%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM641^4 : 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 : n019.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 08:16:40 AM UTC 2026
% Result : Theorem 0.53s 0.38s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 80 ( 6 ~; 2 |; 1 &; 66 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 33 ( 26 ^; 7 !; 0 ?; 33 :)
% 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_131,type,
n_1: $i ).
thf(decl_143,type,
n_pl: $i > $i > $i ).
thf(decl_144,type,
esk1_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jhKntL45av/E---3.1_681011.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/sandbox/tmp/tmp.jhKntL45av/E---3.1_681011.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jhKntL45av/E---3.1_681011.p',def_is_of) ).
thf(satz4g,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( ordsucc @ X1 ) @ ( n_pl @ n_1 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jhKntL45av/E---3.1_681011.p',satz4g) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jhKntL45av/E---3.1_681011.p',def_n_is) ).
thf(satz4c,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( n_pl @ n_1 @ X1 ) @ ( ordsucc @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jhKntL45av/E---3.1_681011.p',satz4c) ).
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] : ( n_is @ ( ordsucc @ X1 ) @ ( n_pl @ n_1 @ X1 ) ) ),
inference(assume_negation,[status(cth)],[satz4g]) ).
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,
~ ! [X279: $i] :
( ( in @ X279 @ nat )
=> ( ( ordsucc @ X279 )
= ( n_pl @ n_1 @ X279 ) ) ),
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,
! [X285: $i] :
( ( in @ X285 @ nat )
=> ( ( n_pl @ n_1 @ X285 )
= ( ordsucc @ X285 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz4c]),c_0_10]),c_0_11]) ).
thf(c_0_14,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( ( ordsucc @ esk1_0 )
!= ( n_pl @ n_1 @ esk1_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,
! [X349: $i] :
( ~ ( in @ X349 @ nat )
| ( ( n_pl @ n_1 @ X349 )
= ( ordsucc @ X349 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
thf(c_0_16,negated_conjecture,
( ( ordsucc @ esk1_0 )
!= ( n_pl @ n_1 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,plain,
! [X1: $i] :
( ( ( n_pl @ n_1 @ X1 )
= ( ordsucc @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM641^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 % Computer : n019.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 12:23:17 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 Running higher-order theorem proving
% 0.26/0.32 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.jhKntL45av/E---3.1_681011.p
% 0.53/0.38 % Version: 3.5.1-ho
% 0.53/0.38 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.53/0.38 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.38 % Starting lpo1_fix with 900s (3) cores
% 0.53/0.38 % Starting full_lambda_9 with 300s (1) cores
% 0.53/0.38 % Starting almost_fo_4 with 300s (1) cores
% 0.53/0.38 % Starting new_ho_9 with 300s (1) cores
% 0.53/0.38 % Starting pre_casc_4 with 300s (1) cores
% 0.53/0.38 % Starting ho_unfolding_6 with 300s (1) cores
% 0.53/0.38 % pre_casc_4 with pid 681028 completed with status 0
% 0.53/0.38 % Result found by pre_casc_4
% 0.53/0.38 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.53/0.38 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.38 % Starting lpo1_fix with 900s (3) cores
% 0.53/0.38 % Starting full_lambda_9 with 300s (1) cores
% 0.53/0.38 % Starting almost_fo_4 with 300s (1) cores
% 0.53/0.38 % Starting new_ho_9 with 300s (1) cores
% 0.53/0.38 % Starting pre_casc_4 with 300s (1) cores
% 0.53/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.53/0.38 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.53/0.38 % Search class: HGUSM-FFMM31-DHSMMSBN
% 0.53/0.38 % partial match(3): HGHSM-FFMM31-SHSSMSBN
% 0.53/0.38 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.53/0.38 % Starting SubtermCWHack with 28s (1) cores
% 0.53/0.38 % SubtermCWHack with pid 681031 completed with status 0
% 0.53/0.38 % Result found by SubtermCWHack
% 0.53/0.38 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.53/0.38 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.38 % Starting lpo1_fix with 900s (3) cores
% 0.53/0.38 % Starting full_lambda_9 with 300s (1) cores
% 0.53/0.38 % Starting almost_fo_4 with 300s (1) cores
% 0.53/0.38 % Starting new_ho_9 with 300s (1) cores
% 0.53/0.38 % Starting pre_casc_4 with 300s (1) cores
% 0.53/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.53/0.38 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.53/0.38 % Search class: HGUSM-FFMM31-DHSMMSBN
% 0.53/0.38 % partial match(3): HGHSM-FFMM31-SHSSMSBN
% 0.53/0.38 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.53/0.38 % Starting SubtermCWHack with 28s (1) cores
% 0.53/0.38 % Preprocessing time : 0.005 s
% 0.53/0.38
% 0.53/0.38 % Proof found!
