%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM016-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 07:55:01 PM UTC 2025
% Result : Unsatisfiable 2.90s 1.71s
% Output : CNFRefutation 2.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 24 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 20 ( 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less > divides > prime > #nlpp > prime_divisor > factorial_plus_one > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(prime_divisor,type,
prime_divisor: $i > $i ).
tff(factorial_plus_one,type,
factorial_plus_one: $i > $i ).
tff(a,type,
a: $i ).
tff(less,type,
less: ( $i * $i ) > $o ).
tff(prime,type,
prime: $i > $o ).
tff(divides,type,
divides: ( $i * $i ) > $o ).
tff(f_54,axiom,
! [X] : less(X,factorial_plus_one(X)),
file(unknown,unknown) ).
tff(f_80,axiom,
! [X] :
( ~ prime(X)
| ~ less(a,X)
| less(factorial_plus_one(a),X) ),
file(unknown,unknown) ).
tff(f_30,axiom,
! [X] : ~ less(X,X),
file(unknown,unknown) ).
tff(f_63,axiom,
! [X] :
( prime(X)
| divides(prime_divisor(X),X) ),
file(unknown,unknown) ).
tff(f_59,axiom,
! [X,Y] :
( ~ divides(X,factorial_plus_one(Y))
| less(Y,X) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [X] :
( prime(X)
| prime(prime_divisor(X)) ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [X,Y] :
( ~ divides(X,Y)
| ~ less(Y,X) ),
file(unknown,unknown) ).
tff(c_12,plain,
! [X_10] : less(X_10,factorial_plus_one(X_10)),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_71,plain,
! [X_34] :
( less(factorial_plus_one(a),X_34)
| ~ less(a,X_34)
| ~ prime(X_34) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_2,plain,
! [X_1] : ~ less(X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_88,plain,
( ~ less(a,factorial_plus_one(a))
| ~ prime(factorial_plus_one(a)) ),
inference(resolution,[status(thm)],[c_71,c_2]) ).
tff(c_97,plain,
~ prime(factorial_plus_one(a)),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_88]) ).
tff(c_16,plain,
! [X_13] :
( divides(prime_divisor(X_13),X_13)
| prime(X_13) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_51,plain,
! [Y_31,X_32] :
( less(Y_31,X_32)
| ~ divides(X_32,factorial_plus_one(Y_31)) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_60,plain,
! [Y_31] :
( less(Y_31,prime_divisor(factorial_plus_one(Y_31)))
| prime(factorial_plus_one(Y_31)) ),
inference(resolution,[status(thm)],[c_16,c_51]) ).
tff(c_18,plain,
! [X_14] :
( prime(prime_divisor(X_14))
| prime(X_14) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_10,plain,
! [Y_9,X_8] :
( ~ less(Y_9,X_8)
| ~ divides(X_8,Y_9) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_107,plain,
! [X_40] :
( ~ divides(X_40,factorial_plus_one(a))
| ~ less(a,X_40)
| ~ prime(X_40) ),
inference(resolution,[status(thm)],[c_71,c_10]) ).
tff(c_111,plain,
( ~ less(a,prime_divisor(factorial_plus_one(a)))
| ~ prime(prime_divisor(factorial_plus_one(a)))
| prime(factorial_plus_one(a)) ),
inference(resolution,[status(thm)],[c_16,c_107]) ).
tff(c_118,plain,
( ~ less(a,prime_divisor(factorial_plus_one(a)))
| ~ prime(prime_divisor(factorial_plus_one(a))) ),
inference(negUnitSimplification,[status(thm)],[c_97,c_111]) ).
tff(c_155,plain,
~ prime(prime_divisor(factorial_plus_one(a))),
inference(splitLeft,[status(thm)],[c_118]) ).
tff(c_158,plain,
prime(factorial_plus_one(a)),
inference(resolution,[status(thm)],[c_18,c_155]) ).
tff(c_162,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_97,c_158]) ).
tff(c_163,plain,
~ less(a,prime_divisor(factorial_plus_one(a))),
inference(splitRight,[status(thm)],[c_118]) ).
tff(c_167,plain,
prime(factorial_plus_one(a)),
inference(resolution,[status(thm)],[c_60,c_163]) ).
tff(c_171,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_97,c_167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM016-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 09:56:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 2.90/1.71 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.90/1.72
% 2.90/1.72 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------