%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 : Fri Sep 25 02:23:14 PM UTC 2026
% Result : Unsatisfiable 1.63s 1.18s
% Output : CNFRefutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 10 unt; 1 def)
% Number of atoms : 71 ( 1 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 45 ( 22 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn 23 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ less(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nothing_is_less_than_itself) ).
fof(f2,axiom,
! [X0,X1] :
( ~ less(X1,X0)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',numbers_are_different) ).
fof(f6,axiom,
! [X0] : less(X0,factorial_plus_one(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).
fof(f7,axiom,
! [X0,X1] :
( less(X1,X0)
| ~ divides(X0,factorial_plus_one(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divisor_is_smaller) ).
fof(f8,axiom,
! [X0] :
( divides(prime_divisor(X0),X0)
| prime(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',division_by_prime_divisor) ).
fof(f9,axiom,
! [X0] :
( prime(prime_divisor(X0))
| prime(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_divsiors) ).
fof(f10,axiom,
! [X0] :
( less(prime_divisor(X0),X0)
| prime(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',smaller_prime_divisors) ).
fof(f12,negated_conjecture,
! [X0] :
( less(factorial_plus_one(a),X0)
| ~ less(a,X0)
| ~ prime(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_another_prime) ).
tcf(c_61,plain,
! [X0: $i] : ~ less(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_66,plain,
! [X0: $i] : less(X0,factorial_plus_one(X0)),
inference(cnf_transformation,[],[f6]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( less(X1,X0)
| ~ divides(X0,factorial_plus_one(X1)) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_68,plain,
! [X0: $i] :
( prime(X0)
| divides(prime_divisor(X0),X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_69,plain,
! [X0: $i] :
( prime(X0)
| prime(prime_divisor(X0)) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_70,plain,
! [X0: $i] :
( prime(X0)
| less(prime_divisor(X0),X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_72,negated_conjecture,
! [X0: $i] :
( less(factorial_plus_one(a),X0)
| ~ prime(X0)
| ~ less(a,X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_121,definition,
iPr_def_10 = factorial_plus_one(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_122,negated_conjecture,
! [X0: $i] :
( less(iPr_def_10,X0)
| ~ prime(X0)
| ~ less(a,X0) ),
inference(demodulation,[status(thm)],[c_72,c_121]) ).
tcf(c_298,plain,
( less(iPr_def_10,factorial_plus_one(a))
| ~ prime(factorial_plus_one(a)) ),
inference(superposition,[status(thm)],[c_66,c_122]) ).
tcf(c_299,plain,
( less(iPr_def_10,iPr_def_10)
| ~ prime(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_298,c_121]) ).
tcf(c_300,plain,
~ prime(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_299,c_61]) ).
tcf(c_320,plain,
! [X0: $i] :
( prime(X0)
| ~ less(X0,prime_divisor(X0)) ),
inference(superposition,[status(thm)],[c_70,c_62]) ).
tcf(c_351,plain,
! [X0: $i] :
( less(a,X0)
| ~ divides(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_121,c_67]) ).
tcf(c_363,plain,
( prime(iPr_def_10)
| less(a,prime_divisor(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_68,c_351]) ).
tcf(c_364,plain,
less(a,prime_divisor(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_363,c_300]) ).
tcf(c_367,plain,
( less(iPr_def_10,prime_divisor(iPr_def_10))
| ~ prime(prime_divisor(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_364,c_122]) ).
tcf(c_376,plain,
( prime(iPr_def_10)
| ~ prime(prime_divisor(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_367,c_320]) ).
tcf(c_377,plain,
~ prime(prime_divisor(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_376,c_300]) ).
tcf(c_378,plain,
prime(iPr_def_10),
inference(superposition,[status(thm)],[c_69,c_377]) ).
tcf(c_379,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_378,c_300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 02:39:47 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.63/1.18 % SZS status Started for theBenchmark.p
% 1.63/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 1.63/1.18
% 1.63/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.63/1.18
% 1.63/1.18 % ------ iProver source info
% 1.63/1.18
% 1.63/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 1.63/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.63/1.18 % git: non_committed_changes: false
% 1.63/1.18
% 1.63/1.18 % ------ Parsing...% successful
% 1.63/1.18
% 1.63/1.18
% 1.63/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.63/1.18
% 1.63/1.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.63/1.18
% 1.63/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.63/1.18
% 1.63/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.63/1.18 % ------ Proving...
% 1.63/1.18 % ------ Problem Properties
% 1.63/1.18
% 1.63/1.18 %
% 1.63/1.18 % clauses 13
% 1.63/1.18 % conjectures 1
% 1.63/1.18 % EPR 7
% 1.63/1.18 % Horn 10
% 1.63/1.18 % unary 5
% 1.63/1.18 % binary 6
% 1.63/1.18 % lits 23
% 1.63/1.18 % lits eq 1
% 1.63/1.18 % fd_pure 0
% 1.63/1.18 % fd_pseudo 0
% 1.63/1.18 % fd_cond 0
% 1.63/1.18 % fd_pseudo_cond 0
% 1.63/1.18 % AC symbols 0
% 1.63/1.18
% 1.63/1.18 % ------ Schedule dynamic 5 is on
% 1.63/1.18
% 1.63/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.63/1.18
% 1.63/1.18
% 1.63/1.18 % ------
% 1.63/1.18 % Current options:
% 1.63/1.18 % ------
% 1.63/1.18
% 1.63/1.18
% 1.63/1.18 %
% 1.63/1.18
% 1.63/1.18 % ------ Proving...
% 1.63/1.18 %
% 1.63/1.18
% 1.63/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 1.63/1.18
% 1.63/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.63/1.18
% 1.63/1.18
%------------------------------------------------------------------------------