%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP134^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:04:27 AM UTC 2026
% Result : Theorem 0.53s 0.39s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 6 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 130 ( 8 ~; 4 |; 6 &; 104 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 14 ^; 18 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
set_nat_nat: $tType ).
thf(decl_37,type,
finite570312790at_nat: set_nat_nat > $o ).
thf(decl_44,type,
one_one_nat: nat ).
thf(decl_45,type,
plus_plus_nat: nat > nat > nat ).
thf(decl_46,type,
zero_zero_nat: nat ).
thf(decl_47,type,
number1551313001itions: ( nat > nat ) > nat > $o ).
thf(decl_56,type,
ord_less_eq_nat: nat > nat > $o ).
thf(decl_60,type,
ord_le1415039317at_nat: set_nat_nat > set_nat_nat > $o ).
thf(decl_71,type,
collect_nat_nat: ( ( nat > nat ) > $o ) > set_nat_nat ).
thf(decl_84,type,
n: nat ).
thf(conj_0,conjecture,
( finite570312790at_nat
@ ( collect_nat_nat
@ ^ [X3: nat > nat] : ( number1551313001itions @ X3 @ n ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fCPpFfvfYx/E---3.1_1774458.p',conj_0) ).
thf(fact_62_rev__finite__subset,axiom,
! [X190: set_nat_nat,X191: set_nat_nat] :
( ( finite570312790at_nat @ X190 )
=> ( ( ord_le1415039317at_nat @ X191 @ X190 )
=> ( finite570312790at_nat @ X191 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fCPpFfvfYx/E---3.1_1774458.p',fact_62_rev__finite__subset) ).
thf(fact_1__092_060open_062_123p_O_Ap_Apartitions_An_125_A_092_060subseteq_062_A_123f_O_A_I_092_060forall_062i_O_Af_Ai_A_092_060le_062_An_J_A_092_060and_062_A_I_092_060forall_062i_092_060ge_062n_A_L_A1_O_Af_Ai_A_061_A0_J_125_092_060close_062,axiom,
( ord_le1415039317at_nat
@ ( collect_nat_nat
@ ^ [X3: nat > nat] : ( number1551313001itions @ X3 @ n ) )
@ ( collect_nat_nat
@ ^ [X1: nat > nat] :
( ! [X2: nat] : ( ord_less_eq_nat @ ( X1 @ X2 ) @ n )
& ! [X2: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ n @ one_one_nat ) @ X2 )
=> ( ( X1 @ X2 )
= zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fCPpFfvfYx/E---3.1_1774458.p',fact_1__092_060open_062_123p_O_Ap_Apartitions_An_125_A_092_060subseteq_062_A_123f_O_A_I_092_060forall_062i_O_Af_Ai_A_092_060le_062_An_J_A_092_060and_062_A_I_092_060forall_062i_092_060ge_062n_A_L_A1_O_Af_Ai_A_061_A0_J_125_092_060close_062) ).
thf(fact_0__092_060open_062finite_A_123f_O_A_I_092_060forall_062i_O_Af_Ai_A_092_060le_062_An_J_A_092_060and_062_A_I_092_060forall_062i_092_060ge_062n_A_L_A1_O_Af_Ai_A_061_A0_J_125_092_060close_062,axiom,
( finite570312790at_nat
@ ( collect_nat_nat
@ ^ [X1: nat > nat] :
( ! [X2: nat] : ( ord_less_eq_nat @ ( X1 @ X2 ) @ n )
& ! [X2: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ n @ one_one_nat ) @ X2 )
=> ( ( X1 @ X2 )
= zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fCPpFfvfYx/E---3.1_1774458.p',fact_0__092_060open_062finite_A_123f_O_A_I_092_060forall_062i_O_Af_Ai_A_092_060le_062_An_J_A_092_060and_062_A_I_092_060forall_062i_092_060ge_062n_A_L_A1_O_Af_Ai_A_061_A0_J_125_092_060close_062) ).
thf(c_0_4,negated_conjecture,
~ ( finite570312790at_nat
@ ( collect_nat_nat
@ ^ [X3: nat > nat] : ( number1551313001itions @ X3 @ n ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_5,negated_conjecture,
~ ( finite570312790at_nat
@ ( collect_nat_nat
@ ^ [Z0: nat > nat] : ( number1551313001itions @ Z0 @ n ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_4])]) ).
thf(c_0_6,plain,
! [X1574: set_nat_nat,X1575: set_nat_nat] :
( ~ ( finite570312790at_nat @ X1574 )
| ~ ( ord_le1415039317at_nat @ X1575 @ X1574 )
| ( finite570312790at_nat @ X1575 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_62_rev__finite__subset])])]) ).
