%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM016^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:16:37 AM UTC 2026
% Result : Theorem 0.27s 0.28s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 112 ( 0 equ; 0 cnn)
% Maximal formula atoms : 22 ( 6 avg)
% Number of connectives : 380 ( 56 ~; 50 |; 44 &; 230 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 0 ^; 76 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
a: $i ).
thf(decl_24,type,
factorial_plus_one: $i > $i ).
thf(decl_25,type,
less: $i > $i > $o ).
thf(decl_26,type,
prime: $i > $o ).
thf(decl_27,type,
prime_divisor: $i > $i ).
thf(decl_28,type,
divides: $i > $i > $o ).
thf(cNUM016_1,conjecture,
~ ( ! [X1: $i] :
~ ( less @ X1 @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( less @ X1 @ X2 )
| ~ ( less @ X2 @ X1 ) )
& ! [X1: $i] : ( divides @ X1 @ X1 )
& ! [X1: $i,X2: $i,X3: $i] :
( ~ ( divides @ X1 @ X2 )
| ~ ( divides @ X2 @ X3 )
| ( divides @ X1 @ X3 ) )
& ! [X1: $i,X2: $i] :
( ~ ( divides @ X1 @ X2 )
| ~ ( less @ X2 @ X1 ) )
& ! [X1: $i] : ( less @ X1 @ ( factorial_plus_one @ X1 ) )
& ! [X1: $i,X2: $i] :
( ~ ( divides @ X1 @ ( factorial_plus_one @ X2 ) )
| ( less @ X2 @ X1 ) )
& ! [X1: $i] :
( ( prime @ X1 )
| ( divides @ ( prime_divisor @ X1 ) @ X1 ) )
& ! [X1: $i] :
( ( prime @ X1 )
| ( prime @ ( prime_divisor @ X1 ) ) )
& ! [X1: $i] :
( ( prime @ X1 )
| ( less @ ( prime_divisor @ X1 ) @ X1 ) )
& ( prime @ a )
& ! [X1: $i] :
( ~ ( prime @ X1 )
| ~ ( less @ a @ X1 )
| ( less @ ( factorial_plus_one @ a ) @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1pvIELs2F0/E---3.1_3432925.p',cNUM016_1) ).
thf(c_0_1,negated_conjecture,
~ ~ ( ! [X1: $i] :
~ ( less @ X1 @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( less @ X1 @ X2 )
| ~ ( less @ X2 @ X1 ) )
& ! [X1: $i] : ( divides @ X1 @ X1 )
& ! [X1: $i,X2: $i,X3: $i] :
( ~ ( divides @ X1 @ X2 )
| ~ ( divides @ X2 @ X3 )
| ( divides @ X1 @ X3 ) )
& ! [X1: $i,X2: $i] :
( ~ ( divides @ X1 @ X2 )
| ~ ( less @ X2 @ X1 ) )
& ! [X1: $i] : ( less @ X1 @ ( factorial_plus_one @ X1 ) )
& ! [X1: $i,X2: $i] :
( ~ ( divides @ X1 @ ( factorial_plus_one @ X2 ) )
| ( less @ X2 @ X1 ) )
& ! [X1: $i] :
( ( prime @ X1 )
| ( divides @ ( prime_divisor @ X1 ) @ X1 ) )
& ! [X1: $i] :
( ( prime @ X1 )
| ( prime @ ( prime_divisor @ X1 ) ) )
& ! [X1: $i] :
( ( prime @ X1 )
| ( less @ ( prime_divisor @ X1 ) @ X1 ) )
& ( prime @ a )
& ! [X1: $i] :
( ~ ( prime @ X1 )
| ~ ( less @ a @ X1 )
| ( less @ ( factorial_plus_one @ a ) @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cNUM016_1]) ).
