%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM648^4 : 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 : 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 08:16:41 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 35 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 204 ( 14 ~; 10 |; 6 &; 150 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 67 ( 46 ^; 21 !; 0 ?; 67 :)
% 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_79,type,
amone: $i > ( $i > $o ) > $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_149,type,
esk1_0: $i ).
thf(decl_150,type,
esk2_0: $i ).
thf(decl_151,type,
esk3_0: $i ).
thf(decl_152,type,
esk4_0: $i ).
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.YgBL5z8jAT/E---3.1_644874.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YgBL5z8jAT/E---3.1_644874.p',def_is_of) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YgBL5z8jAT/E---3.1_644874.p',def_e_is) ).
thf(def_amone,axiom,
( amone
= ( ^ [X1: $i,X2: $i > $o] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ X1 )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ X1 )
@ ^ [X13: $i] :
( ( X2 @ X4 )
=> ( ( X2 @ X13 )
=> ( e_is @ X1 @ X4 @ X13 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YgBL5z8jAT/E---3.1_644874.p',def_amone) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YgBL5z8jAT/E---3.1_644874.p',def_n_is) ).
thf(satz8b,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X208: $i] : ( in @ X208 @ nat )
@ ^ [X209: $i] :
( amone @ nat
@ ^ [X4: $i] : ( n_is @ X1 @ ( n_pl @ X209 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YgBL5z8jAT/E---3.1_644874.p',satz8b) ).
thf(satz8a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X205: $i] : ( in @ X205 @ nat )
@ ^ [X206: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( n_is @ ( n_pl @ X1 @ X206 ) @ ( n_pl @ X1 @ X4 ) )
=> ( n_is @ X206 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YgBL5z8jAT/E---3.1_644874.p',satz8a) ).
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,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_10,plain,
( amone
= ( ^ [Z0: $i,Z1: $i > $o] :
! [X311: $i] :
( ( in @ X311 @ Z0 )
=> ! [X310: $i] :
( ( in @ X310 @ Z0 )
=> ( ( Z1 @ X311 )
=> ( ( Z1 @ X310 )
=> ( X311 = X310 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_amone]) ).
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,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_9]) ).
thf(c_0_13,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X208: $i] : ( in @ X208 @ nat )
@ ^ [X209: $i] :
( amone @ nat
@ ^ [X4: $i] : ( n_is @ X1 @ ( n_pl @ X209 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz8b]) ).
thf(c_0_14,plain,
( amone
= ( ^ [Z0: $i,Z1: $i > $o] :
! [X311: $i] :
( ( in @ X311 @ Z0 )
=> ! [X310: $i] :
( ( in @ X310 @ Z0 )
=> ( ( Z1 @ X311 )
=> ( ( Z1 @ X310 )
=> ( X311 = X310 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_10,c_0_11]),c_0_9]) ).
thf(c_0_15,plain,
! [X351: $i] :
( ( in @ X351 @ nat )
=> ! [X350: $i] :
( ( in @ X350 @ nat )
=> ! [X349: $i] :
( ( in @ X349 @ nat )
=> ( ( ( n_pl @ X351 @ X350 )
= ( n_pl @ X351 @ X349 ) )
=> ( X350 = X349 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz8a]),c_0_11]),c_0_12]) ).
thf(c_0_16,negated_conjecture,
~ ! [X326: $i] :
( ( in @ X326 @ nat )
=> ! [X325: $i] :
( ( in @ X325 @ nat )
=> ! [X323: $i] :
( ( in @ X323 @ nat )
=> ! [X324: $i] :
( ( in @ X324 @ nat )
=> ( ( X326
= ( n_pl @ X325 @ X323 ) )
=> ( ( X326
= ( n_pl @ X325 @ X324 ) )
=> ( X323 = X324 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_13]),c_0_14]),c_0_11]),c_0_12]) ).
thf(c_0_17,plain,
! [X436: $i,X437: $i,X438: $i] :
( ~ ( in @ X436 @ nat )
| ~ ( in @ X437 @ nat )
| ~ ( in @ X438 @ nat )
| ( ( n_pl @ X436 @ X437 )
!= ( n_pl @ X436 @ X438 ) )
| ( X437 = X438 ) ),
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 )
& ( in @ esk4_0 @ nat )
& ( esk1_0
= ( n_pl @ esk2_0 @ esk3_0 ) )
& ( esk1_0
= ( n_pl @ esk2_0 @ esk4_0 ) )
& ( esk3_0 != esk4_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] :
( ( X4 = X5 )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ( ( n_pl @ X1 @ X4 )
!= ( n_pl @ X1 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
( esk1_0
= ( n_pl @ esk2_0 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
in @ esk4_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i] :
( ( X1 = esk4_0 )
| ( ( n_pl @ esk2_0 @ X1 )
!= esk1_0 )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[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])]) ).
