%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM015-1 : 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/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 3.19s 1.86s
% Output : CNFRefutation 3.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 69 ( 36 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 24 ( 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less > divides > prime > #nlpp > factor_of > divisor > n1 > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(factor_of,type,
factor_of: $i > $i ).
tff(a,type,
a: $i ).
tff(divisor,type,
divisor: $i > $i ).
tff(n1,type,
n1: $i ).
tff(less,type,
less: ( $i * $i ) > $o ).
tff(prime,type,
prime: $i > $o ).
tff(divides,type,
divides: ( $i * $i ) > $o ).
tff(f_33,axiom,
! [X] : divides(X,X),
file(unknown,unknown) ).
tff(f_76,axiom,
! [X] :
( ~ prime(X)
| ~ divides(X,a) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X] :
( prime(X)
| less(divisor(X),X) ),
file(unknown,unknown) ).
tff(f_49,axiom,
! [X] :
( prime(X)
| less(n1,divisor(X)) ),
file(unknown,unknown) ).
tff(f_69,axiom,
! [X] :
( ~ less(n1,X)
| ~ less(X,a)
| divides(factor_of(X),X) ),
file(unknown,unknown) ).
tff(f_45,axiom,
! [X] :
( prime(X)
| divides(divisor(X),X) ),
file(unknown,unknown) ).
tff(f_41,axiom,
! [X,Y,Z] :
( ~ divides(X,Y)
| ~ divides(Y,Z)
| divides(X,Z) ),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X] :
( ~ less(n1,X)
| ~ less(X,a)
| prime(factor_of(X)) ),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : divides(X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_20,plain,
! [X_12] :
( ~ divides(X_12,a)
| ~ prime(X_12) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_25,plain,
~ prime(a),
inference(resolution,[status(thm)],[c_2,c_20]) ).
tff(c_10,plain,
! [X_7] :
( less(divisor(X_7),X_7)
| prime(X_7) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_8,plain,
! [X_6] :
( less(n1,divisor(X_6))
| prime(X_6) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_55,plain,
! [X_22] :
( divides(factor_of(X_22),X_22)
| ~ less(X_22,a)
| ~ less(n1,X_22) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_6,plain,
! [X_5] :
( divides(divisor(X_5),X_5)
| prime(X_5) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_36,plain,
! [X_16,Z_17,Y_18] :
( divides(X_16,Z_17)
| ~ divides(Y_18,Z_17)
| ~ divides(X_16,Y_18) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_41,plain,
! [X_16,X_5] :
( divides(X_16,X_5)
| ~ divides(X_16,divisor(X_5))
| prime(X_5) ),
inference(resolution,[status(thm)],[c_6,c_36]) ).
tff(c_130,plain,
! [X_28] :
( divides(factor_of(divisor(X_28)),X_28)
| prime(X_28)
| ~ less(divisor(X_28),a)
| ~ less(n1,divisor(X_28)) ),
inference(resolution,[status(thm)],[c_55,c_41]) ).
tff(c_18,plain,
! [X_10] :
( ~ divides(X_10,a)
| ~ prime(X_10) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_148,plain,
( ~ prime(factor_of(divisor(a)))
| prime(a)
| ~ less(divisor(a),a)
| ~ less(n1,divisor(a)) ),
inference(resolution,[status(thm)],[c_130,c_18]) ).
tff(c_155,plain,
( ~ prime(factor_of(divisor(a)))
| ~ less(divisor(a),a)
| ~ less(n1,divisor(a)) ),
inference(negUnitSimplification,[status(thm)],[c_25,c_148]) ).
tff(c_182,plain,
~ less(n1,divisor(a)),
inference(splitLeft,[status(thm)],[c_155]) ).
tff(c_185,plain,
prime(a),
inference(resolution,[status(thm)],[c_8,c_182]) ).
tff(c_189,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_25,c_185]) ).
tff(c_191,plain,
less(n1,divisor(a)),
inference(splitRight,[status(thm)],[c_155]) ).
tff(c_12,plain,
! [X_8] :
( prime(factor_of(X_8))
| ~ less(X_8,a)
| ~ less(n1,X_8) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_190,plain,
( ~ less(divisor(a),a)
| ~ prime(factor_of(divisor(a))) ),
inference(splitRight,[status(thm)],[c_155]) ).
tff(c_192,plain,
~ prime(factor_of(divisor(a))),
inference(splitLeft,[status(thm)],[c_190]) ).
tff(c_221,plain,
( ~ less(divisor(a),a)
| ~ less(n1,divisor(a)) ),
inference(resolution,[status(thm)],[c_12,c_192]) ).
tff(c_224,plain,
~ less(divisor(a),a),
inference(demodulation,[status(thm),theory(equality)],[c_191,c_221]) ).
tff(c_227,plain,
prime(a),
inference(resolution,[status(thm)],[c_10,c_224]) ).
tff(c_231,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_25,c_227]) ).
tff(c_232,plain,
~ less(divisor(a),a),
inference(splitRight,[status(thm)],[c_190]) ).
tff(c_236,plain,
prime(a),
inference(resolution,[status(thm)],[c_10,c_232]) ).
tff(c_240,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_25,c_236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM015-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.13 % 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 09:57:13 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.19/1.86 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.19/1.86
% 3.19/1.86 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------