% 0.53/0.38 % SZS status Theorem
% 0.53/0.38 % SZS output start CNFRefutation
% See solution above
% 0.53/0.38 % Parsed axioms : 313
% 0.53/0.38 % Removed by relevancy pruning/SinE : 244
% 0.53/0.38 % Initial clauses : 108
% 0.53/0.38 % Removed in clause preprocessing : 3
% 0.53/0.38 % Initial clauses in saturation : 105
% 0.53/0.38 % Processed clauses : 47
% 0.53/0.38 % ...of these trivial : 2
% 0.53/0.38 % ...subsumed : 2
% 0.53/0.38 % ...remaining for further processing : 43
% 0.53/0.38 % Other redundant clauses eliminated : 4
% 0.53/0.38 % Clauses deleted for lack of memory : 0
% 0.53/0.38 % Backward-subsumed : 0
% 0.53/0.38 % Backward-rewritten : 0
% 0.53/0.38 % Generated clauses : 28
% 0.53/0.38 % ...of the previous two non-redundant : 17
% 0.53/0.38 % ...aggressively subsumed : 0
% 0.53/0.38 % Contextual simplify-reflections : 0
% 0.53/0.38 % Paramodulations : 20
% 0.53/0.38 % Factorizations : 0
% 0.53/0.38 % NegExts : 0
% 0.53/0.38 % Equation resolutions : 5
% 0.53/0.38 % Disequality decompositions : 0
% 0.53/0.38 % Total rewrite steps : 9
% 0.53/0.38 % ...of those cached : 2
% 0.53/0.38 % Propositional unsat checks : 0
% 0.53/0.38 % Propositional check models : 0
% 0.53/0.38 % Propositional check unsatisfiable : 0
% 0.53/0.38 % Propositional clauses : 0
% 0.53/0.38 % Propositional clauses after purity: 0
% 0.53/0.38 % Propositional unsat core size : 0
% 0.53/0.38 % Propositional preprocessing time : 0.000
% 0.53/0.38 % Propositional encoding time : 0.000
% 0.53/0.38 % Propositional solver time : 0.000
% 0.53/0.38 % Success case prop preproc time : 0.000
% 0.53/0.38 % Success case prop encoding time : 0.000
% 0.53/0.38 % Success case prop solver time : 0.000
% 0.53/0.38 % Current number of processed clauses : 43
% 0.53/0.38 % Positive orientable unit clauses : 20
% 0.53/0.38 % Positive unorientable unit clauses: 2
% 0.53/0.38 % Negative unit clauses : 5
% 0.53/0.38 % Non-unit-clauses : 16
% 0.53/0.38 % Current number of unprocessed clauses: 75
% 0.53/0.38 % ...number of literals in the above : 241
% 0.53/0.38 % Current number of archived formulas : 0
% 0.53/0.38 % Current number of archived clauses : 0
% 0.53/0.38 % Clause-clause subsumption calls (NU) : 24
% 0.53/0.38 % Rec. Clause-clause subsumption calls : 23
% 0.53/0.38 % Non-unit clause-clause subsumptions : 2
% 0.53/0.38 % Unit Clause-clause subsumption calls : 8
% 0.53/0.38 % Rewrite failures with RHS unbound : 0
% 0.53/0.38 % BW rewrite match attempts : 3
% 0.53/0.38 % BW rewrite match successes : 0
% 0.53/0.38 % Condensation attempts : 0
% 0.53/0.38 % Condensation successes : 0
% 0.53/0.38 % Termbank termtop insertions : 12999
% 0.53/0.38 % Search garbage collected termcells : 4500
% 0.53/0.38
% 0.53/0.38 % -------------------------------------------------
% 0.53/0.38 % User time : 0.019 s
% 0.53/0.38 % System time : 0.009 s
% 0.53/0.38 % Total time : 0.029 s
% 0.53/0.38 % Maximum resident set size: 4820 pages
% 0.53/0.38
% 0.53/0.38 % -------------------------------------------------
% 0.53/0.38 % User time : 0.028 s
% 0.53/0.38 % System time : 0.016 s
% 0.53/0.38 % Total time : 0.044 s
% 0.53/0.38 % Maximum resident set size: 5376 pages
% 0.53/0.38 % E exiting
%------------------------------------------------------------------------------