%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : BOO006-2 : 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 : n008.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 05:45:01 PM UTC 2025
% Result : Unsatisfiable 3.43s 1.99s
% Output : CNFRefutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > add > #nlpp > inverse > multiplicative_identity > additive_identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $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(add,type,
add: ( $i * $i ) > $i ).
tff(f_64,axiom,
! [X] : ( multiply(X,multiplicative_identity) = X ),
file(unknown,unknown) ).
tff(f_58,axiom,
! [X] : ( add(inverse(X),X) = multiplicative_identity ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X] : ( multiply(multiplicative_identity,X) = X ),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y,Z] : ( add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X,Y,Z] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
file(unknown,unknown) ).
tff(f_70,axiom,
! [X] : ( add(additive_identity,X) = X ),
file(unknown,unknown) ).
tff(f_46,axiom,
! [X,Y] : ( multiply(X,Y) = multiply(Y,X) ),
file(unknown,unknown) ).
tff(f_74,axiom,
multiply(a,additive_identity) != additive_identity,
file(unknown,unknown) ).
tff(c_22,plain,
! [X_21] : ( multiply(X_21,multiplicative_identity) = X_21 ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_16,plain,
! [X_18] : ( add(inverse(X_18),X_18) = multiplicative_identity ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_24,plain,
! [X_22] : ( multiply(multiplicative_identity,X_22) = X_22 ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_367,plain,
! [X_37,Z_38,Y_39] : ( multiply(add(X_37,Z_38),add(Y_39,Z_38)) = add(multiply(X_37,Y_39),Z_38) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_406,plain,
! [X_18,Y_39] : ( add(multiply(inverse(X_18),Y_39),X_18) = multiply(multiplicative_identity,add(Y_39,X_18)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_367]) ).
tff(c_430,plain,
! [X_40,Y_41] : ( add(multiply(inverse(X_40),Y_41),X_40) = add(Y_41,X_40) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_406]) ).
tff(c_489,plain,
! [X_40] : ( add(inverse(X_40),X_40) = add(multiplicative_identity,X_40) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_430]) ).
tff(c_499,plain,
! [X_40] : ( add(multiplicative_identity,X_40) = multiplicative_identity ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_489]) ).
tff(c_594,plain,
! [X_44,Y_45,Z_46] : ( add(multiply(X_44,Y_45),multiply(X_44,Z_46)) = multiply(X_44,add(Y_45,Z_46)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_659,plain,
! [X_21,Z_46] : ( multiply(X_21,add(multiplicative_identity,Z_46)) = add(X_21,multiply(X_21,Z_46)) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_594]) ).
tff(c_762,plain,
! [X_48,Z_49] : ( add(X_48,multiply(X_48,Z_49)) = X_48 ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_499,c_659]) ).
tff(c_28,plain,
! [X_24] : ( add(additive_identity,X_24) = X_24 ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_943,plain,
! [Z_53] : ( multiply(additive_identity,Z_53) = additive_identity ),
inference(superposition,[status(thm),theory(equality)],[c_762,c_28]) ).
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_957,plain,
! [Z_53] : ( multiply(Z_53,additive_identity) = additive_identity ),
inference(superposition,[status(thm),theory(equality)],[c_943,c_4]) ).
tff(c_30,plain,
multiply(a,additive_identity) != additive_identity,
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_997,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_957,c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO006-2 : 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 : n008.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 15:21:02 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.43/1.99 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.43/2.00
% 3.43/2.00 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------