%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : BOO010-4 : TPTP v9.0.0. Released v1.1.0.
% 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 : n009.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 05:45:03 PM UTC 2025
% Result : Unsatisfiable 4.12s 2.25s
% Output : CNFRefutation 4.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 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 ( 2 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > add > #nlpp > inverse > multiplicative_identity > b > 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(b,type,
b: $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(f_54,axiom,
! [X] : ( multiply(X,multiplicative_identity) = X ),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X] : ( add(X,inverse(X)) = multiplicative_identity ),
file(unknown,unknown) ).
tff(f_46,axiom,
! [X,Y] : ( multiply(X,Y) = multiply(Y,X) ),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y,Z] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ),
file(unknown,unknown) ).
tff(f_50,axiom,
! [X,Y,Z] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
file(unknown,unknown) ).
tff(f_44,axiom,
! [X,Y] : ( add(X,Y) = add(Y,X) ),
file(unknown,unknown) ).
tff(f_62,axiom,
add(a,multiply(a,b)) != a,
file(unknown,unknown) ).
tff(c_12,plain,
! [X_12] : ( multiply(X_12,multiplicative_identity) = X_12 ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_14,plain,
! [X_13] : ( add(X_13,inverse(X_13)) = multiplicative_identity ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_51,plain,
! [Y_19,X_20] : ( multiply(Y_19,X_20) = multiply(X_20,Y_19) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_67,plain,
! [X_20] : ( multiply(multiplicative_identity,X_20) = X_20 ),
inference(superposition,[status(thm),theory(equality)],[c_51,c_12]) ).
tff(c_321,plain,
! [X_28,Y_29,Z_30] : ( multiply(add(X_28,Y_29),add(X_28,Z_30)) = add(X_28,multiply(Y_29,Z_30)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_375,plain,
! [X_13,Y_29] : ( add(X_13,multiply(Y_29,inverse(X_13))) = multiply(add(X_13,Y_29),multiplicative_identity) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_321]) ).
tff(c_748,plain,
! [X_39,Y_40] : ( add(X_39,multiply(Y_40,inverse(X_39))) = add(X_39,Y_40) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_375]) ).
tff(c_801,plain,
! [X_39] : ( add(X_39,inverse(X_39)) = add(X_39,multiplicative_identity) ),
inference(superposition,[status(thm),theory(equality)],[c_67,c_748]) ).
tff(c_827,plain,
! [X_39] : ( add(X_39,multiplicative_identity) = multiplicative_identity ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_801]) ).
tff(c_263,plain,
! [X_25,Y_26,Z_27] : ( add(multiply(X_25,Y_26),multiply(X_25,Z_27)) = multiply(X_25,add(Y_26,Z_27)) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_311,plain,
! [X_12,Y_26] : ( multiply(X_12,add(Y_26,multiplicative_identity)) = add(multiply(X_12,Y_26),X_12) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_263]) ).
tff(c_1923,plain,
! [X_60,Y_61] : ( add(multiply(X_60,Y_61),X_60) = X_60 ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_827,c_311]) ).
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_1953,plain,
! [X_60,Y_61] : ( add(X_60,multiply(X_60,Y_61)) = X_60 ),
inference(superposition,[status(thm),theory(equality)],[c_1923,c_2]) ).
tff(c_18,plain,
add(a,multiply(a,b)) != a,
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_2053,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1953,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : BOO010-4 : TPTP v9.0.0. Released v1.1.0.
% 0.07/0.14 % 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
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 7 15:21:56 EDT 2025
% 0.13/0.35 % CPUTime :
% 4.12/2.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.12/2.25
% 4.12/2.25 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------