thf(c_0_7,plain,
( ord_le1415039317at_nat
@ ( collect_nat_nat
@ ^ [Z0: nat > nat] : ( number1551313001itions @ Z0 @ n ) )
@ ( collect_nat_nat
@ ^ [Z0: nat > nat] :
( ! [X2: nat] : ( ord_less_eq_nat @ ( Z0 @ X2 ) @ n )
& ! [X2: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ n @ one_one_nat ) @ X2 )
=> ( ( Z0 @ X2 )
= zero_zero_nat ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_1__092_060open_062_123p_O_Ap_Apartitions_An_125_A_092_060subseteq_062_A_123f_O_A_I_092_060forall_062i_O_Af_Ai_A_092_060le_062_An_J_A_092_060and_062_A_I_092_060forall_062i_092_060ge_062n_A_L_A1_O_Af_Ai_A_061_A0_J_125_092_060close_062]) ).
thf(c_0_8,plain,
( finite570312790at_nat
@ ( collect_nat_nat
@ ^ [Z0: nat > nat] :
( ! [X2: nat] : ( ord_less_eq_nat @ ( Z0 @ X2 ) @ n )
& ! [X2: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ n @ one_one_nat ) @ X2 )
=> ( ( Z0 @ X2 )
= zero_zero_nat ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_0__092_060open_062finite_A_123f_O_A_I_092_060forall_062i_O_Af_Ai_A_092_060le_062_An_J_A_092_060and_062_A_I_092_060forall_062i_092_060ge_062n_A_L_A1_O_Af_Ai_A_061_A0_J_125_092_060close_062]) ).
thf(c_0_9,negated_conjecture,
~ ( finite570312790at_nat
@ ( collect_nat_nat
@ ^ [Z0: nat > nat] : ( number1551313001itions @ Z0 @ n ) ) ),
inference(fof_nnf,[status(thm)],[c_0_5]) ).
thf(c_0_10,plain,
! [X41: set_nat_nat,X38: set_nat_nat] :
( ( finite570312790at_nat @ X41 )
| ~ ( finite570312790at_nat @ X38 )
| ~ ( ord_le1415039317at_nat @ X41 @ X38 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,plain,
( ord_le1415039317at_nat
@ ( collect_nat_nat
@ ^ [Z0: nat > nat] : ( number1551313001itions @ Z0 @ n ) )
@ ( collect_nat_nat
@ ^ [Z0: nat > nat] :
( ! [X2425: nat] : ( ord_less_eq_nat @ ( Z0 @ X2425 ) @ n )
& ! [X2426: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ n @ one_one_nat ) @ X2426 )
=> ( ( Z0 @ X2426 )
= zero_zero_nat ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
( finite570312790at_nat
@ ( collect_nat_nat
@ ^ [Z0: nat > nat] :
( ! [X2427: nat] : ( ord_less_eq_nat @ ( Z0 @ X2427 ) @ n )
& ! [X2428: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ n @ one_one_nat ) @ X2428 )
=> ( ( Z0 @ X2428 )
= zero_zero_nat ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,negated_conjecture,
~ ( finite570312790at_nat
@ ( collect_nat_nat
@ ^ [Z0: nat > nat] : ( number1551313001itions @ Z0 @ n ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP134^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n002.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 20:01:07 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.23/0.28 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.fCPpFfvfYx/E---3.1_1774458.p
% 0.53/0.39 % Version: 3.5.1-ho
% 0.53/0.39 % Preprocessing class: HSLSSMSSSSLNHHA.
% 0.53/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.39 % Starting full_lambda_1 with 1200s (4) cores
% 0.53/0.39 % Starting additional_ho_7 with 600s (2) cores
% 0.53/0.39 % Starting full_lambda_3 with 300s (1) cores
% 0.53/0.39 % Starting lpo8_s with 300s (1) cores
% 0.53/0.39 % additional_ho_7 with pid 1774504 completed with status 0
% 0.53/0.39 % Result found by additional_ho_7
% 0.53/0.39 % Preprocessing class: HSLSSMSSSSLNHHA.
% 0.53/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.39 % Starting full_lambda_1 with 1200s (4) cores
% 0.53/0.39 % Starting additional_ho_7 with 600s (2) cores
% 0.53/0.39 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4.0,,2,20000,1.0))
% 0.53/0.39 % SinE strategy is GSinE(CountFormulas,hypos,4.0,,2,20000,1.0)
% 0.53/0.39 % Search class: HGHSM-FSLS32-DHHFFSBN
% 0.53/0.39 % partial match(1): HGHSM-FSLS32-MHHFFSBN
% 0.53/0.39 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.53/0.39 % Starting SubtermCWHack with 55s (1) cores
% 0.53/0.39 % Starting additional_ho_7 with 61s (1) cores
% 0.53/0.39 % additional_ho_7 with pid 1774517 completed with status 0
% 0.53/0.39 % Result found by additional_ho_7
% 0.53/0.39 % Preprocessing class: HSLSSMSSSSLNHHA.
