%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 : Thu Sep 24 01:44:14 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 26 ( 8 unt; 7 nHn; 17 RR)
% Number of literals : 47 ( 0 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(numbers_are_different,axiom,
( ~ less(X2,X1)
| ~ less(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',numbers_are_different) ).
cnf(nothing_is_less_than_itself,axiom,
~ less(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nothing_is_less_than_itself) ).
cnf(prove_there_is_another_prime,negated_conjecture,
( ~ less(a,X1)
| ~ prime(X1)
| less(factorial_plus_one(a),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_another_prime) ).
cnf(smaller_prime_divisors,axiom,
( less(prime_divisor(X1),X1)
| prime(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_prime_divisors) ).
cnf(a_prime_is_less_than_the_next_one,axiom,
less(X1,factorial_plus_one(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).
cnf(divisor_is_smaller,axiom,
( ~ divides(X1,factorial_plus_one(X2))
| less(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_is_smaller) ).
cnf(prime_divsiors,axiom,
( prime(prime_divisor(X1))
| prime(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_divsiors) ).
cnf(division_by_prime_divisor,axiom,
( divides(prime_divisor(X1),X1)
| prime(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',division_by_prime_divisor) ).
cnf(c_0_8,plain,
( ~ less(X2,X1)
| ~ less(X1,X2) ),
inference(fof_simplification,[status(thm)],[numbers_are_different]) ).
cnf(c_0_9,plain,
~ less(X1,X1),
inference(fof_simplification,[status(thm)],[nothing_is_less_than_itself]) ).
cnf(c_0_10,negated_conjecture,
( ~ less(a,X1)
| ~ prime(X1)
| less(factorial_plus_one(a),X1) ),
inference(fof_simplification,[status(thm)],[prove_there_is_another_prime]) ).
cnf(c_0_11,plain,
( ~ less(X2,X1)
| ~ less(X1,X2) ),
c_0_8 ).
cnf(c_0_12,axiom,
( less(prime_divisor(X1),X1)
| prime(X1) ),
smaller_prime_divisors ).
cnf(c_0_13,plain,
~ less(X1,X1),
c_0_9 ).
cnf(c_0_14,negated_conjecture,
( ~ less(a,X1)
| ~ prime(X1)
| less(factorial_plus_one(a),X1) ),
c_0_10 ).
cnf(c_0_15,axiom,
less(X1,factorial_plus_one(X1)),
a_prime_is_less_than_the_next_one ).
cnf(c_0_16,plain,
( ~ less(X1,prime_divisor(X1))
| prime(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
~ prime(factorial_plus_one(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_18,plain,
( ~ divides(X1,factorial_plus_one(X2))
| less(X2,X1) ),
inference(fof_simplification,[status(thm)],[divisor_is_smaller]) ).
cnf(c_0_19,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_16,c_0_14]),c_0_17]) ).
cnf(c_0_20,axiom,
( prime(prime_divisor(X1))
| prime(X1) ),
prime_divsiors ).
cnf(c_0_21,plain,
( ~ divides(X1,factorial_plus_one(X2))
| less(X2,X1) ),
c_0_18 ).
cnf(c_0_22,axiom,
( divides(prime_divisor(X1),X1)
| prime(X1) ),
division_by_prime_divisor ).
cnf(c_0_23,negated_conjecture,
~ less(a,prime_divisor(factorial_plus_one(a))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17]) ).
cnf(c_0_24,plain,
( less(X1,prime_divisor(factorial_plus_one(X1)))
| prime(factorial_plus_one(X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 01:59:23 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.43 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 % Version: 3.5.1
% 0.16/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.44 % Starting sh5l with 300s (1) cores
% 0.16/0.44 % sh5l with pid 4110046 completed with status 0
% 0.16/0.44 % Result found by sh5l
% 0.16/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.44 % Starting sh5l with 300s (1) cores
% 0.16/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.16/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.16/0.44 % Search class: FGHNS-FFSF11-SFFFFFNN
% 0.16/0.44 % partial match(1): FGHNF-FFSF11-SFFFFFNN
% 0.16/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.45 % SubtermCWHack with pid 4110053 completed with status 0
% 0.16/0.45 % Result found by SubtermCWHack
% 0.16/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.45 % Starting sh5l with 300s (1) cores
% 0.16/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.16/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.16/0.45 % Search class: FGHNS-FFSF11-SFFFFFNN
% 0.16/0.45 % partial match(1): FGHNF-FFSF11-SFFFFFNN
% 0.16/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.45 % Preprocessing time : 0.001 s
% 0.16/0.45
% 0.16/0.45 % Proof found!