thf(c_0_24,negated_conjecture,
( esk1_0
= ( n_pl @ esk2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_25,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_26,negated_conjecture,
esk3_0 != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM648^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n006.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 12:30:54 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 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.YgBL5z8jAT/E---3.1_644874.p
% 0.22/0.32 % Version: 3.5.1-ho
% 0.22/0.32 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.22/0.32 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.32 % Starting lpo1_fix with 900s (3) cores
% 0.22/0.32 % Starting full_lambda_9 with 300s (1) cores
% 0.22/0.32 % Starting almost_fo_4 with 300s (1) cores
% 0.22/0.32 % Starting new_ho_9 with 300s (1) cores
% 0.22/0.32 % Starting pre_casc_4 with 300s (1) cores
% 0.22/0.32 % Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.32 % full_lambda_9 with pid 644907 completed with status 0
% 0.22/0.32 % Result found by full_lambda_9
% 0.22/0.32 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.22/0.32 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.32 % Starting lpo1_fix with 900s (3) cores
% 0.22/0.32 % Starting full_lambda_9 with 300s (1) cores
% 0.22/0.32 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.22/0.32 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.22/0.32 % Search class: HGHSM-FFLM32-DHSMMSBN
% 0.22/0.32 % partial match(2): HGHSM-FSLM32-MHSMMSBN
% 0.22/0.32 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.32 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.32 % SubtermCWHack with pid 644924 completed with status 0
% 0.22/0.32 % Result found by SubtermCWHack
% 0.22/0.32 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.22/0.32 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.32 % Starting lpo1_fix with 900s (3) cores
% 0.22/0.32 % Starting full_lambda_9 with 300s (1) cores
% 0.22/0.32 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.22/0.32 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.22/0.32 % Search class: HGHSM-FFLM32-DHSMMSBN
% 0.22/0.32 % partial match(2): HGHSM-FSLM32-MHSMMSBN
% 0.22/0.32 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.32 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.32 % Preprocessing time : 0.003 s
% 0.22/0.32
% 0.22/0.32 % Proof found!
% 0.22/0.32 % SZS status Theorem
% 0.22/0.32 % SZS output start CNFRefutation
% See solution above
% 0.22/0.32 % Parsed axioms : 330
% 0.22/0.32 % Removed by relevancy pruning/SinE : 218
% 0.22/0.32 % Initial clauses : 176
% 0.22/0.32 % Removed in clause preprocessing : 35
% 0.22/0.32 % Initial clauses in saturation : 141
% 0.22/0.32 % Processed clauses : 322
% 0.22/0.32 % ...of these trivial : 15
% 0.22/0.32 % ...subsumed : 140
% 0.22/0.32 % ...remaining for further processing : 167
% 0.22/0.32 % Other redundant clauses eliminated : 14
% 0.22/0.32 % Clauses deleted for lack of memory : 0
% 0.22/0.32 % Backward-subsumed : 6
% 0.22/0.32 % Backward-rewritten : 0
% 0.22/0.32 % Generated clauses : 429
% 0.22/0.32 % ...of the previous two non-redundant : 395
% 0.22/0.32 % ...aggressively subsumed : 0
% 0.22/0.32 % Contextual simplify-reflections : 0
% 0.22/0.32 % Paramodulations : 320
% 0.22/0.32 % Factorizations : 2
% 0.22/0.32 % NegExts : 0
% 0.22/0.32 % Equation resolutions : 16
% 0.22/0.32 % Disequality decompositions : 0
% 0.22/0.32 % Total rewrite steps : 70
% 0.22/0.32 % ...of those cached : 41
% 0.22/0.32 % Propositional unsat checks : 0
% 0.22/0.32 % Propositional check models : 0
% 0.22/0.32 % Propositional check unsatisfiable : 0
% 0.22/0.32 % Propositional clauses : 0
% 0.22/0.32 % Propositional clauses after purity: 0
% 0.22/0.32 % Propositional unsat core size : 0
% 0.22/0.32 % Propositional preprocessing time : 0.000
% 0.22/0.32 % Propositional encoding time : 0.000
% 0.22/0.32 % Propositional solver time : 0.000
% 0.22/0.32 % Success case prop preproc time : 0.000
% 0.22/0.32 % Success case prop encoding time : 0.000
% 0.22/0.32 % Success case prop solver time : 0.000
% 0.22/0.32 % Current number of processed clauses : 159
% 0.22/0.32 % Positive orientable unit clauses : 46
% 0.22/0.32 % Positive unorientable unit clauses: 25
% 0.22/0.32 % Negative unit clauses : 23
% 0.22/0.32 % Non-unit-clauses : 65
% 0.22/0.32 % Current number of unprocessed clauses: 177
% 0.22/0.32 % ...number of literals in the above : 635
% 0.22/0.32 % Current number of archived formulas : 0
% 0.22/0.32 % Current number of archived clauses : 6
% 0.22/0.32 % Clause-clause subsumption calls (NU) : 936
% 0.22/0.32 % Rec. Clause-clause subsumption calls : 603
% 0.22/0.32 % Non-unit clause-clause subsumptions : 27
% 0.22/0.32 % Unit Clause-clause subsumption calls : 1098
% 0.22/0.32 % Rewrite failures with RHS unbound : 424
% 0.22/0.32 % BW rewrite match attempts : 275
% 0.22/0.32 % BW rewrite match successes : 48
% 0.22/0.32 % Condensation attempts : 0
% 0.22/0.32 % Condensation successes : 0
% 0.22/0.32 % Termbank termtop insertions : 28748
% 0.22/0.32 % Search garbage collected termcells : 8557
% 0.22/0.32
% 0.22/0.32 % -------------------------------------------------
% 0.22/0.32 % User time : 0.037 s
% 0.22/0.32 % System time : 0.006 s
% 0.22/0.32 % Total time : 0.043 s
% 0.22/0.32 % Maximum resident set size: 5368 pages
% 0.22/0.32
% 0.22/0.32 % -------------------------------------------------
% 0.22/0.32 % User time : 0.045 s
% 0.22/0.32 % System time : 0.011 s
% 0.22/0.32 % Total time : 0.056 s
% 0.22/0.32 % Maximum resident set size: 5120 pages
% 0.22/0.32 % E exiting
%------------------------------------------------------------------------------