% 0.53/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.39 % Starting full_lambda_1 with 1200s (4) cores
% 0.53/0.39 % Starting additional_ho_7 with 600s (2) cores
% 0.53/0.39 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4.0,,2,20000,1.0))
% 0.53/0.39 % SinE strategy is GSinE(CountFormulas,hypos,4.0,,2,20000,1.0)
% 0.53/0.39 % Search class: HGHSM-FSLS32-DHHFFSBN
% 0.53/0.39 % partial match(1): HGHSM-FSLS32-MHHFFSBN
% 0.53/0.39 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.53/0.39 % Starting SubtermCWHack with 55s (1) cores
% 0.53/0.39 % Starting additional_ho_7 with 61s (1) cores
% 0.53/0.39 % Preprocessing time : 0.015 s
% 0.53/0.39
% 0.53/0.39 % Proof found!
% 0.53/0.39 % SZS status Theorem
% 0.53/0.39 % SZS output start CNFRefutation
% See solution above
% 0.53/0.39 % Parsed axioms : 429
% 0.53/0.39 % Removed by relevancy pruning/SinE : 119
% 0.53/0.39 % Initial clauses : 598
% 0.53/0.39 % Removed in clause preprocessing : 13
% 0.53/0.39 % Initial clauses in saturation : 585
% 0.53/0.39 % Processed clauses : 19
% 0.53/0.39 % ...of these trivial : 3
% 0.53/0.39 % ...subsumed : 1
% 0.53/0.39 % ...remaining for further processing : 15
% 0.53/0.39 % Other redundant clauses eliminated : 0
% 0.53/0.39 % Clauses deleted for lack of memory : 0
% 0.53/0.39 % Backward-subsumed : 0
% 0.53/0.39 % Backward-rewritten : 2
% 0.53/0.39 % Generated clauses : 3
% 0.53/0.39 % ...of the previous two non-redundant : 1
% 0.53/0.39 % ...aggressively subsumed : 0
% 0.53/0.39 % Contextual simplify-reflections : 0
% 0.53/0.39 % Paramodulations : 2
% 0.53/0.39 % Factorizations : 0
% 0.53/0.39 % NegExts : 0
% 0.53/0.39 % Equation resolutions : 0
% 0.53/0.39 % Disequality decompositions : 0
% 0.53/0.39 % Total rewrite steps : 6
% 0.53/0.39 % ...of those cached : 1
% 0.53/0.39 % Propositional unsat checks : 0
% 0.53/0.39 % Propositional check models : 0
% 0.53/0.39 % Propositional check unsatisfiable : 0
% 0.53/0.39 % Propositional clauses : 0
% 0.53/0.39 % Propositional clauses after purity: 0
% 0.53/0.39 % Propositional unsat core size : 0
% 0.53/0.39 % Propositional preprocessing time : 0.000
% 0.53/0.39 % Propositional encoding time : 0.000
% 0.53/0.39 % Propositional solver time : 0.000
% 0.53/0.39 % Success case prop preproc time : 0.000
% 0.53/0.39 % Success case prop encoding time : 0.000
% 0.53/0.39 % Success case prop solver time : 0.000
% 0.53/0.39 % Current number of processed clauses : 13
% 0.53/0.39 % Positive orientable unit clauses : 5
% 0.53/0.39 % Positive unorientable unit clauses: 0
% 0.53/0.39 % Negative unit clauses : 4
% 0.53/0.39 % Non-unit-clauses : 4
% 0.53/0.39 % Current number of unprocessed clauses: 567
% 0.53/0.39 % ...number of literals in the above : 1630
% 0.53/0.39 % Current number of archived formulas : 0
% 0.53/0.39 % Current number of archived clauses : 2
% 0.53/0.39 % Clause-clause subsumption calls (NU) : 1
% 0.53/0.39 % Rec. Clause-clause subsumption calls : 1
% 0.53/0.39 % Non-unit clause-clause subsumptions : 1
% 0.53/0.39 % Unit Clause-clause subsumption calls : 3
% 0.53/0.39 % Rewrite failures with RHS unbound : 0
% 0.53/0.39 % BW rewrite match attempts : 3
% 0.53/0.39 % BW rewrite match successes : 2
% 0.53/0.39 % Condensation attempts : 0
% 0.53/0.39 % Condensation successes : 0
% 0.53/0.39 % Termbank termtop insertions : 53663
% 0.53/0.39 % Search garbage collected termcells : 15605
% 0.53/0.39
% 0.53/0.39 % -------------------------------------------------
% 0.53/0.39 % User time : 0.049 s
% 0.53/0.39 % System time : 0.016 s
% 0.53/0.39 % Total time : 0.065 s
% 0.53/0.39 % Maximum resident set size: 7508 pages
% 0.53/0.39
% 0.53/0.39 % -------------------------------------------------
% 0.53/0.39 % User time : 0.085 s
% 0.53/0.39 % System time : 0.024 s
% 0.53/0.39 % Total time : 0.109 s
% 0.53/0.39 % Maximum resident set size: 5888 pages
% 0.53/0.39 % E exiting
%------------------------------------------------------------------------------