%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM647^4 : 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 : n020.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 0.23s 0.37s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 122 ( 40 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 240 ( 32 ~; 21 |; 5 &; 160 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 70 ( 51 ^; 19 !; 0 ?; 70 :)
% 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_62,type,
imp: $o > $o > $o ).
thf(decl_63,type,
d_not: $o > $o ).
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_126,type,
nis: $i > $i > $o ).
thf(decl_143,type,
n_pl: $i > $i > $i ).
thf(decl_148,type,
esk1_0: $i ).
thf(decl_149,type,
esk2_0: $i ).
thf(decl_150,type,
esk3_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EXGPT1ot1l/E---3.1_984258.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EXGPT1ot1l/E---3.1_984258.p',def_imp) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EXGPT1ot1l/E---3.1_984258.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.EXGPT1ot1l/E---3.1_984258.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EXGPT1ot1l/E---3.1_984258.p',def_is_of) ).
thf(def_nis,axiom,
( nis
= ( ^ [X1: $i,X165: $i] : ( d_not @ ( n_is @ X1 @ X165 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EXGPT1ot1l/E---3.1_984258.p',def_nis) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EXGPT1ot1l/E---3.1_984258.p',def_n_is) ).
thf(satz8,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X203: $i] : ( in @ X203 @ nat )
@ ^ [X204: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( nis @ X204 @ X4 )
=> ( nis @ ( n_pl @ X1 @ X204 ) @ ( n_pl @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EXGPT1ot1l/E---3.1_984258.p',satz8) ).
thf(satz8a,conjecture,
( 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.EXGPT1ot1l/E---3.1_984258.p',satz8a) ).
thf(c_0_9,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_10,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_11,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_12,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_13,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_14,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_nis]) ).
thf(c_0_15,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_16,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_11]) ).
thf(c_0_17,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_18,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
thf(c_0_19,plain,
! [X348: $i] :
( ( in @ X348 @ nat )
=> ! [X347: $i] :
( ( in @ X347 @ nat )
=> ! [X346: $i] :
( ( in @ X346 @ nat )
=> ( ( ( X347 = X346 )
=> ~ $true )
=> ( ( ( n_pl @ X348 @ X347 )
= ( n_pl @ X348 @ X346 ) )
=> ~ $true ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz8]),c_0_17]),c_0_18]) ).
thf(c_0_20,negated_conjecture,
~ ( 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 ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz8a]) ).
thf(c_0_21,plain,
! [X424: $i,X425: $i,X426: $i] :
( ( ( X425 = X426 )
| ( ( n_pl @ X424 @ X425 )
!= ( n_pl @ X424 @ X426 ) )
| ~ $true
| ~ ( in @ X426 @ nat )
| ~ ( in @ X425 @ nat )
| ~ ( in @ X424 @ nat ) )
& ( $true
| ( ( n_pl @ X424 @ X425 )
!= ( n_pl @ X424 @ X426 ) )
| ~ $true
| ~ ( in @ X426 @ nat )
| ~ ( in @ X425 @ nat )
| ~ ( in @ X424 @ nat ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])]) ).
thf(c_0_22,negated_conjecture,
~ ! [X315: $i] :
( ( in @ X315 @ nat )
=> ! [X314: $i] :
( ( in @ X314 @ nat )
=> ! [X313: $i] :
( ( in @ X313 @ nat )
=> ( ( ( n_pl @ X315 @ X314 )
= ( n_pl @ X315 @ X313 ) )
=> ( X314 = X313 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_20]),c_0_17]),c_0_16]) ).
thf(c_0_23,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( X1 = X4 )
| ( ( n_pl @ X5 @ X1 )
!= ( n_pl @ X5 @ X4 ) )
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X5 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( ( n_pl @ esk1_0 @ esk2_0 )
= ( n_pl @ esk1_0 @ esk3_0 ) )
& ( esk2_0 != esk3_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
thf(c_0_25,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( X1 = X4 )
| ( ( n_pl @ X5 @ X1 )
!= ( n_pl @ X5 @ X4 ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_23]) ).
thf(c_0_26,negated_conjecture,
( ( n_pl @ esk1_0 @ esk2_0 )
= ( n_pl @ esk1_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_27,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_28,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i] :
( ( X1 = esk3_0 )
| ( ( n_pl @ esk1_0 @ X1 )
!= ( n_pl @ esk1_0 @ esk2_0 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
thf(c_0_30,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_31,negated_conjecture,
esk2_0 != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_29]),c_0_30])]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM647^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n020.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % 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 12:32:04 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.27 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.EXGPT1ot1l/E---3.1_984258.p
% 0.23/0.37 % Version: 3.5.1-ho
% 0.23/0.37 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.23/0.37 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.37 % Starting lpo1_fix with 900s (3) cores
% 0.23/0.37 % Starting full_lambda_9 with 300s (1) cores
% 0.23/0.37 % Starting almost_fo_4 with 300s (1) cores
% 0.23/0.37 % Starting new_ho_9 with 300s (1) cores
% 0.23/0.37 % Starting pre_casc_4 with 300s (1) cores
% 0.23/0.37 % Starting ho_unfolding_6 with 300s (1) cores
% 0.23/0.37 % full_lambda_9 with pid 984299 completed with status 0
% 0.23/0.37 % Result found by full_lambda_9
% 0.23/0.37 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.23/0.37 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.37 % Starting lpo1_fix with 900s (3) cores
% 0.23/0.37 % Starting full_lambda_9 with 300s (1) cores
% 0.23/0.37 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.23/0.37 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.23/0.37 % Search class: HGHSM-FFLM32-DHSMMSBN
% 0.23/0.37 % partial match(2): HGHSM-FSLM32-MHSMMSBN
% 0.23/0.37 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.37 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.37 % SubtermCWHack with pid 984307 completed with status 0
% 0.23/0.37 % Result found by SubtermCWHack
% 0.23/0.37 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.23/0.37 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.37 % Starting lpo1_fix with 900s (3) cores
% 0.23/0.37 % Starting full_lambda_9 with 300s (1) cores
% 0.23/0.37 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.23/0.37 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.23/0.37 % Search class: HGHSM-FFLM32-DHSMMSBN
% 0.23/0.37 % partial match(2): HGHSM-FSLM32-MHSMMSBN
% 0.23/0.37 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.37 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.37 % Preprocessing time : 0.005 s
% 0.23/0.37
% 0.23/0.37 % Proof found!
