nat @ ( diffprop @ X1 @ X4 ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ X1 @ X5 ) @ ( n_pl @ X4 @ X5 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk3_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_23,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_25,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[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]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM682^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 12:41:04 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.20/0.27 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.jFOHJAjeDQ/E---3.1_286595.p
% 0.59/0.45 % Version: 3.5.1-ho
% 0.59/0.45 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.59/0.45 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.45 % Starting lpo1_fix with 900s (3) cores
% 0.59/0.45 % Starting full_lambda_9 with 300s (1) cores
% 0.59/0.45 % Starting almost_fo_4 with 300s (1) cores
% 0.59/0.45 % Starting new_ho_9 with 300s (1) cores
% 0.59/0.45 % Starting pre_casc_4 with 300s (1) cores
% 0.59/0.45 % Starting ho_unfolding_6 with 300s (1) cores
% 0.59/0.45 % full_lambda_9 with pid 286609 completed with status 0
% 0.59/0.45 % Result found by full_lambda_9
% 0.59/0.45 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.59/0.45 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.45 % Starting lpo1_fix with 900s (3) cores
% 0.59/0.45 % Starting full_lambda_9 with 300s (1) cores
% 0.59/0.45 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.59/0.45 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.59/0.45 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.59/0.45 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.59/0.45 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.59/0.45 % Starting SubtermCWHack with 28s (1) cores
% 0.59/0.45 % SubtermCWHack with pid 286614 completed with status 0
% 0.59/0.45 % Result found by SubtermCWHack
% 0.59/0.45 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.59/0.45 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.45 % Starting lpo1_fix with 900s (3) cores
% 0.59/0.45 % Starting full_lambda_9 with 300s (1) cores
% 0.59/0.45 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.59/0.45 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.59/0.45 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.59/0.45 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.59/0.45 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.59/0.45 % Starting SubtermCWHack with 28s (1) cores
% 0.59/0.45 % Preprocessing time : 0.006 s
% 0.59/0.45
% 0.59/0.45 % Proof found!
% 0.59/0.45 % SZS status Theorem
% 0.59/0.45 % SZS output start CNFRefutation
% See solution above
% 0.59/0.45 % Parsed axioms : 385
% 0.59/0.45 % Removed by relevancy pruning/SinE : 263
% 0.59/0.45 % Initial clauses : 331
% 0.59/0.45 % Removed in clause preprocessing : 174
% 0.59/0.45 % Initial clauses in saturation : 157
% 0.59/0.45 % Processed clauses : 1034
% 0.59/0.45 % ...of these trivial : 8
% 0.59/0.45 % ...subsumed : 423
% 0.59/0.45 % ...remaining for further processing : 603
% 0.59/0.45 % Other redundant clauses eliminated : 28
% 0.59/0.45 % Clauses deleted for lack of memory : 0
% 0.59/0.45 % Backward-subsumed : 1
% 0.59/0.45 % Backward-rewritten : 0
% 0.59/0.45 % Generated clauses : 3082
% 0.59/0.45 % ...of the previous two non-redundant : 2885
% 0.59/0.45 % ...aggressively subsumed : 0
% 0.59/0.45 % Contextual simplify-reflections : 0
% 0.59/0.45 % Paramodulations : 3044
% 0.59/0.45 % Factorizations : 2
% 0.59/0.45 % NegExts : 0
% 0.59/0.45 % Equation resolutions : 33
% 0.59/0.45 % Disequality decompositions : 0
% 0.59/0.45 % Total rewrite steps : 990
% 0.59/0.45 % ...of those cached : 957
% 0.59/0.45 % Propositional unsat checks : 0
% 0.59/0.45 % Propositional check models : 0
% 0.59/0.45 % Propositional check unsatisfiable : 0
% 0.59/0.45 % Propositional clauses : 0
% 0.59/0.45 % Propositional clauses after purity: 0
% 0.59/0.45 % Propositional unsat core size : 0
% 0.59/0.45 % Propositional preprocessing time : 0.000
% 0.59/0.45 % Propositional encoding time : 0.000
% 0.59/0.45 % Propositional solver time : 0.000
% 0.59/0.45 % Success case prop preproc time : 0.000
% 0.59/0.45 % Success case prop encoding time : 0.000
% 0.59/0.45 % Success case prop solver time : 0.000
% 0.59/0.45 % Current number of processed clauses : 591
% 0.59/0.45 % Positive orientable unit clauses : 29
% 0.59/0.45 % Positive unorientable unit clauses: 0
% 0.59/0.45 % Negative unit clauses : 381
% 0.59/0.45 % Non-unit-clauses : 181
% 0.59/0.45 % Current number of unprocessed clauses: 1988
% 0.59/0.45 % ...number of literals in the above : 4738
% 0.59/0.45 % Current number of archived formulas : 0
% 0.59/0.45 % Current number of archived clauses : 1
% 0.59/0.45 % Clause-clause subsumption calls (NU) : 7214
% 0.59/0.45 % Rec. Clause-clause subsumption calls : 4608
% 0.59/0.45 % Non-unit clause-clause subsumptions : 315
% 0.59/0.45 % Unit Clause-clause subsumption calls : 40812
% 0.59/0.45 % Rewrite failures with RHS unbound : 0
% 0.59/0.45 % BW rewrite match attempts : 7
% 0.59/0.45 % BW rewrite match successes : 0
% 0.59/0.45 % Condensation attempts : 0
% 0.59/0.45 % Condensation successes : 0
% 0.59/0.45 % Termbank termtop insertions : 88550
% 0.59/0.45 % Search garbage collected termcells : 15210
% 0.59/0.45
% 0.59/0.45 % -------------------------------------------------
% 0.59/0.45 % User time : 0.124 s
% 0.59/0.45 % System time : 0.017 s
% 0.59/0.45 % Total time : 0.141 s
% 0.59/0.45 % Maximum resident set size: 6308 pages
% 0.59/0.45
% 0.59/0.45 % -------------------------------------------------
% 0.59/0.45 % User time : 0.135 s
% 0.59/0.45 % System time : 0.023 s
% 0.59/0.45 % Total time : 0.158 s
% 0.59/0.45 % Maximum resident set size: 5376 pages
% 0.59/0.45 % E exiting
%------------------------------------------------------------------------------