%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM016-2 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n021.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 2.67s 1.75s
% Output : CNFRefutation 2.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 24 ~; 21 |; 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 : 22 ( 22 !; 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_36,axiom,
! [X] : less(X,factorial_plus_one(X)),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X] :
( ~ prime(X)
| ~ less(a,X)
| less(factorial_plus_one(a),X) ),
file(unknown,unknown) ).
tff(f_28,axiom,
! [X] : ~ less(X,X),
file(unknown,unknown) ).
tff(f_45,axiom,
! [X] :
( prime(X)
| divides(prime_divisor(X),X) ),
file(unknown,unknown) ).
tff(f_41,axiom,
! [X,Y] :
( ~ divides(X,factorial_plus_one(Y))
| less(Y,X) ),
file(unknown,unknown) ).
tff(f_49,axiom,
! [X] :
( prime(X)
| prime(prime_divisor(X)) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X] :
( prime(X)
| less(prime_divisor(X),X) ),
file(unknown,unknown) ).
tff(f_34,axiom,
! [X,Y] :
( ~ less(X,Y)
| ~ less(Y,X) ),
file(unknown,unknown) ).
tff(c_6,plain,
! [X_4] : less(X_4,factorial_plus_one(X_4)),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_37,plain,
! [X_22] :
( less(factorial_plus_one(a),X_22)
| ~ less(a,X_22)
| ~ prime(X_22) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_2,plain,
! [X_1] : ~ less(X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_51,plain,
( ~ less(a,factorial_plus_one(a))
| ~ prime(factorial_plus_one(a)) ),
inference(resolution,[status(thm)],[c_37,c_2]) ).
tff(c_57,plain,
~ prime(factorial_plus_one(a)),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_51]) ).
tff(c_10,plain,
! [X_7] :
( divides(prime_divisor(X_7),X_7)
| prime(X_7) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_31,plain,
! [Y_20,X_21] :
( less(Y_20,X_21)
| ~ divides(X_21,factorial_plus_one(Y_20)) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_36,plain,
! [Y_20] :
( less(Y_20,prime_divisor(factorial_plus_one(Y_20)))
| prime(factorial_plus_one(Y_20)) ),
inference(resolution,[status(thm)],[c_10,c_31]) ).
tff(c_12,plain,
! [X_8] :
( prime(prime_divisor(X_8))
| prime(X_8) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_14,plain,
! [X_9] :
( less(prime_divisor(X_9),X_9)
| prime(X_9) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_4,plain,
! [Y_3,X_2] :
( ~ less(Y_3,X_2)
| ~ less(X_2,Y_3) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_63,plain,
! [X_25] :
( ~ less(X_25,factorial_plus_one(a))
| ~ less(a,X_25)
| ~ prime(X_25) ),
inference(resolution,[status(thm)],[c_37,c_4]) ).
tff(c_71,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_14,c_63]) ).
tff(c_81,plain,
( ~ less(a,prime_divisor(factorial_plus_one(a)))
| ~ prime(prime_divisor(factorial_plus_one(a))) ),
inference(negUnitSimplification,[status(thm)],[c_57,c_71]) ).
tff(c_83,plain,
~ prime(prime_divisor(factorial_plus_one(a))),
inference(splitLeft,[status(thm)],[c_81]) ).
tff(c_86,plain,
prime(factorial_plus_one(a)),
inference(resolution,[status(thm)],[c_12,c_83]) ).
tff(c_90,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_57,c_86]) ).
tff(c_91,plain,
~ less(a,prime_divisor(factorial_plus_one(a))),
inference(splitRight,[status(thm)],[c_81]) ).
tff(c_95,plain,
prime(factorial_plus_one(a)),
inference(resolution,[status(thm)],[c_36,c_91]) ).
tff(c_99,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_57,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM016-2 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 09:56:58 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.67/1.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.67/1.76
% 2.67/1.76 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------