% 0.16/0.45 % SZS status Unsatisfiable
% 0.16/0.45 % SZS output start CNFRefutation
% See solution above
% 0.16/0.45 % Parsed axioms : 12
% 0.16/0.45 % Removed by relevancy pruning/SinE : 0
% 0.16/0.45 % Initial clauses : 12
% 0.16/0.45 % Removed in clause preprocessing : 0
% 0.16/0.45 % Initial clauses in saturation : 12
% 0.16/0.45 % Processed clauses : 25
% 0.16/0.45 % ...of these trivial : 0
% 0.16/0.45 % ...subsumed : 5
% 0.16/0.45 % ...remaining for further processing : 20
% 0.16/0.45 % Other redundant clauses eliminated : 0
% 0.16/0.45 % Clauses deleted for lack of memory : 0
% 0.16/0.45 % Backward-subsumed : 1
% 0.16/0.45 % Backward-rewritten : 0
% 0.16/0.45 % Generated clauses : 18
% 0.16/0.45 % ...of the previous two non-redundant : 15
% 0.16/0.45 % ...aggressively subsumed : 0
% 0.16/0.45 % Contextual simplify-reflections : 0
% 0.16/0.45 % Paramodulations : 18
% 0.16/0.45 % Factorizations : 0
% 0.16/0.45 % NegExts : 0
% 0.16/0.45 % Equation resolutions : 0
% 0.16/0.45 % Disequality decompositions : 0
% 0.16/0.45 % Total rewrite steps : 5
% 0.16/0.45 % ...of those cached : 2
% 0.16/0.45 % Propositional unsat checks : 0
% 0.16/0.45 % Propositional check models : 0
% 0.16/0.45 % Propositional check unsatisfiable : 0
% 0.16/0.45 % Propositional clauses : 0
% 0.16/0.45 % Propositional clauses after purity: 0
% 0.16/0.45 % Propositional unsat core size : 0
% 0.16/0.45 % Propositional preprocessing time : 0.000
% 0.16/0.45 % Propositional encoding time : 0.000
% 0.16/0.45 % Propositional solver time : 0.000
% 0.16/0.45 % Success case prop preproc time : 0.000
% 0.16/0.45 % Success case prop encoding time : 0.000
% 0.16/0.45 % Success case prop solver time : 0.000
% 0.16/0.45 % Current number of processed clauses : 19
% 0.16/0.45 % Positive orientable unit clauses : 3
% 0.16/0.45 % Positive unorientable unit clauses: 0
% 0.16/0.45 % Negative unit clauses : 4
% 0.16/0.45 % Non-unit-clauses : 12
% 0.16/0.45 % Current number of unprocessed clauses: 2
% 0.16/0.45 % ...number of literals in the above : 5
% 0.16/0.45 % Current number of archived formulas : 0
% 0.16/0.45 % Current number of archived clauses : 1
% 0.16/0.45 % Clause-clause subsumption calls (NU) : 15
% 0.16/0.45 % Rec. Clause-clause subsumption calls : 15
% 0.16/0.45 % Non-unit clause-clause subsumptions : 1
% 0.16/0.45 % Unit Clause-clause subsumption calls : 2
% 0.16/0.45 % Rewrite failures with RHS unbound : 0
% 0.16/0.45 % BW rewrite match attempts : 0
% 0.16/0.45 % BW rewrite match successes : 0
% 0.16/0.45 % Condensation attempts : 0
% 0.16/0.45 % Condensation successes : 0
% 0.16/0.45 % Termbank termtop insertions : 460
% 0.16/0.45 % Search garbage collected termcells : 21
% 0.16/0.45
% 0.16/0.45 % -------------------------------------------------
% 0.16/0.45 % User time : 0.004 s
% 0.16/0.45 % System time : 0.001 s
% 0.16/0.45 % Total time : 0.005 s
% 0.16/0.45 % Maximum resident set size: 3636 pages
% 0.16/0.45
% 0.16/0.45 % -------------------------------------------------
% 0.16/0.45 % User time : 0.005 s
% 0.16/0.45 % System time : 0.006 s
% 0.16/0.45 % Total time : 0.012 s
% 0.16/0.45 % Maximum resident set size: 4608 pages
% 0.16/0.45 % E exiting
%------------------------------------------------------------------------------