%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM016-2 : 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 : n020.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 1.57s 1.27s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 9 unt; 1 def)
% Number of atoms : 75 ( 1 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 49 ( 23 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 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(f3,axiom,
! [X0] : less(X0,factorial_plus_one(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).
fof(f4,axiom,
! [X0,X1] :
( less(X1,X0)
| ~ divides(X0,factorial_plus_one(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divisor_is_smaller) ).
fof(f5,axiom,
! [X0] :
( divides(prime_divisor(X0),X0)
| prime(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',division_by_prime_divisor) ).
fof(f6,axiom,
! [X0] :
( prime(prime_divisor(X0))
| prime(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_divsiors) ).
fof(f7,axiom,
! [X0] :
( less(prime_divisor(X0),X0)
| prime(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',smaller_prime_divisors) ).
fof(f8,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_57,plain,
! [X0: $i] : ~ less(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_59,plain,
! [X0: $i] : less(X0,factorial_plus_one(X0)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( less(X1,X0)
| ~ divides(X0,factorial_plus_one(X1)) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_61,plain,
! [X0: $i] :
( prime(X0)
| divides(prime_divisor(X0),X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_62,plain,
! [X0: $i] :
( prime(X0)
| prime(prime_divisor(X0)) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_63,plain,
! [X0: $i] :
( prime(X0)
| less(prime_divisor(X0),X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_64,negated_conjecture,
! [X0: $i] :
( less(factorial_plus_one(a),X0)
| ~ prime(X0)
| ~ less(a,X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_101,plain,
! [X0: $i] :
( prime(factorial_plus_one(X0))
| less(X0,prime_divisor(factorial_plus_one(X0))) ),
inference(resolution,[status(thm)],[c_60,c_61]) ).
tcf(c_137,definition,
iPr_def_10 = factorial_plus_one(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_138,negated_conjecture,
! [X0: $i] :
( less(iPr_def_10,X0)
| ~ prime(X0)
| ~ less(a,X0) ),
inference(demodulation,[status(thm)],[c_64,c_137]) ).
tcf(c_271,plain,
( less(iPr_def_10,factorial_plus_one(a))
| ~ prime(factorial_plus_one(a)) ),
inference(superposition,[status(thm)],[c_59,c_138]) ).
tcf(c_272,plain,
( less(iPr_def_10,iPr_def_10)
| ~ prime(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_271,c_137]) ).
tcf(c_273,plain,
~ prime(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_272,c_57]) ).
tcf(c_289,plain,
( prime(factorial_plus_one(a))
| less(iPr_def_10,prime_divisor(factorial_plus_one(a)))
| ~ prime(prime_divisor(factorial_plus_one(a))) ),
inference(superposition,[status(thm)],[c_101,c_138]) ).
tcf(c_292,plain,
( prime(iPr_def_10)
| less(iPr_def_10,prime_divisor(iPr_def_10))
| ~ prime(prime_divisor(iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_289,c_137]) ).
tcf(c_293,plain,
( less(iPr_def_10,prime_divisor(iPr_def_10))
| ~ prime(prime_divisor(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_292,c_273]) ).
tcf(c_301,plain,
! [X0: $i] :
( prime(X0)
| ~ less(X0,prime_divisor(X0)) ),
inference(superposition,[status(thm)],[c_63,c_58]) ).
tcf(c_323,plain,
( prime(iPr_def_10)
| ~ prime(prime_divisor(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_293,c_301]) ).
tcf(c_324,plain,
~ prime(prime_divisor(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_323,c_273]) ).
tcf(c_325,plain,
prime(iPr_def_10),
inference(superposition,[status(thm)],[c_62,c_324]) ).
tcf(c_326,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_325,c_273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM016-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 02:40:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.57/1.27 % SZS status Started for theBenchmark.p
% 1.57/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 1.57/1.27
% 1.57/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.57/1.27
% 1.57/1.27 % ------ iProver source info
% 1.57/1.27
% 1.57/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.57/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.57/1.27 % git: non_committed_changes: false
% 1.57/1.27
% 1.57/1.27 % ------ Parsing...% successful
% 1.57/1.27
% 1.57/1.27
% 1.57/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.57/1.27
% 1.57/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.57/1.27
% 1.57/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.57/1.27
% 1.57/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.57/1.27 % ------ Proving...
% 1.57/1.27 % ------ Problem Properties
% 1.57/1.27
% 1.57/1.27 %
% 1.57/1.27 % clauses 8
% 1.57/1.27 % conjectures 1
% 1.57/1.27 % EPR 3
% 1.57/1.27 % Horn 5
% 1.57/1.27 % unary 3
% 1.57/1.27 % binary 4
% 1.57/1.27 % lits 14
% 1.57/1.27 % lits eq 1
% 1.57/1.27 % fd_pure 0
% 1.57/1.27 % fd_pseudo 0
% 1.57/1.27 % fd_cond 0
% 1.57/1.27 % fd_pseudo_cond 0
% 1.57/1.27 % AC symbols 0
% 1.57/1.27
% 1.57/1.27 % ------ Schedule dynamic 5 is on
% 1.57/1.27
% 1.57/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.57/1.27
% 1.57/1.27
% 1.57/1.27 % ------
% 1.57/1.27 % Current options:
% 1.57/1.27 % ------
% 1.57/1.27
% 1.57/1.27
% 1.57/1.27 %
% 1.57/1.27
% 1.57/1.27 % ------ Proving...
% 1.57/1.27 %
% 1.57/1.27
% 1.57/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 1.57/1.27
% 1.57/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.57/1.27
% 1.57/1.27
%------------------------------------------------------------------------------