%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM014-1 : 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 2.73s 1.67s
% Output : CNFRefutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 28 ( 13 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 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; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 20 ( 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > divides > prime > #nlpp > square > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(square,type,
square: $i > $i ).
tff(b,type,
b: $i ).
tff(prime,type,
prime: $i > $o ).
tff(divides,type,
divides: ( $i * $i ) > $o ).
tff(c,type,
c: $i ).
tff(f_58,axiom,
~ divides(a,b),
file(unknown,unknown) ).
tff(f_31,axiom,
! [X] : product(X,X,square(X)),
file(unknown,unknown) ).
tff(f_55,axiom,
prime(a),
file(unknown,unknown) ).
tff(f_56,axiom,
product(a,square(c),square(b)),
file(unknown,unknown) ).
tff(f_41,axiom,
! [X,Y,Z] :
( ~ product(X,Y,Z)
| divides(X,Z) ),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X,Y,Z,U] :
( ~ prime(X)
| ~ product(Y,Z,U)
| ~ divides(X,U)
| divides(X,Y)
| divides(X,Z) ),
file(unknown,unknown) ).
tff(c_14,plain,
~ divides(a,b),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_2,plain,
! [X_1] : product(X_1,X_1,square(X_1)),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_10,plain,
prime(a),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_12,plain,
product(a,square(c),square(b)),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_16,plain,
! [X_13,Z_14,Y_15] :
( divides(X_13,Z_14)
| ~ product(X_13,Y_15,Z_14) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_23,plain,
divides(a,square(b)),
inference(resolution,[status(thm)],[c_12,c_16]) ).
tff(c_42,plain,
! [X_20,Z_21,Y_22,U_23] :
( divides(X_20,Z_21)
| divides(X_20,Y_22)
| ~ divides(X_20,U_23)
| ~ product(Y_22,Z_21,U_23)
| ~ prime(X_20) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_46,plain,
! [Z_21,Y_22] :
( divides(a,Z_21)
| divides(a,Y_22)
| ~ product(Y_22,Z_21,square(b))
| ~ prime(a) ),
inference(resolution,[status(thm)],[c_23,c_42]) ).
tff(c_54,plain,
! [Z_24,Y_25] :
( divides(a,Z_24)
| divides(a,Y_25)
| ~ product(Y_25,Z_24,square(b)) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_46]) ).
tff(c_64,plain,
divides(a,b),
inference(resolution,[status(thm)],[c_2,c_54]) ).
tff(c_70,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_14,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM014-1 : 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
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 8 09:55:52 EDT 2025
% 0.14/0.35 % CPUTime :
% 2.73/1.67 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.73/1.67
% 2.73/1.67 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------