% 0.23/0.37 % SZS status Theorem
% 0.23/0.37 % SZS output start CNFRefutation
% See solution above
% 0.23/0.37 % Parsed axioms : 327
% 0.23/0.37 % Removed by relevancy pruning/SinE : 216
% 0.23/0.37 % Initial clauses : 152
% 0.23/0.37 % Removed in clause preprocessing : 19
% 0.23/0.37 % Initial clauses in saturation : 133
% 0.23/0.37 % Processed clauses : 499
% 0.23/0.37 % ...of these trivial : 18
% 0.23/0.37 % ...subsumed : 207
% 0.23/0.37 % ...remaining for further processing : 274
% 0.23/0.37 % Other redundant clauses eliminated : 13
% 0.23/0.37 % Clauses deleted for lack of memory : 0
% 0.23/0.37 % Backward-subsumed : 7
% 0.23/0.37 % Backward-rewritten : 0
% 0.23/0.37 % Generated clauses : 1513
% 0.23/0.37 % ...of the previous two non-redundant : 862
% 0.23/0.37 % ...aggressively subsumed : 0
% 0.23/0.37 % Contextual simplify-reflections : 1
% 0.23/0.37 % Paramodulations : 1402
% 0.23/0.37 % Factorizations : 2
% 0.23/0.37 % NegExts : 0
% 0.23/0.37 % Equation resolutions : 16
% 0.23/0.37 % Disequality decompositions : 0
% 0.23/0.37 % Total rewrite steps : 1202
% 0.23/0.37 % ...of those cached : 655
% 0.23/0.37 % Propositional unsat checks : 0
% 0.23/0.37 % Propositional check models : 0
% 0.23/0.37 % Propositional check unsatisfiable : 0
% 0.23/0.37 % Propositional clauses : 0
% 0.23/0.37 % Propositional clauses after purity: 0
% 0.23/0.37 % Propositional unsat core size : 0
% 0.23/0.37 % Propositional preprocessing time : 0.000
% 0.23/0.37 % Propositional encoding time : 0.000
% 0.23/0.37 % Propositional solver time : 0.000
% 0.23/0.37 % Success case prop preproc time : 0.000
% 0.23/0.37 % Success case prop encoding time : 0.000
% 0.23/0.37 % Success case prop solver time : 0.000
% 0.23/0.37 % Current number of processed clauses : 266
% 0.23/0.37 % Positive orientable unit clauses : 96
% 0.23/0.37 % Positive unorientable unit clauses: 26
% 0.23/0.37 % Negative unit clauses : 23
% 0.23/0.37 % Non-unit-clauses : 121
% 0.23/0.37 % Current number of unprocessed clauses: 460
% 0.23/0.37 % ...number of literals in the above : 1736
% 0.23/0.37 % Current number of archived formulas : 0
% 0.23/0.37 % Current number of archived clauses : 7
% 0.23/0.37 % Clause-clause subsumption calls (NU) : 2473
% 0.23/0.37 % Rec. Clause-clause subsumption calls : 1388
% 0.23/0.37 % Non-unit clause-clause subsumptions : 58
% 0.23/0.37 % Unit Clause-clause subsumption calls : 1052
% 0.23/0.37 % Rewrite failures with RHS unbound : 452
% 0.23/0.37 % BW rewrite match attempts : 560
% 0.23/0.37 % BW rewrite match successes : 50
% 0.23/0.37 % Condensation attempts : 0
% 0.23/0.37 % Condensation successes : 0
% 0.23/0.37 % Termbank termtop insertions : 49709
% 0.23/0.37 % Search garbage collected termcells : 7336
% 0.23/0.37
% 0.23/0.37 % -------------------------------------------------
% 0.23/0.37 % User time : 0.065 s
% 0.23/0.37 % System time : 0.008 s
% 0.23/0.37 % Total time : 0.073 s
% 0.23/0.37 % Maximum resident set size: 5364 pages
% 0.23/0.37
% 0.23/0.37 % -------------------------------------------------
% 0.23/0.37 % User time : 0.072 s
% 0.23/0.37 % System time : 0.015 s
% 0.23/0.37 % Total time : 0.087 s
% 0.23/0.37 % Maximum resident set size: 5376 pages
% 0.23/0.37 % E exiting
%------------------------------------------------------------------------------