thf(c_0_2,negated_conjecture,
~ ~ ( ! [X1: $i] :
~ ( less @ X1 @ X1 )
& ! [X1: $i,X2: $i] :
( ~ ( less @ X1 @ X2 )
| ~ ( less @ X2 @ X1 ) )
& ! [X1: $i] : ( divides @ X1 @ X1 )
& ! [X1: $i,X2: $i,X3: $i] :
( ~ ( divides @ X1 @ X2 )
| ~ ( divides @ X2 @ X3 )
| ( divides @ X1 @ X3 ) )
& ! [X1: $i,X2: $i] :
( ~ ( divides @ X1 @ X2 )
| ~ ( less @ X2 @ X1 ) )
& ! [X1: $i] : ( less @ X1 @ ( factorial_plus_one @ X1 ) )
& ! [X1: $i,X2: $i] :
( ~ ( divides @ X1 @ ( factorial_plus_one @ X2 ) )
| ( less @ X2 @ X1 ) )
& ! [X1: $i] :
( ( prime @ X1 )
| ( divides @ ( prime_divisor @ X1 ) @ X1 ) )
& ! [X1: $i] :
( ( prime @ X1 )
| ( prime @ ( prime_divisor @ X1 ) ) )
& ! [X1: $i] :
( ( prime @ X1 )
| ( less @ ( prime_divisor @ X1 ) @ X1 ) )
& ( prime @ a )
& ! [X1: $i] :
( ~ ( prime @ X1 )
| ~ ( less @ a @ X1 )
| ( less @ ( factorial_plus_one @ a ) @ X1 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X20: $i,X21: $i,X22: $i,X23: $i,X24: $i,X25: $i,X26: $i,X27: $i,X28: $i,X29: $i,X30: $i,X31: $i,X32: $i,X33: $i,X34: $i,X35: $i] :
( ~ ( less @ X20 @ X20 )
& ( ~ ( less @ X21 @ X22 )
| ~ ( less @ X22 @ X21 ) )
& ( divides @ X23 @ X23 )
& ( ~ ( divides @ X24 @ X25 )
| ~ ( divides @ X25 @ X26 )
| ( divides @ X24 @ X26 ) )
& ( ~ ( divides @ X27 @ X28 )
| ~ ( less @ X28 @ X27 ) )
& ( less @ X29 @ ( factorial_plus_one @ X29 ) )
& ( ~ ( divides @ X30 @ ( factorial_plus_one @ X31 ) )
| ( less @ X31 @ X30 ) )
& ( ( prime @ X32 )
| ( divides @ ( prime_divisor @ X32 ) @ X32 ) )
& ( ( prime @ X33 )
| ( prime @ ( prime_divisor @ X33 ) ) )
& ( ( prime @ X34 )
| ( less @ ( prime_divisor @ X34 ) @ X34 ) )
& ( prime @ a )
& ( ~ ( prime @ X35 )
| ~ ( less @ a @ X35 )
| ( less @ ( factorial_plus_one @ a ) @ X35 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])]) ).
thf(c_0_4,negated_conjecture,
! [X2: $i,X1: $i] :
( ~ ( less @ X1 @ X2 )
| ~ ( less @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X1: $i] :
( ( prime @ X1 )
| ( less @ ( prime_divisor @ X1 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i] :
~ ( less @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i] :
( ( less @ ( factorial_plus_one @ a ) @ X1 )
| ~ ( prime @ X1 )
| ~ ( less @ a @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i] : ( less @ X1 @ ( factorial_plus_one @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i] :
( ( prime @ X1 )
| ~ ( less @ X1 @ ( prime_divisor @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_10,negated_conjecture,
~ ( prime @ ( factorial_plus_one @ a ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]) ).
thf(c_0_11,negated_conjecture,
( ~ ( less @ a @ ( prime_divisor @ ( factorial_plus_one @ a ) ) )
| ~ ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_7]),c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ( prime @ X1 )
| ( prime @ ( prime_divisor @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X2: $i] :
( ( less @ X2 @ X1 )
| ~ ( divides @ X1 @ ( factorial_plus_one @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i] :
( ( prime @ X1 )
| ( divides @ ( prime_divisor @ X1 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_15,negated_conjecture,
~ ( less @ a @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_10]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] :
( ( less @ X1 @ ( prime_divisor @ ( factorial_plus_one @ X1 ) ) )
| ( prime @ ( factorial_plus_one @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM016^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n015.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 11:56:32 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.25 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.1pvIELs2F0/E---3.1_3432925.p
% 0.27/0.28 % Version: 3.5.1-ho
% 0.27/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.27/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.27/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.28 % Starting full_lambda_5 with 300s (1) cores
% 0.27/0.28 % Starting new_ho_10_unif with 300s (1) cores
% 0.27/0.28 % new_bool_1 with pid 3432940 completed with status 0
% 0.27/0.28 % Result found by new_bool_1
% 0.27/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.27/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.27/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.27/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.27/0.28 % Search class: HGHNS-FFSF11-SFFFFFNN
% 0.27/0.28 % partial match(1): HGHNF-FFSF11-SFFFFFNN
% 0.27/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.27/0.28 % SubtermCWHack with pid 3432945 completed with status 0
% 0.27/0.28 % Result found by SubtermCWHack
% 0.27/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.27/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.27/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.27/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.27/0.28 % Search class: HGHNS-FFSF11-SFFFFFNN
% 0.27/0.28 % partial match(1): HGHNF-FFSF11-SFFFFFNN
% 0.27/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.27/0.28 % Preprocessing time : 0.001 s
% 0.27/0.28
% 0.27/0.28 % Proof found!
