%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : BOO016-2 : 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/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 : n026.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 05:45:05 PM UTC 2025
% Result : Unsatisfiable 4.09s 2.17s
% Output : CNFRefutation 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 38 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > add > #nlpp > inverse > z > y > x > multiplicative_identity > additive_identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(x,type,
x: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(additive_identity,type,
additive_identity: $i ).
tff(multiplicative_identity,type,
multiplicative_identity: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(y,type,
y: $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(z,type,
z: $i ).
tff(f_75,axiom,
add(x,z) != x,
file(unknown,unknown) ).
tff(f_73,axiom,
multiply(x,y) = z,
file(unknown,unknown) ).
tff(f_46,axiom,
! [X,Y] : ( multiply(X,Y) = multiply(Y,X) ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X] : ( multiply(multiplicative_identity,X) = X ),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X] : ( add(X,inverse(X)) = multiplicative_identity ),
file(unknown,unknown) ).
tff(f_64,axiom,
! [X] : ( multiply(X,multiplicative_identity) = X ),
file(unknown,unknown) ).
tff(f_50,axiom,
! [X,Y,Z] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [X,Y,Z] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_44,axiom,
! [X,Y] : ( add(X,Y) = add(Y,X) ),
file(unknown,unknown) ).
tff(c_32,plain,
add(x,z) != x,
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_30,plain,
multiply(x,y) = z,
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_4,plain,
! [Y_4,X_3] : ( multiply(Y_4,X_3) = multiply(X_3,Y_4) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_24,plain,
! [X_22] : ( multiply(multiplicative_identity,X_22) = X_22 ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_14,plain,
! [X_17] : ( add(X_17,inverse(X_17)) = multiplicative_identity ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_22,plain,
! [X_21] : ( multiply(X_21,multiplicative_identity) = X_21 ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_373,plain,
! [X_37,Y_38,Z_39] : ( multiply(add(X_37,Y_38),add(X_37,Z_39)) = add(X_37,multiply(Y_38,Z_39)) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_412,plain,
! [X_17,Z_39] : ( add(X_17,multiply(inverse(X_17),Z_39)) = multiply(multiplicative_identity,add(X_17,Z_39)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_373]) ).
tff(c_436,plain,
! [X_40,Z_41] : ( add(X_40,multiply(inverse(X_40),Z_41)) = add(X_40,Z_41) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_412]) ).
tff(c_477,plain,
! [X_40] : ( add(X_40,inverse(X_40)) = add(X_40,multiplicative_identity) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_436]) ).
tff(c_490,plain,
! [X_40] : ( add(X_40,multiplicative_identity) = multiplicative_identity ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_477]) ).
tff(c_758,plain,
! [X_48,Z_49,Y_50] : ( add(multiply(X_48,Z_49),multiply(Y_50,Z_49)) = multiply(add(X_48,Y_50),Z_49) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_848,plain,
! [X_48,X_22] : ( multiply(add(X_48,multiplicative_identity),X_22) = add(multiply(X_48,X_22),X_22) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_758]) ).
tff(c_916,plain,
! [X_52,X_53] : ( add(multiply(X_52,X_53),X_53) = X_53 ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_490,c_848]) ).
tff(c_1648,plain,
! [X_64,Y_65] : ( add(multiply(X_64,Y_65),X_64) = X_64 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_916]) ).
tff(c_1751,plain,
add(z,x) = x,
inference(superposition,[status(thm),theory(equality)],[c_30,c_1648]) ).
tff(c_2,plain,
! [Y_2,X_1] : ( add(Y_2,X_1) = add(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_1916,plain,
add(x,z) = x,
inference(superposition,[status(thm),theory(equality)],[c_1751,c_2]) ).
tff(c_1931,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_1916]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO016-2 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n026.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 : Mon Apr 7 15:23:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 4.09/2.17 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.09/2.18
% 4.09/2.18 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------