% 0.27/0.28 % SZS status Theorem
% 0.27/0.28 % SZS output start CNFRefutation
% See solution above
% 0.27/0.28 % Parsed axioms : 7
% 0.27/0.28 % Removed by relevancy pruning/SinE : 6
% 0.27/0.28 % Initial clauses : 12
% 0.27/0.28 % Removed in clause preprocessing : 0
% 0.27/0.28 % Initial clauses in saturation : 12
% 0.27/0.28 % Processed clauses : 25
% 0.27/0.28 % ...of these trivial : 0
% 0.27/0.28 % ...subsumed : 5
% 0.27/0.28 % ...remaining for further processing : 20
% 0.27/0.28 % Other redundant clauses eliminated : 0
% 0.27/0.28 % Clauses deleted for lack of memory : 0
% 0.27/0.28 % Backward-subsumed : 1
% 0.27/0.28 % Backward-rewritten : 0
% 0.27/0.28 % Generated clauses : 18
% 0.27/0.28 % ...of the previous two non-redundant : 15
% 0.27/0.28 % ...aggressively subsumed : 0
% 0.27/0.28 % Contextual simplify-reflections : 0
% 0.27/0.28 % Paramodulations : 18
% 0.27/0.28 % Factorizations : 0
% 0.27/0.28 % NegExts : 0
% 0.27/0.28 % Equation resolutions : 0
% 0.27/0.28 % Disequality decompositions : 0
% 0.27/0.28 % Total rewrite steps : 5
% 0.27/0.28 % ...of those cached : 2
% 0.27/0.28 % Propositional unsat checks : 0
% 0.27/0.28 % Propositional check models : 0
% 0.27/0.28 % Propositional check unsatisfiable : 0
% 0.27/0.28 % Propositional clauses : 0
% 0.27/0.28 % Propositional clauses after purity: 0
% 0.27/0.28 % Propositional unsat core size : 0
% 0.27/0.28 % Propositional preprocessing time : 0.000
% 0.27/0.28 % Propositional encoding time : 0.000
% 0.27/0.28 % Propositional solver time : 0.000
% 0.27/0.28 % Success case prop preproc time : 0.000
% 0.27/0.28 % Success case prop encoding time : 0.000
% 0.27/0.28 % Success case prop solver time : 0.000
% 0.27/0.28 % Current number of processed clauses : 19
% 0.27/0.28 % Positive orientable unit clauses : 3
% 0.27/0.28 % Positive unorientable unit clauses: 0
% 0.27/0.28 % Negative unit clauses : 4
% 0.27/0.28 % Non-unit-clauses : 12
% 0.27/0.28 % Current number of unprocessed clauses: 2
% 0.27/0.28 % ...number of literals in the above : 5
% 0.27/0.28 % Current number of archived formulas : 0
% 0.27/0.28 % Current number of archived clauses : 1
% 0.27/0.28 % Clause-clause subsumption calls (NU) : 15
% 0.27/0.28 % Rec. Clause-clause subsumption calls : 15
% 0.27/0.28 % Non-unit clause-clause subsumptions : 1
% 0.27/0.28 % Unit Clause-clause subsumption calls : 2
% 0.27/0.28 % Rewrite failures with RHS unbound : 0
% 0.27/0.28 % BW rewrite match attempts : 0
% 0.27/0.28 % BW rewrite match successes : 0
% 0.27/0.28 % Condensation attempts : 0
% 0.27/0.28 % Condensation successes : 0
% 0.27/0.28 % Termbank termtop insertions : 1155
% 0.27/0.28 % Search garbage collected termcells : 183
% 0.27/0.28
% 0.27/0.28 % -------------------------------------------------
% 0.27/0.28 % User time : 0.002 s
% 0.27/0.28 % System time : 0.004 s
% 0.27/0.28 % Total time : 0.007 s
% 0.27/0.28 % Maximum resident set size: 3636 pages
% 0.27/0.28
% 0.27/0.28 % -------------------------------------------------
% 0.27/0.28 % User time : 0.003 s
% 0.27/0.28 % System time : 0.010 s
% 0.27/0.28 % Total time : 0.013 s
% 0.27/0.28 % Maximum resident set size: 4864 pages
% 0.27/0.28 % E exiting
%------------------------------------------------------------------------------